%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG133+1 : TPTP v8.1.2. Released v2.7.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n007.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 16:36:43 EDT 2023 % Result : Unsatisfiable 25.83s 4.30s % Output : Proof 136.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : ALG133+1 : TPTP v8.1.2. Released v2.7.0. % 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n007.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Mon Aug 28 02:55:58 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.69/1.43 Prover 4: Preprocessing ... % 4.69/1.44 Prover 1: Preprocessing ... % 4.69/1.48 Prover 3: Preprocessing ... % 4.69/1.48 Prover 2: Preprocessing ... % 4.69/1.48 Prover 6: Preprocessing ... % 4.69/1.48 Prover 5: Preprocessing ... % 4.69/1.48 Prover 0: Preprocessing ... % 8.10/1.91 Prover 3: Constructing countermodel ... % 8.10/1.92 Prover 2: Constructing countermodel ... % 8.10/1.94 Prover 0: Constructing countermodel ... % 8.10/1.95 Prover 6: Constructing countermodel ... % 8.10/1.95 Prover 1: Constructing countermodel ... % 8.88/1.97 Prover 4: Constructing countermodel ... % 10.62/2.23 Prover 5: Constructing countermodel ... % 25.83/4.29 Prover 3: proved (3654ms) % 25.83/4.30 % 25.83/4.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p % 25.83/4.30 % 25.83/4.30 Prover 2: stopped % 25.83/4.30 Prover 5: stopped % 25.83/4.30 Prover 6: stopped % 25.83/4.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 25.83/4.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 25.83/4.31 Prover 0: stopped % 25.83/4.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 25.83/4.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 25.83/4.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 27.77/4.56 Prover 7: Preprocessing ... % 28.47/4.57 Prover 11: Preprocessing ... % 28.47/4.57 Prover 10: Preprocessing ... % 28.47/4.58 Prover 8: Preprocessing ... % 28.47/4.58 Prover 13: Preprocessing ... % 29.08/4.69 Prover 8: Constructing countermodel ... % 30.08/4.79 Prover 10: Constructing countermodel ... % 30.08/4.79 Prover 13: Constructing countermodel ... % 30.08/4.80 Prover 11: Constructing countermodel ... % 30.08/4.81 Prover 7: Constructing countermodel ... % 67.66/9.65 Prover 13: stopped % 67.66/9.68 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 68.26/9.78 Prover 16: Preprocessing ... % 69.45/9.96 Prover 16: Constructing countermodel ... % 112.58/15.52 Prover 16: stopped % 112.66/15.54 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 112.66/15.60 Prover 19: Preprocessing ... % 113.88/15.73 Prover 19: Constructing countermodel ... % 115.76/15.98 Prover 1: stopped % 126.83/17.47 Prover 10: Found proof (size 60597) % 126.83/17.47 Prover 10: proved (13167ms) % 126.83/17.47 Prover 11: stopped % 126.83/17.47 Prover 8: stopped % 126.83/17.47 Prover 7: stopped % 126.83/17.47 Prover 4: stopped % 126.83/17.47 Prover 19: stopped % 126.83/17.47 % 126.83/17.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p % 126.83/17.47 % 128.21/17.80 % SZS output start Proof for theBenchmark % 128.59/17.88 Assumptions after simplification: % 128.59/17.88 --------------------------------- % 128.59/17.88 % 128.59/17.88 (ax1) % 128.59/17.93 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.59/17.93 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 128.59/17.93 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 128.59/17.93 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & % 128.59/17.93 op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & % 128.59/17.93 op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & % 128.59/17.93 op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 128.59/17.93 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 128.59/17.93 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 128.59/17.93 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 = % 128.59/17.93 e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 | % 128.59/17.93 v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 % 128.59/17.93 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | % 128.59/17.93 v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | % 128.86/17.93 v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | % 128.86/17.93 v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & % 128.86/17.93 (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3 % 128.86/17.93 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1 % 128.86/17.93 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0)) % 128.86/17.93 % 128.86/17.93 (ax10) % 128.86/17.93 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.86/17.93 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e0, e2) = v2 & % 128.86/17.93 $i(v2)) | ( ~ (v1 = e3) & op(e0, e0) = v1 & $i(v1)))) % 128.86/17.93 % 128.86/17.93 (ax11) % 128.86/17.94 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.86/17.94 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e0, e1) = v2 & % 128.86/17.94 $i(v2)) | ( ~ (v1 = e3) & op(e0, e0) = v1 & $i(v1)))) % 128.86/17.94 % 128.86/17.94 (ax12) % 128.86/17.94 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.86/17.94 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e1, e3) = v2 & % 128.86/17.94 $i(v2)) | ( ~ (v1 = e0) & op(e1, e1) = v1 & $i(v1)))) % 128.86/17.94 % 128.86/17.94 (ax13) % 128.86/17.94 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.86/17.94 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e1, e2) = v2 & % 128.86/17.94 $i(v2)) | ( ~ (v1 = e0) & op(e1, e1) = v1 & $i(v1)))) % 128.86/17.94 % 128.86/17.94 (ax14) % 128.86/17.94 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.86/17.94 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e1, e3) = v2 & % 128.86/17.94 $i(v2)) | ( ~ (v1 = e2) & op(e1, e1) = v1 & $i(v1)))) % 128.86/17.94 % 128.86/17.94 (ax15) % 128.86/17.95 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.86/17.95 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e1, e0) = v2 & % 128.86/17.95 $i(v2)) | ( ~ (v1 = e2) & op(e1, e1) = v1 & $i(v1)))) % 128.86/17.95 % 128.86/17.95 (ax16) % 128.86/17.95 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.86/17.95 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e1, e2) = v2 & % 128.86/17.95 $i(v2)) | ( ~ (v1 = e3) & op(e1, e1) = v1 & $i(v1)))) % 128.86/17.95 % 128.86/17.95 (ax17) % 128.86/17.95 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.86/17.95 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e1, e0) = v2 & % 128.86/17.95 $i(v2)) | ( ~ (v1 = e3) & op(e1, e1) = v1 & $i(v1)))) % 128.86/17.95 % 128.86/17.95 (ax18) % 128.86/17.95 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.86/17.95 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e2, e3) = v2 & % 128.86/17.95 $i(v2)) | ( ~ (v1 = e0) & op(e2, e2) = v1 & $i(v1)))) % 128.86/17.95 % 128.86/17.95 (ax19) % 128.86/17.96 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.86/17.96 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2, e1) = v2 & % 128.86/17.96 $i(v2)) | ( ~ (v1 = e0) & op(e2, e2) = v1 & $i(v1)))) % 128.86/17.96 % 128.86/17.96 (ax2) % 128.99/17.99 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.99/17.99 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 128.99/17.99 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 128.99/17.99 $i] : ? [v14: $i] : ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 = % 128.99/17.99 e3 & op(e3, e2) = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3, % 128.99/17.99 e0) = e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) = % 128.99/17.99 e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) & ((v15 % 128.99/17.99 = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11 = e2 & % 128.99/17.99 op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 = e2 & op(e3, % 128.99/17.99 e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 & op(e1, e3) = e2) % 128.99/17.99 | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 & op(e3, e3) = e1) | (v14 = e1 % 128.99/17.99 & op(e3, e2) = e1) | (v11 = e1 & op(e3, e1) = e1) | (v6 = e1 & op(e3, % 128.99/17.99 e0) = e1)) & ((v15 = e1 & op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) = % 128.99/17.99 e1) | (v9 = e1 & op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15 % 128.99/17.99 = e0 & op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 & % 128.99/17.99 op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 & op(e3, % 128.99/17.99 e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 & op(e1, e3) = e0) % 128.99/17.99 | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 & op(e3, e2) = e3) | (v12 = e3 % 128.99/17.99 & op(e2, e2) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) % 128.99/17.99 = e3)) & ((v14 = e2 & op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) | % 128.99/17.99 (v8 = e2 & op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 & % 128.99/17.99 op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 & op(e1, e2) % 128.99/17.99 = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 & op(e3, e2) = e0) | % 128.99/17.99 (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v2 = e0 & % 128.99/17.99 op(e0, e2) = e0)) & ((v13 = e3 & op(e2, e3) = e3) | (v12 = e3 & op(e2, % 128.99/17.99 e2) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) = % 128.99/17.99 e3)) & ((v13 = e2 & op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) | % 128.99/17.99 (v10 = e2 & op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 & % 128.99/17.99 op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 & op(e2, e1) % 128.99/17.99 = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 & op(e2, e3) = e0) | % 128.99/17.99 (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v5 = e0 & % 128.99/17.99 op(e2, e0) = e0)) & ((v11 = e3 & op(e3, e1) = e3) | (v10 = e3 & op(e2, % 128.99/17.99 e1) = e3) | (v7 = e3 & op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) % 128.99/17.99 & ((v11 = e2 & op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 & % 128.99/17.99 op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 & op(e3, % 128.99/17.99 e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 & op(e1, e1) = e1) % 128.99/17.99 | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 & op(e3, e1) = e0) | (v10 = e0 % 128.99/17.99 & op(e2, e1) = e0) | (v7 = e0 & op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) % 128.99/17.99 = e0)) & ((v9 = e3 & op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) | % 128.99/17.99 (v7 = e3 & op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 & % 128.99/17.99 op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 & op(e1, e1) = % 128.99/17.99 e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 & op(e1, e3) = e1) | (v8 % 128.99/17.99 = e1 & op(e1, e2) = e1) | (v7 = e1 & op(e1, e1) = e1) | (v4 = e1 & % 128.99/17.99 op(e1, e0) = e1)) & ((v9 = e0 & op(e1, e3) = e0) | (v8 = e0 & op(e1, e2) % 128.99/17.99 = e0) | (v7 = e0 & op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) & % 128.99/17.99 ((v6 = e3 & op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 & % 128.99/17.99 op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 & op(e3, e0) % 128.99/17.99 = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 & op(e1, e0) = e2) | (v0 % 128.99/17.99 = e2 & op(e0, e0) = e2)) & ((v6 = e1 & op(e3, e0) = e1) | (v5 = e1 & % 128.99/17.99 op(e2, e0) = e1) | (v4 = e1 & op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) = % 128.99/17.99 e1)) & ((v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 % 128.99/17.99 = e3 & op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 & % 128.99/17.99 op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 & op(e0, e1) = % 128.99/17.99 e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 & op(e0, e3) = e1) | (v2 % 128.99/17.99 = e1 & op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 & % 128.99/17.99 op(e0, e0) = e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v6 = e0 & op(e3, % 128.99/17.99 e0) = e0) | (v5 = e0 & op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) = % 128.99/17.99 e0)) & ((v3 = e0 & op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | % 128.99/17.99 (v1 = e0 & op(e0, e1) = e0))))) % 128.99/17.99 % 128.99/17.99 (ax20) % 128.99/17.99 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.99/17.99 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e2, e3) = v2 & % 128.99/17.99 $i(v2)) | ( ~ (v1 = e1) & op(e2, e2) = v1 & $i(v1)))) % 128.99/17.99 % 128.99/17.99 (ax21) % 128.99/17.99 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.99/17.99 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2, e0) = v2 & % 128.99/17.99 $i(v2)) | ( ~ (v1 = e1) & op(e2, e2) = v1 & $i(v1)))) % 128.99/17.99 % 128.99/17.99 (ax22) % 128.99/17.99 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.99/17.99 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e2, e1) = v2 & % 128.99/17.99 $i(v2)) | ( ~ (v1 = e3) & op(e2, e2) = v1 & $i(v1)))) % 128.99/17.99 % 128.99/17.99 (ax23) % 128.99/18.00 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.99/18.00 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e2, e0) = v2 & % 128.99/18.00 $i(v2)) | ( ~ (v1 = e3) & op(e2, e2) = v1 & $i(v1)))) % 128.99/18.00 % 128.99/18.00 (ax24) % 128.99/18.00 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.99/18.00 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3, e2) = v2 & % 128.99/18.00 $i(v2)) | ( ~ (v1 = e0) & op(e3, e3) = v1 & $i(v1)))) % 128.99/18.00 % 128.99/18.00 (ax25) % 128.99/18.00 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.99/18.00 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3, e1) = v2 & % 128.99/18.00 $i(v2)) | ( ~ (v1 = e0) & op(e3, e3) = v1 & $i(v1)))) % 128.99/18.00 % 128.99/18.00 (ax26) % 128.99/18.00 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.99/18.00 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3, e2) = v2 & % 128.99/18.00 $i(v2)) | ( ~ (v1 = e1) & op(e3, e3) = v1 & $i(v1)))) % 128.99/18.00 % 128.99/18.00 (ax27) % 128.99/18.00 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.99/18.00 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3, e0) = v2 & % 128.99/18.00 $i(v2)) | ( ~ (v1 = e1) & op(e3, e3) = v1 & $i(v1)))) % 128.99/18.00 % 128.99/18.00 (ax28) % 128.99/18.00 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.99/18.00 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3, e1) = v2 & % 128.99/18.00 $i(v2)) | ( ~ (v1 = e2) & op(e3, e3) = v1 & $i(v1)))) % 128.99/18.00 % 128.99/18.00 (ax29) % 128.99/18.00 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.99/18.00 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3, e0) = v2 & % 128.99/18.00 $i(v2)) | ( ~ (v1 = e2) & op(e3, e3) = v1 & $i(v1)))) % 128.99/18.00 % 128.99/18.00 (ax3) % 128.99/18.01 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 128.99/18.01 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 128.99/18.01 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 128.99/18.01 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ % 128.99/18.01 (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = % 128.99/18.01 v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & % 128.99/18.01 ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 = % 128.99/18.01 v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~ % 128.99/18.01 (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) & % 128.99/18.01 ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) & % 128.99/18.01 ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) & % 128.99/18.01 ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ % 128.99/18.01 (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ % 128.99/18.01 (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = % 128.99/18.01 v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = % 128.99/18.01 v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9 % 128.99/18.01 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 & % 128.99/18.01 op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 128.99/18.01 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 128.99/18.01 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 128.99/18.01 % 128.99/18.01 (ax4) % 128.99/18.01 ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ % 128.99/18.01 (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0) % 128.99/18.01 % 128.99/18.01 (ax5) % 129.33/18.03 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 129.33/18.03 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 129.33/18.03 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 129.33/18.03 $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: % 129.33/18.03 $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: % 129.33/18.03 $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: % 129.33/18.03 $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : (((v31 = v30 & op(v30, % 129.33/18.03 e3) = v30 & op(e3, e3) = v30 & $i(v30)) | (v29 = v28 & op(v28, e2) = % 129.33/18.03 v28 & op(e2, e3) = v28 & $i(v28)) | (v27 = v26 & op(v26, e1) = v26 & % 129.33/18.03 op(e1, e3) = v26 & $i(v26)) | (v25 = v24 & op(v24, e0) = v24 & op(e0, % 129.33/18.03 e3) = v24 & $i(v24))) & ((v30 = e2 & v22 = e3 & ~ (v28 = e3) & ~ % 129.33/18.03 (v20 = e2) & ~ (v12 = e1) & ~ (v4 = e0) & op(e3, e3) = e2 & op(e3, e2) % 129.33/18.03 = e3 & op(e2, e3) = v28 & op(e2, e2) = v20 & op(e2, e1) = v12 & op(e2, % 129.33/18.03 e0) = v4 & $i(v28) & $i(v20) & $i(v12) & $i(v4)) | (v30 = e1 & v14 = % 129.33/18.03 e3 & ~ (v26 = e3) & ~ (v18 = e2) & ~ (v10 = e1) & ~ (v2 = e0) & % 129.33/18.03 op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = v26 & op(e1, e2) = v18 % 129.33/18.03 & op(e1, e1) = v10 & op(e1, e0) = v2 & $i(v26) & $i(v18) & $i(v10) & % 129.33/18.03 $i(v2)) | (v30 = e0 & v6 = e3 & ~ (v24 = e3) & ~ (v16 = e2) & ~ (v8 = % 129.33/18.03 e1) & ~ (v0 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 129.33/18.03 v24 & op(e0, e2) = v16 & op(e0, e1) = v8 & op(e0, e0) = v0 & $i(v24) & % 129.33/18.03 $i(v16) & $i(v8) & $i(v0)) | (v28 = e2 & v20 = e3 & ~ (v30 = e3) & ~ % 129.33/18.03 (v22 = e2) & ~ (v14 = e1) & ~ (v6 = e0) & op(e3, e3) = v30 & op(e3, % 129.33/18.03 e2) = v22 & op(e3, e1) = v14 & op(e3, e0) = v6 & op(e2, e3) = e2 & % 129.33/18.03 op(e2, e2) = e3 & $i(v30) & $i(v22) & $i(v14) & $i(v6)) | (v26 = e1 & % 129.33/18.03 v10 = e3 & ~ (v30 = e3) & ~ (v22 = e2) & ~ (v14 = e1) & ~ (v6 = e0) % 129.33/18.03 & op(e3, e3) = v30 & op(e3, e2) = v22 & op(e3, e1) = v14 & op(e3, e0) = % 129.33/18.03 v6 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(v30) & $i(v22) & $i(v14) & % 129.33/18.03 $i(v6)) | (v20 = e1 & v12 = e2 & ~ (v26 = e3) & ~ (v18 = e2) & ~ (v10 % 129.33/18.03 = e1) & ~ (v2 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) % 129.33/18.03 = v26 & op(e1, e2) = v18 & op(e1, e1) = v10 & op(e1, e0) = v2 & $i(v26) % 129.33/18.03 & $i(v18) & $i(v10) & $i(v2)) | (v20 = e0 & v4 = e2 & ~ (v24 = e3) & ~ % 129.33/18.03 (v16 = e2) & ~ (v8 = e1) & ~ (v0 = e0) & op(e2, e2) = e0 & op(e2, e0) % 129.33/18.03 = e2 & op(e0, e3) = v24 & op(e0, e2) = v16 & op(e0, e1) = v8 & op(e0, % 129.33/18.03 e0) = v0 & $i(v24) & $i(v16) & $i(v8) & $i(v0)) | (v18 = e1 & v10 = e2 % 129.33/18.03 & ~ (v28 = e3) & ~ (v20 = e2) & ~ (v12 = e1) & ~ (v4 = e0) & op(e2, % 129.33/18.03 e3) = v28 & op(e2, e2) = v20 & op(e2, e1) = v12 & op(e2, e0) = v4 & % 129.33/18.03 op(e1, e2) = e1 & op(e1, e1) = e2 & $i(v28) & $i(v20) & $i(v12) & % 129.33/18.03 $i(v4)) | (op(e0, e0) = v0 & $i(v0) & ((v24 = e0 & v0 = e3 & ~ (v30 = % 129.33/18.03 e3) & ~ (v22 = e2) & ~ (v14 = e1) & ~ (v6 = e0) & op(e3, e3) = % 129.33/18.03 v30 & op(e3, e2) = v22 & op(e3, e1) = v14 & op(e3, e0) = v6 & op(e0, % 129.33/18.03 e3) = e0 & $i(v30) & $i(v22) & $i(v14) & $i(v6)) | (v16 = e0 & v0 % 129.33/18.03 = e2 & ~ (v28 = e3) & ~ (v20 = e2) & ~ (v12 = e1) & ~ (v4 = e0) % 129.33/18.03 & op(e2, e3) = v28 & op(e2, e2) = v20 & op(e2, e1) = v12 & op(e2, % 129.33/18.03 e0) = v4 & op(e0, e2) = e0 & $i(v28) & $i(v20) & $i(v12) & $i(v4)) % 129.33/18.03 | (v10 = e0 & v2 = e1 & ~ (v24 = e3) & ~ (v16 = e2) & ~ (v8 = e1) & % 129.33/18.03 ~ (v0 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = v24 % 129.33/18.03 & op(e0, e2) = v16 & op(e0, e1) = v8 & $i(v24) & $i(v16) & $i(v8)) | % 129.33/18.03 (v8 = e0 & v0 = e1 & ~ (v26 = e3) & ~ (v18 = e2) & ~ (v10 = e1) & % 129.33/18.03 ~ (v2 = e0) & op(e1, e3) = v26 & op(e1, e2) = v18 & op(e1, e1) = v10 % 129.33/18.03 & op(e1, e0) = v2 & op(e0, e1) = e0 & $i(v26) & $i(v18) & $i(v10) & % 129.33/18.03 $i(v2))))) & ((v23 = v22 & op(v22, e3) = v22 & op(e3, e2) = v22 & % 129.33/18.03 $i(v22)) | (v21 = v20 & op(v20, e2) = v20 & op(e2, e2) = v20 & $i(v20)) % 129.33/18.03 | (v19 = v18 & op(v18, e1) = v18 & op(e1, e2) = v18 & $i(v18)) | (v17 = % 129.33/18.03 v16 & op(v16, e0) = v16 & op(e0, e2) = v16 & $i(v16))) & ((v15 = v14 & % 129.33/18.03 op(v14, e3) = v14 & op(e3, e1) = v14 & $i(v14)) | (v13 = v12 & op(v12, % 129.33/18.03 e2) = v12 & op(e2, e1) = v12 & $i(v12)) | (v11 = v10 & op(v10, e1) = % 129.33/18.03 v10 & op(e1, e1) = v10 & $i(v10)) | (v9 = v8 & op(v8, e0) = v8 & op(e0, % 129.33/18.03 e1) = v8 & $i(v8))) & ((v7 = v6 & op(v6, e3) = v6 & op(e3, e0) = v6 & % 129.33/18.03 $i(v6)) | (v5 = v4 & op(v4, e2) = v4 & op(e2, e0) = v4 & $i(v4)) | (v3 = % 129.33/18.03 v2 & op(v2, e1) = v2 & op(e1, e0) = v2 & $i(v2)) | (v1 = v0 & op(v0, e0) % 129.33/18.03 = v0 & op(e0, e0) = v0 & $i(v0)))) % 129.33/18.03 % 129.33/18.03 (ax6) % 129.33/18.04 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 129.33/18.04 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e0, e3) = v2 & % 129.33/18.04 $i(v2)) | ( ~ (v1 = e1) & op(e0, e0) = v1 & $i(v1)))) % 129.33/18.04 % 129.33/18.04 (ax7) % 129.33/18.04 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 129.33/18.04 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e0, e2) = v2 & % 129.33/18.04 $i(v2)) | ( ~ (v1 = e1) & op(e0, e0) = v1 & $i(v1)))) % 129.33/18.04 % 129.33/18.04 (ax8) % 129.33/18.04 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 129.33/18.04 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e0, e3) = v2 & % 129.33/18.04 $i(v2)) | ( ~ (v1 = e2) & op(e0, e0) = v1 & $i(v1)))) % 129.33/18.04 % 129.33/18.04 (ax9) % 129.33/18.04 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 129.33/18.04 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e0, e1) = v2 & % 129.33/18.04 $i(v2)) | ( ~ (v1 = e2) & op(e0, e0) = v1 & $i(v1)))) % 129.33/18.04 % 129.33/18.04 (function-axioms) % 129.33/18.04 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3, % 129.33/18.04 v2) = v1) | ~ (op(v3, v2) = v0)) % 129.33/18.04 % 129.33/18.04 Those formulas are unsatisfiable: % 129.33/18.04 --------------------------------- % 129.33/18.04 % 129.33/18.04 Begin of proof % 129.33/18.04 | % 129.33/18.04 | ALPHA: (ax1) implies: % 129.33/18.05 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 129.33/18.05 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 129.33/18.05 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 129.33/18.05 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13 % 129.33/18.05 | & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1) % 129.33/18.05 | = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1, % 129.33/18.05 | e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 129.33/18.05 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & % 129.33/18.05 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 129.33/18.05 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 % 129.33/18.05 | = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 % 129.33/18.05 | = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 | % 129.33/18.05 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 | % 129.33/18.05 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3 % 129.33/18.05 | | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8 % 129.33/18.05 | = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 = % 129.33/18.05 | e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & % 129.33/18.05 | (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = % 129.33/18.05 | e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 % 129.33/18.05 | | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 % 129.33/18.05 | = e0)) % 129.33/18.05 | % 129.33/18.05 | ALPHA: (ax2) implies: % 129.52/18.07 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 129.52/18.07 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 129.52/18.07 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 129.52/18.07 | ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 = e3 & op(e3, e2) % 129.52/18.07 | = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3, e0) = % 129.52/18.07 | e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) = % 129.52/18.07 | e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) % 129.52/18.07 | & ((v15 = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11 % 129.52/18.07 | = e2 & op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 = % 129.52/18.07 | e2 & op(e3, e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 & % 129.52/18.07 | op(e1, e3) = e2) | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 & % 129.52/18.07 | op(e3, e3) = e1) | (v14 = e1 & op(e3, e2) = e1) | (v11 = e1 & % 129.52/18.07 | op(e3, e1) = e1) | (v6 = e1 & op(e3, e0) = e1)) & ((v15 = e1 & % 129.52/18.07 | op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) = e1) | (v9 = e1 & % 129.52/18.07 | op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15 = e0 & % 129.52/18.07 | op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 & % 129.52/18.07 | op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 & % 129.52/18.07 | op(e3, e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 & % 129.52/18.07 | op(e1, e3) = e0) | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 & % 129.52/18.07 | op(e3, e2) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v8 = e3 & % 129.52/18.07 | op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) = e3)) & ((v14 = e2 & % 129.52/18.07 | op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v8 = e2 & % 129.52/18.07 | op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 & % 129.52/18.07 | op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 & % 129.52/18.07 | op(e1, e2) = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 & % 129.52/18.07 | op(e3, e2) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 & % 129.52/18.07 | op(e1, e2) = e0) | (v2 = e0 & op(e0, e2) = e0)) & ((v13 = e3 & % 129.52/18.07 | op(e2, e3) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v10 = e3 & % 129.52/18.07 | op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) = e3)) & ((v13 = e2 & % 129.52/18.07 | op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v10 = e2 & % 129.52/18.07 | op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 & % 129.52/18.07 | op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 & % 129.52/18.07 | op(e2, e1) = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 & % 129.52/18.07 | op(e2, e3) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 & % 129.52/18.07 | op(e2, e1) = e0) | (v5 = e0 & op(e2, e0) = e0)) & ((v11 = e3 & % 129.52/18.07 | op(e3, e1) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v7 = e3 & % 129.52/18.07 | op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) & ((v11 = e2 & % 129.52/18.07 | op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 & % 129.52/18.07 | op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 & % 129.52/18.07 | op(e3, e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 & % 129.52/18.07 | op(e1, e1) = e1) | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 & % 129.52/18.07 | op(e3, e1) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v7 = e0 & % 129.52/18.07 | op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) = e0)) & ((v9 = e3 & % 129.52/18.07 | op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v7 = e3 & % 129.52/18.07 | op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 & % 129.52/18.07 | op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 & % 129.52/18.07 | op(e1, e1) = e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 & % 129.52/18.07 | op(e1, e3) = e1) | (v8 = e1 & op(e1, e2) = e1) | (v7 = e1 & % 129.52/18.07 | op(e1, e1) = e1) | (v4 = e1 & op(e1, e0) = e1)) & ((v9 = e0 & % 129.52/18.07 | op(e1, e3) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v7 = e0 & % 129.52/18.07 | op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v6 = e3 & % 129.52/18.07 | op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 & % 129.52/18.07 | op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 & % 129.52/18.07 | op(e3, e0) = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 & % 129.52/18.07 | op(e1, e0) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v6 = e1 & % 129.52/18.07 | op(e3, e0) = e1) | (v5 = e1 & op(e2, e0) = e1) | (v4 = e1 & % 129.52/18.07 | op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v3 = e3 & % 129.52/18.07 | op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 = e3 & % 129.52/18.07 | op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 & % 129.52/18.07 | op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 & % 129.52/18.07 | op(e0, e1) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 & % 129.52/18.07 | op(e0, e3) = e1) | (v2 = e1 & op(e0, e2) = e1) | (v1 = e1 & % 129.52/18.07 | op(e0, e1) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v0 = e0 & % 129.52/18.07 | op(e0, e0) = e0) | (((v6 = e0 & op(e3, e0) = e0) | (v5 = e0 & % 129.52/18.07 | op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v3 = e0 & % 129.52/18.07 | op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | (v1 = e0 & % 129.52/18.07 | op(e0, e1) = e0))))) % 129.52/18.07 | % 129.52/18.07 | ALPHA: (ax3) implies: % 129.52/18.08 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 129.52/18.08 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 129.52/18.08 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 129.52/18.08 | ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~ % 129.52/18.08 | (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = v13) & ~ % 129.52/18.08 | (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~ % 129.52/18.08 | (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 % 129.52/18.08 | = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = % 129.52/18.08 | v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) % 129.52/18.08 | & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ % 129.52/18.08 | (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) % 129.52/18.08 | & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 % 129.52/18.08 | = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v4 = v0) & % 129.52/18.08 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = % 129.52/18.08 | v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3, % 129.52/18.08 | e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 & % 129.52/18.08 | op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = % 129.52/18.08 | v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, % 129.52/18.08 | e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & % 129.52/18.08 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & % 129.52/18.08 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 129.52/18.08 | % 129.52/18.08 | ALPHA: (ax4) implies: % 129.52/18.08 | (4) ~ (e1 = e0) % 129.52/18.08 | (5) ~ (e2 = e0) % 129.52/18.08 | (6) ~ (e2 = e1) % 129.52/18.08 | (7) ~ (e3 = e0) % 129.52/18.08 | (8) ~ (e3 = e1) % 129.52/18.08 | (9) ~ (e3 = e2) % 129.52/18.08 | % 129.52/18.08 | ALPHA: (ax5) implies: % 129.52/18.09 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 129.52/18.09 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 129.52/18.09 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 129.52/18.09 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 129.52/18.09 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] % 129.52/18.09 | : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28: % 129.52/18.09 | $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : (((v31 = v30 & % 129.52/18.09 | op(v30, e3) = v30 & op(e3, e3) = v30 & $i(v30)) | (v29 = v28 & % 129.52/18.09 | op(v28, e2) = v28 & op(e2, e3) = v28 & $i(v28)) | (v27 = v26 & % 129.52/18.09 | op(v26, e1) = v26 & op(e1, e3) = v26 & $i(v26)) | (v25 = v24 & % 129.52/18.09 | op(v24, e0) = v24 & op(e0, e3) = v24 & $i(v24))) & ((v30 = e2 & % 129.52/18.09 | v22 = e3 & ~ (v28 = e3) & ~ (v20 = e2) & ~ (v12 = e1) & ~ % 129.52/18.09 | (v4 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = v28 % 129.52/18.09 | & op(e2, e2) = v20 & op(e2, e1) = v12 & op(e2, e0) = v4 & % 129.52/18.09 | $i(v28) & $i(v20) & $i(v12) & $i(v4)) | (v30 = e1 & v14 = e3 & % 129.52/18.09 | ~ (v26 = e3) & ~ (v18 = e2) & ~ (v10 = e1) & ~ (v2 = e0) & % 129.52/18.09 | op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = v26 & op(e1, % 129.52/18.09 | e2) = v18 & op(e1, e1) = v10 & op(e1, e0) = v2 & $i(v26) & % 129.52/18.09 | $i(v18) & $i(v10) & $i(v2)) | (v30 = e0 & v6 = e3 & ~ (v24 = % 129.52/18.09 | e3) & ~ (v16 = e2) & ~ (v8 = e1) & ~ (v0 = e0) & op(e3, e3) % 129.52/18.09 | = e0 & op(e3, e0) = e3 & op(e0, e3) = v24 & op(e0, e2) = v16 & % 129.52/18.09 | op(e0, e1) = v8 & op(e0, e0) = v0 & $i(v24) & $i(v16) & $i(v8) & % 129.52/18.09 | $i(v0)) | (v28 = e2 & v20 = e3 & ~ (v30 = e3) & ~ (v22 = e2) & % 129.52/18.09 | ~ (v14 = e1) & ~ (v6 = e0) & op(e3, e3) = v30 & op(e3, e2) = % 129.52/18.09 | v22 & op(e3, e1) = v14 & op(e3, e0) = v6 & op(e2, e3) = e2 & % 129.52/18.09 | op(e2, e2) = e3 & $i(v30) & $i(v22) & $i(v14) & $i(v6)) | (v26 = % 129.52/18.09 | e1 & v10 = e3 & ~ (v30 = e3) & ~ (v22 = e2) & ~ (v14 = e1) & % 129.52/18.09 | ~ (v6 = e0) & op(e3, e3) = v30 & op(e3, e2) = v22 & op(e3, e1) = % 129.52/18.09 | v14 & op(e3, e0) = v6 & op(e1, e3) = e1 & op(e1, e1) = e3 & % 129.52/18.09 | $i(v30) & $i(v22) & $i(v14) & $i(v6)) | (v20 = e1 & v12 = e2 & % 129.52/18.09 | ~ (v26 = e3) & ~ (v18 = e2) & ~ (v10 = e1) & ~ (v2 = e0) & % 129.52/18.09 | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = v26 & op(e1, % 129.52/18.09 | e2) = v18 & op(e1, e1) = v10 & op(e1, e0) = v2 & $i(v26) & % 129.52/18.09 | $i(v18) & $i(v10) & $i(v2)) | (v20 = e0 & v4 = e2 & ~ (v24 = % 129.52/18.09 | e3) & ~ (v16 = e2) & ~ (v8 = e1) & ~ (v0 = e0) & op(e2, e2) % 129.52/18.09 | = e0 & op(e2, e0) = e2 & op(e0, e3) = v24 & op(e0, e2) = v16 & % 129.52/18.09 | op(e0, e1) = v8 & op(e0, e0) = v0 & $i(v24) & $i(v16) & $i(v8) & % 129.52/18.09 | $i(v0)) | (v18 = e1 & v10 = e2 & ~ (v28 = e3) & ~ (v20 = e2) & % 129.52/18.09 | ~ (v12 = e1) & ~ (v4 = e0) & op(e2, e3) = v28 & op(e2, e2) = % 129.52/18.09 | v20 & op(e2, e1) = v12 & op(e2, e0) = v4 & op(e1, e2) = e1 & % 129.52/18.09 | op(e1, e1) = e2 & $i(v28) & $i(v20) & $i(v12) & $i(v4)) | % 129.52/18.09 | (op(e0, e0) = v0 & $i(v0) & ((v24 = e0 & v0 = e3 & ~ (v30 = e3) & % 129.52/18.09 | ~ (v22 = e2) & ~ (v14 = e1) & ~ (v6 = e0) & op(e3, e3) = % 129.52/18.09 | v30 & op(e3, e2) = v22 & op(e3, e1) = v14 & op(e3, e0) = v6 % 129.52/18.09 | & op(e0, e3) = e0 & $i(v30) & $i(v22) & $i(v14) & $i(v6)) | % 129.52/18.09 | (v16 = e0 & v0 = e2 & ~ (v28 = e3) & ~ (v20 = e2) & ~ (v12 % 129.52/18.09 | = e1) & ~ (v4 = e0) & op(e2, e3) = v28 & op(e2, e2) = v20 % 129.52/18.09 | & op(e2, e1) = v12 & op(e2, e0) = v4 & op(e0, e2) = e0 & % 129.52/18.09 | $i(v28) & $i(v20) & $i(v12) & $i(v4)) | (v10 = e0 & v2 = e1 % 129.52/18.09 | & ~ (v24 = e3) & ~ (v16 = e2) & ~ (v8 = e1) & ~ (v0 = % 129.52/18.09 | e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = v24 % 129.52/18.09 | & op(e0, e2) = v16 & op(e0, e1) = v8 & $i(v24) & $i(v16) & % 129.52/18.09 | $i(v8)) | (v8 = e0 & v0 = e1 & ~ (v26 = e3) & ~ (v18 = e2) % 129.52/18.09 | & ~ (v10 = e1) & ~ (v2 = e0) & op(e1, e3) = v26 & op(e1, % 129.52/18.09 | e2) = v18 & op(e1, e1) = v10 & op(e1, e0) = v2 & op(e0, % 129.52/18.09 | e1) = e0 & $i(v26) & $i(v18) & $i(v10) & $i(v2))))) & % 129.52/18.09 | ((v23 = v22 & op(v22, e3) = v22 & op(e3, e2) = v22 & $i(v22)) | (v21 % 129.52/18.09 | = v20 & op(v20, e2) = v20 & op(e2, e2) = v20 & $i(v20)) | (v19 = % 129.52/18.09 | v18 & op(v18, e1) = v18 & op(e1, e2) = v18 & $i(v18)) | (v17 = % 129.52/18.09 | v16 & op(v16, e0) = v16 & op(e0, e2) = v16 & $i(v16))) & ((v15 = % 129.52/18.09 | v14 & op(v14, e3) = v14 & op(e3, e1) = v14 & $i(v14)) | (v13 = % 129.52/18.09 | v12 & op(v12, e2) = v12 & op(e2, e1) = v12 & $i(v12)) | (v11 = % 129.52/18.09 | v10 & op(v10, e1) = v10 & op(e1, e1) = v10 & $i(v10)) | (v9 = v8 % 129.52/18.09 | & op(v8, e0) = v8 & op(e0, e1) = v8 & $i(v8))) & ((v7 = v6 & % 129.52/18.09 | op(v6, e3) = v6 & op(e3, e0) = v6 & $i(v6)) | (v5 = v4 & op(v4, % 129.52/18.09 | e2) = v4 & op(e2, e0) = v4 & $i(v4)) | (v3 = v2 & op(v2, e1) = % 129.52/18.09 | v2 & op(e1, e0) = v2 & $i(v2)) | (v1 = v0 & op(v0, e0) = v0 & % 129.52/18.09 | op(e0, e0) = v0 & $i(v0)))) % 129.52/18.09 | % 129.52/18.09 | ALPHA: (ax6) implies: % 129.52/18.09 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) & % 129.52/18.09 | ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e0, e3) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.09 | = e1) & op(e0, e0) = v1 & $i(v1)))) % 129.52/18.09 | % 129.52/18.09 | ALPHA: (ax7) implies: % 129.52/18.09 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) & % 129.52/18.09 | ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e0, e2) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.09 | = e1) & op(e0, e0) = v1 & $i(v1)))) % 129.52/18.09 | % 129.52/18.09 | ALPHA: (ax8) implies: % 129.52/18.10 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) & % 129.52/18.10 | ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e0, e3) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.10 | = e2) & op(e0, e0) = v1 & $i(v1)))) % 129.52/18.10 | % 129.52/18.10 | ALPHA: (ax9) implies: % 129.52/18.10 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) & % 129.52/18.10 | ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(e0, e1) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.10 | = e2) & op(e0, e0) = v1 & $i(v1)))) % 129.52/18.10 | % 129.52/18.10 | ALPHA: (ax10) implies: % 129.52/18.10 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) & % 129.52/18.10 | ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(e0, e2) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.10 | = e3) & op(e0, e0) = v1 & $i(v1)))) % 129.52/18.10 | % 129.52/18.10 | ALPHA: (ax11) implies: % 129.52/18.10 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) & % 129.52/18.10 | ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(e0, e1) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.10 | = e3) & op(e0, e0) = v1 & $i(v1)))) % 129.52/18.10 | % 129.52/18.10 | ALPHA: (ax12) implies: % 129.52/18.10 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) & % 129.52/18.10 | ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e1, e3) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.10 | = e0) & op(e1, e1) = v1 & $i(v1)))) % 129.52/18.10 | % 129.52/18.10 | ALPHA: (ax13) implies: % 129.52/18.10 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) & % 129.52/18.10 | ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e1, e2) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.10 | = e0) & op(e1, e1) = v1 & $i(v1)))) % 129.52/18.10 | % 129.52/18.10 | ALPHA: (ax14) implies: % 129.52/18.10 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) & % 129.52/18.10 | ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e1, e3) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.10 | = e2) & op(e1, e1) = v1 & $i(v1)))) % 129.52/18.10 | % 129.52/18.10 | ALPHA: (ax15) implies: % 129.52/18.10 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) & % 129.52/18.10 | ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(e1, e0) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.10 | = e2) & op(e1, e1) = v1 & $i(v1)))) % 129.52/18.10 | % 129.52/18.10 | ALPHA: (ax16) implies: % 129.52/18.10 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) & % 129.52/18.10 | ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(e1, e2) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.10 | = e3) & op(e1, e1) = v1 & $i(v1)))) % 129.52/18.10 | % 129.52/18.10 | ALPHA: (ax17) implies: % 129.52/18.10 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) & % 129.52/18.10 | ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(e1, e0) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.10 | = e3) & op(e1, e1) = v1 & $i(v1)))) % 129.52/18.10 | % 129.52/18.10 | ALPHA: (ax18) implies: % 129.52/18.10 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) & % 129.52/18.10 | ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e2, e3) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.10 | = e0) & op(e2, e2) = v1 & $i(v1)))) % 129.52/18.10 | % 129.52/18.10 | ALPHA: (ax19) implies: % 129.52/18.10 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) & % 129.52/18.10 | ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2, e1) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.10 | = e0) & op(e2, e2) = v1 & $i(v1)))) % 129.52/18.10 | % 129.52/18.10 | ALPHA: (ax20) implies: % 129.52/18.10 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) & % 129.52/18.10 | ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e2, e3) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.11 | = e1) & op(e2, e2) = v1 & $i(v1)))) % 129.52/18.11 | % 129.52/18.11 | ALPHA: (ax21) implies: % 129.52/18.11 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) & % 129.52/18.11 | ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(e2, e0) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.11 | = e1) & op(e2, e2) = v1 & $i(v1)))) % 129.52/18.11 | % 129.52/18.11 | ALPHA: (ax22) implies: % 129.52/18.11 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) & % 129.52/18.11 | ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(e2, e1) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.11 | = e3) & op(e2, e2) = v1 & $i(v1)))) % 129.52/18.11 | % 129.52/18.11 | ALPHA: (ax23) implies: % 129.52/18.11 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) & % 129.52/18.11 | ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(e2, e0) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.11 | = e3) & op(e2, e2) = v1 & $i(v1)))) % 129.52/18.11 | % 129.52/18.11 | ALPHA: (ax24) implies: % 129.52/18.11 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) & % 129.52/18.11 | ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3, e2) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.11 | = e0) & op(e3, e3) = v1 & $i(v1)))) % 129.52/18.11 | % 129.52/18.11 | ALPHA: (ax25) implies: % 129.52/18.11 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) & % 129.52/18.11 | ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3, e1) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.11 | = e0) & op(e3, e3) = v1 & $i(v1)))) % 129.52/18.11 | % 129.52/18.11 | ALPHA: (ax26) implies: % 129.52/18.11 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) & % 129.52/18.11 | ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3, e2) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.11 | = e1) & op(e3, e3) = v1 & $i(v1)))) % 129.52/18.11 | % 129.52/18.11 | ALPHA: (ax27) implies: % 129.52/18.11 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) & % 129.52/18.11 | ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(e3, e0) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.11 | = e1) & op(e3, e3) = v1 & $i(v1)))) % 129.52/18.11 | % 129.52/18.11 | ALPHA: (ax28) implies: % 129.52/18.11 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) & % 129.52/18.11 | ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(e3, e1) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.11 | = e2) & op(e3, e3) = v1 & $i(v1)))) % 129.52/18.11 | % 129.52/18.11 | ALPHA: (ax29) implies: % 129.52/18.11 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) & % 129.52/18.11 | ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(e3, e0) = v2 & $i(v2)) | ( ~ (v1 % 129.52/18.11 | = e2) & op(e3, e3) = v1 & $i(v1)))) % 129.52/18.11 | % 129.52/18.11 | DELTA: instantiating (20) with fresh symbols all_4_0, all_4_1, all_4_2 gives: % 129.52/18.11 | (35) op(e0, e0) = all_4_2 & $i(all_4_2) & ( ~ (all_4_2 = e1) | ( ~ (all_4_0 % 129.52/18.11 | = e3) & op(e1, e0) = all_4_0 & $i(all_4_0)) | ( ~ (all_4_1 = e2) % 129.52/18.11 | & op(e1, e1) = all_4_1 & $i(all_4_1))) % 129.52/18.11 | % 129.52/18.11 | ALPHA: (35) implies: % 129.52/18.11 | (36) op(e0, e0) = all_4_2 % 129.52/18.11 | (37) ~ (all_4_2 = e1) | ( ~ (all_4_0 = e3) & op(e1, e0) = all_4_0 & % 129.52/18.11 | $i(all_4_0)) | ( ~ (all_4_1 = e2) & op(e1, e1) = all_4_1 & % 129.52/18.11 | $i(all_4_1)) % 129.52/18.11 | % 129.52/18.11 | DELTA: instantiating (27) with fresh symbols all_6_0, all_6_1, all_6_2 gives: % 129.52/18.11 | (38) op(e1, e1) = all_6_2 & $i(all_6_2) & ( ~ (all_6_2 = e2) | ( ~ (all_6_0 % 129.52/18.11 | = e0) & op(e2, e1) = all_6_0 & $i(all_6_0)) | ( ~ (all_6_1 = e3) % 129.52/18.11 | & op(e2, e2) = all_6_1 & $i(all_6_1))) % 129.52/18.11 | % 129.52/18.11 | ALPHA: (38) implies: % 129.52/18.11 | (39) op(e1, e1) = all_6_2 % 129.52/18.11 | (40) ~ (all_6_2 = e2) | ( ~ (all_6_0 = e0) & op(e2, e1) = all_6_0 & % 129.52/18.11 | $i(all_6_0)) | ( ~ (all_6_1 = e3) & op(e2, e2) = all_6_1 & % 129.52/18.11 | $i(all_6_1)) % 129.52/18.11 | % 129.52/18.11 | DELTA: instantiating (21) with fresh symbols all_8_0, all_8_1, all_8_2 gives: % 129.52/18.12 | (41) op(e2, e2) = all_8_2 & $i(all_8_2) & ( ~ (all_8_2 = e1) | ( ~ (all_8_0 % 129.52/18.12 | = e0) & op(e1, e2) = all_8_0 & $i(all_8_0)) | ( ~ (all_8_1 = e3) % 129.52/18.12 | & op(e1, e1) = all_8_1 & $i(all_8_1))) % 129.52/18.12 | % 129.52/18.12 | ALPHA: (41) implies: % 129.52/18.12 | (42) op(e2, e2) = all_8_2 % 129.52/18.12 | (43) ~ (all_8_2 = e1) | ( ~ (all_8_0 = e0) & op(e1, e2) = all_8_0 & % 129.52/18.12 | $i(all_8_0)) | ( ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 & % 129.52/18.12 | $i(all_8_1)) % 129.52/18.12 | % 129.52/18.12 | DELTA: instantiating (11) with fresh symbols all_10_0, all_10_1, all_10_2 % 129.52/18.12 | gives: % 129.52/18.12 | (44) op(e3, e3) = all_10_2 & $i(all_10_2) & ( ~ (all_10_2 = e0) | ( ~ % 129.52/18.12 | (all_10_0 = e2) & op(e0, e3) = all_10_0 & $i(all_10_0)) | ( ~ % 129.52/18.12 | (all_10_1 = e1) & op(e0, e0) = all_10_1 & $i(all_10_1))) % 129.52/18.12 | % 129.52/18.12 | ALPHA: (44) implies: % 129.52/18.12 | (45) op(e3, e3) = all_10_2 % 129.52/18.12 | (46) ~ (all_10_2 = e0) | ( ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 & % 129.52/18.12 | $i(all_10_0)) | ( ~ (all_10_1 = e1) & op(e0, e0) = all_10_1 & % 129.52/18.12 | $i(all_10_1)) % 129.52/18.12 | % 129.52/18.12 | DELTA: instantiating (22) with fresh symbols all_12_0, all_12_1, all_12_2 % 129.52/18.12 | gives: % 129.52/18.12 | (47) op(e0, e0) = all_12_2 & $i(all_12_2) & ( ~ (all_12_2 = e1) | ( ~ % 129.52/18.12 | (all_12_0 = e2) & op(e1, e0) = all_12_0 & $i(all_12_0)) | ( ~ % 129.52/18.12 | (all_12_1 = e3) & op(e1, e1) = all_12_1 & $i(all_12_1))) % 129.52/18.12 | % 129.52/18.12 | ALPHA: (47) implies: % 129.52/18.12 | (48) op(e0, e0) = all_12_2 % 129.52/18.12 | (49) ~ (all_12_2 = e1) | ( ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 & % 129.52/18.12 | $i(all_12_0)) | ( ~ (all_12_1 = e3) & op(e1, e1) = all_12_1 & % 129.52/18.12 | $i(all_12_1)) % 129.52/18.12 | % 129.52/18.12 | DELTA: instantiating (29) with fresh symbols all_14_0, all_14_1, all_14_2 % 129.52/18.12 | gives: % 129.52/18.12 | (50) op(e2, e2) = all_14_2 & $i(all_14_2) & ( ~ (all_14_2 = e3) | ( ~ % 129.52/18.12 | (all_14_0 = e1) & op(e3, e2) = all_14_0 & $i(all_14_0)) | ( ~ % 129.52/18.12 | (all_14_1 = e0) & op(e3, e3) = all_14_1 & $i(all_14_1))) % 129.52/18.12 | % 129.52/18.12 | ALPHA: (50) implies: % 129.52/18.12 | (51) op(e2, e2) = all_14_2 % 129.52/18.12 | (52) ~ (all_14_2 = e3) | ( ~ (all_14_0 = e1) & op(e3, e2) = all_14_0 & % 129.52/18.12 | $i(all_14_0)) | ( ~ (all_14_1 = e0) & op(e3, e3) = all_14_1 & % 129.52/18.12 | $i(all_14_1)) % 129.52/18.12 | % 129.52/18.12 | DELTA: instantiating (23) with fresh symbols all_16_0, all_16_1, all_16_2 % 129.52/18.12 | gives: % 129.52/18.12 | (53) op(e3, e3) = all_16_2 & $i(all_16_2) & ( ~ (all_16_2 = e2) | ( ~ % 129.52/18.12 | (all_16_0 = e1) & op(e2, e3) = all_16_0 & $i(all_16_0)) | ( ~ % 129.52/18.12 | (all_16_1 = e0) & op(e2, e2) = all_16_1 & $i(all_16_1))) % 129.52/18.12 | % 129.52/18.12 | ALPHA: (53) implies: % 129.52/18.12 | (54) op(e3, e3) = all_16_2 % 129.52/18.12 | (55) ~ (all_16_2 = e2) | ( ~ (all_16_0 = e1) & op(e2, e3) = all_16_0 & % 129.52/18.12 | $i(all_16_0)) | ( ~ (all_16_1 = e0) & op(e2, e2) = all_16_1 & % 129.52/18.12 | $i(all_16_1)) % 129.52/18.12 | % 129.52/18.12 | DELTA: instantiating (24) with fresh symbols all_18_0, all_18_1, all_18_2 % 129.52/18.12 | gives: % 129.52/18.12 | (56) op(e1, e1) = all_18_2 & $i(all_18_2) & ( ~ (all_18_2 = e2) | ( ~ % 129.52/18.12 | (all_18_0 = e3) & op(e2, e1) = all_18_0 & $i(all_18_0)) | ( ~ % 129.52/18.12 | (all_18_1 = e0) & op(e2, e2) = all_18_1 & $i(all_18_1))) % 129.52/18.12 | % 129.52/18.12 | ALPHA: (56) implies: % 129.52/18.12 | (57) op(e1, e1) = all_18_2 % 129.52/18.12 | (58) ~ (all_18_2 = e2) | ( ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 & % 129.52/18.12 | $i(all_18_0)) | ( ~ (all_18_1 = e0) & op(e2, e2) = all_18_1 & % 129.52/18.12 | $i(all_18_1)) % 129.52/18.12 | % 129.52/18.12 | DELTA: instantiating (26) with fresh symbols all_20_0, all_20_1, all_20_2 % 129.52/18.12 | gives: % 129.52/18.12 | (59) op(e0, e0) = all_20_2 & $i(all_20_2) & ( ~ (all_20_2 = e2) | ( ~ % 129.52/18.12 | (all_20_0 = e3) & op(e2, e0) = all_20_0 & $i(all_20_0)) | ( ~ % 129.52/18.12 | (all_20_1 = e1) & op(e2, e2) = all_20_1 & $i(all_20_1))) % 129.52/18.12 | % 129.52/18.12 | ALPHA: (59) implies: % 129.52/18.12 | (60) op(e0, e0) = all_20_2 % 129.52/18.12 | (61) ~ (all_20_2 = e2) | ( ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 & % 129.52/18.12 | $i(all_20_0)) | ( ~ (all_20_1 = e1) & op(e2, e2) = all_20_1 & % 129.52/18.12 | $i(all_20_1)) % 129.52/18.12 | % 129.52/18.12 | DELTA: instantiating (31) with fresh symbols all_22_0, all_22_1, all_22_2 % 129.52/18.12 | gives: % 129.52/18.12 | (62) op(e2, e2) = all_22_2 & $i(all_22_2) & ( ~ (all_22_2 = e3) | ( ~ % 129.52/18.12 | (all_22_0 = e0) & op(e3, e2) = all_22_0 & $i(all_22_0)) | ( ~ % 129.52/18.12 | (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1))) % 129.52/18.12 | % 129.52/18.12 | ALPHA: (62) implies: % 129.52/18.12 | (63) op(e2, e2) = all_22_2 % 129.52/18.12 | (64) ~ (all_22_2 = e3) | ( ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 & % 129.52/18.12 | $i(all_22_0)) | ( ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & % 129.52/18.12 | $i(all_22_1)) % 129.52/18.12 | % 129.52/18.12 | DELTA: instantiating (13) with fresh symbols all_24_0, all_24_1, all_24_2 % 129.52/18.12 | gives: % 129.52/18.12 | (65) op(e3, e3) = all_24_2 & $i(all_24_2) & ( ~ (all_24_2 = e0) | ( ~ % 129.52/18.12 | (all_24_0 = e1) & op(e0, e3) = all_24_0 & $i(all_24_0)) | ( ~ % 129.52/18.12 | (all_24_1 = e2) & op(e0, e0) = all_24_1 & $i(all_24_1))) % 129.52/18.12 | % 129.52/18.12 | ALPHA: (65) implies: % 129.52/18.13 | (66) op(e3, e3) = all_24_2 % 129.52/18.13 | (67) ~ (all_24_2 = e0) | ( ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 & % 129.52/18.13 | $i(all_24_0)) | ( ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 & % 129.52/18.13 | $i(all_24_1)) % 129.52/18.13 | % 129.52/18.13 | DELTA: instantiating (28) with fresh symbols all_26_0, all_26_1, all_26_2 % 129.52/18.13 | gives: % 129.52/18.13 | (68) op(e0, e0) = all_26_2 & $i(all_26_2) & ( ~ (all_26_2 = e2) | ( ~ % 129.52/18.13 | (all_26_0 = e1) & op(e2, e0) = all_26_0 & $i(all_26_0)) | ( ~ % 129.52/18.13 | (all_26_1 = e3) & op(e2, e2) = all_26_1 & $i(all_26_1))) % 129.52/18.13 | % 129.52/18.13 | ALPHA: (68) implies: % 129.52/18.13 | (69) op(e0, e0) = all_26_2 % 129.52/18.13 | (70) ~ (all_26_2 = e2) | ( ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 & % 129.52/18.13 | $i(all_26_0)) | ( ~ (all_26_1 = e3) & op(e2, e2) = all_26_1 & % 129.52/18.13 | $i(all_26_1)) % 129.52/18.13 | % 129.52/18.13 | DELTA: instantiating (30) with fresh symbols all_28_0, all_28_1, all_28_2 % 129.52/18.13 | gives: % 129.52/18.13 | (71) op(e1, e1) = all_28_2 & $i(all_28_2) & ( ~ (all_28_2 = e3) | ( ~ % 129.52/18.13 | (all_28_0 = e2) & op(e3, e1) = all_28_0 & $i(all_28_0)) | ( ~ % 129.52/18.13 | (all_28_1 = e0) & op(e3, e3) = all_28_1 & $i(all_28_1))) % 129.52/18.13 | % 129.52/18.13 | ALPHA: (71) implies: % 129.52/18.13 | (72) op(e1, e1) = all_28_2 % 129.52/18.13 | (73) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 & % 129.52/18.13 | $i(all_28_0)) | ( ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 & % 129.52/18.13 | $i(all_28_1)) % 129.52/18.13 | % 129.52/18.13 | DELTA: instantiating (12) with fresh symbols all_30_0, all_30_1, all_30_2 % 129.52/18.13 | gives: % 129.52/18.13 | (74) op(e2, e2) = all_30_2 & $i(all_30_2) & ( ~ (all_30_2 = e0) | ( ~ % 129.52/18.13 | (all_30_0 = e3) & op(e0, e2) = all_30_0 & $i(all_30_0)) | ( ~ % 129.52/18.13 | (all_30_1 = e1) & op(e0, e0) = all_30_1 & $i(all_30_1))) % 129.52/18.13 | % 129.52/18.13 | ALPHA: (74) implies: % 129.52/18.13 | (75) op(e2, e2) = all_30_2 % 129.52/18.13 | (76) ~ (all_30_2 = e0) | ( ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 & % 129.52/18.13 | $i(all_30_0)) | ( ~ (all_30_1 = e1) & op(e0, e0) = all_30_1 & % 129.52/18.13 | $i(all_30_1)) % 129.52/18.13 | % 129.52/18.13 | DELTA: instantiating (19) with fresh symbols all_32_0, all_32_1, all_32_2 % 129.52/18.13 | gives: % 129.52/18.13 | (77) op(e3, e3) = all_32_2 & $i(all_32_2) & ( ~ (all_32_2 = e1) | ( ~ % 129.52/18.13 | (all_32_0 = e0) & op(e1, e3) = all_32_0 & $i(all_32_0)) | ( ~ % 129.52/18.13 | (all_32_1 = e2) & op(e1, e1) = all_32_1 & $i(all_32_1))) % 129.52/18.13 | % 129.52/18.13 | ALPHA: (77) implies: % 129.52/18.13 | (78) op(e3, e3) = all_32_2 % 129.52/18.13 | (79) ~ (all_32_2 = e1) | ( ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 & % 129.52/18.13 | $i(all_32_0)) | ( ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 & % 129.52/18.13 | $i(all_32_1)) % 129.52/18.13 | % 129.52/18.13 | DELTA: instantiating (32) with fresh symbols all_34_0, all_34_1, all_34_2 % 129.52/18.13 | gives: % 129.52/18.13 | (80) op(e0, e0) = all_34_2 & $i(all_34_2) & ( ~ (all_34_2 = e3) | ( ~ % 129.52/18.13 | (all_34_0 = e2) & op(e3, e0) = all_34_0 & $i(all_34_0)) | ( ~ % 129.52/18.13 | (all_34_1 = e1) & op(e3, e3) = all_34_1 & $i(all_34_1))) % 129.52/18.13 | % 129.52/18.13 | ALPHA: (80) implies: % 129.52/18.13 | (81) op(e0, e0) = all_34_2 % 129.52/18.13 | (82) ~ (all_34_2 = e3) | ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & % 129.52/18.13 | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 & % 129.52/18.13 | $i(all_34_1)) % 129.52/18.13 | % 129.52/18.13 | DELTA: instantiating (33) with fresh symbols all_36_0, all_36_1, all_36_2 % 129.52/18.13 | gives: % 129.52/18.13 | (83) op(e1, e1) = all_36_2 & $i(all_36_2) & ( ~ (all_36_2 = e3) | ( ~ % 129.52/18.13 | (all_36_0 = e0) & op(e3, e1) = all_36_0 & $i(all_36_0)) | ( ~ % 129.52/18.13 | (all_36_1 = e2) & op(e3, e3) = all_36_1 & $i(all_36_1))) % 129.52/18.13 | % 129.52/18.13 | ALPHA: (83) implies: % 129.52/18.13 | (84) op(e1, e1) = all_36_2 % 129.52/18.13 | (85) ~ (all_36_2 = e3) | ( ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 & % 129.52/18.13 | $i(all_36_0)) | ( ~ (all_36_1 = e2) & op(e3, e3) = all_36_1 & % 129.52/18.13 | $i(all_36_1)) % 129.52/18.13 | % 129.52/18.13 | DELTA: instantiating (25) with fresh symbols all_38_0, all_38_1, all_38_2 % 129.52/18.13 | gives: % 129.52/18.13 | (86) op(e3, e3) = all_38_2 & $i(all_38_2) & ( ~ (all_38_2 = e2) | ( ~ % 129.52/18.13 | (all_38_0 = e0) & op(e2, e3) = all_38_0 & $i(all_38_0)) | ( ~ % 129.52/18.13 | (all_38_1 = e1) & op(e2, e2) = all_38_1 & $i(all_38_1))) % 129.52/18.13 | % 129.52/18.13 | ALPHA: (86) implies: % 129.52/18.13 | (87) op(e3, e3) = all_38_2 % 129.52/18.13 | (88) ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(e2, e3) = all_38_0 & % 129.52/18.13 | $i(all_38_0)) | ( ~ (all_38_1 = e1) & op(e2, e2) = all_38_1 & % 129.52/18.13 | $i(all_38_1)) % 129.52/18.13 | % 129.52/18.13 | DELTA: instantiating (14) with fresh symbols all_40_0, all_40_1, all_40_2 % 129.52/18.13 | gives: % 129.52/18.13 | (89) op(e1, e1) = all_40_2 & $i(all_40_2) & ( ~ (all_40_2 = e0) | ( ~ % 129.52/18.13 | (all_40_0 = e3) & op(e0, e1) = all_40_0 & $i(all_40_0)) | ( ~ % 129.52/18.13 | (all_40_1 = e2) & op(e0, e0) = all_40_1 & $i(all_40_1))) % 129.52/18.13 | % 129.52/18.13 | ALPHA: (89) implies: % 129.52/18.13 | (90) op(e1, e1) = all_40_2 % 129.52/18.13 | (91) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & % 129.52/18.13 | $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & % 129.52/18.13 | $i(all_40_1)) % 129.52/18.13 | % 129.52/18.13 | DELTA: instantiating (15) with fresh symbols all_42_0, all_42_1, all_42_2 % 129.52/18.13 | gives: % 129.52/18.14 | (92) op(e2, e2) = all_42_2 & $i(all_42_2) & ( ~ (all_42_2 = e0) | ( ~ % 129.52/18.14 | (all_42_0 = e1) & op(e0, e2) = all_42_0 & $i(all_42_0)) | ( ~ % 129.52/18.14 | (all_42_1 = e3) & op(e0, e0) = all_42_1 & $i(all_42_1))) % 129.52/18.14 | % 129.52/18.14 | ALPHA: (92) implies: % 129.52/18.14 | (93) op(e2, e2) = all_42_2 % 129.84/18.14 | (94) ~ (all_42_2 = e0) | ( ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 & % 129.84/18.14 | $i(all_42_0)) | ( ~ (all_42_1 = e3) & op(e0, e0) = all_42_1 & % 129.84/18.14 | $i(all_42_1)) % 129.84/18.14 | % 129.84/18.14 | DELTA: instantiating (34) with fresh symbols all_44_0, all_44_1, all_44_2 % 129.84/18.14 | gives: % 129.84/18.14 | (95) op(e0, e0) = all_44_2 & $i(all_44_2) & ( ~ (all_44_2 = e3) | ( ~ % 129.84/18.14 | (all_44_0 = e1) & op(e3, e0) = all_44_0 & $i(all_44_0)) | ( ~ % 129.84/18.14 | (all_44_1 = e2) & op(e3, e3) = all_44_1 & $i(all_44_1))) % 129.84/18.14 | % 129.84/18.14 | ALPHA: (95) implies: % 129.84/18.14 | (96) op(e0, e0) = all_44_2 % 129.84/18.14 | (97) ~ (all_44_2 = e3) | ( ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 & % 129.84/18.14 | $i(all_44_0)) | ( ~ (all_44_1 = e2) & op(e3, e3) = all_44_1 & % 129.84/18.14 | $i(all_44_1)) % 129.84/18.14 | % 129.84/18.14 | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2 % 129.84/18.14 | gives: % 129.84/18.14 | (98) op(e1, e1) = all_46_2 & $i(all_46_2) & ( ~ (all_46_2 = e0) | ( ~ % 129.84/18.14 | (all_46_0 = e2) & op(e0, e1) = all_46_0 & $i(all_46_0)) | ( ~ % 129.84/18.14 | (all_46_1 = e3) & op(e0, e0) = all_46_1 & $i(all_46_1))) % 129.84/18.14 | % 129.84/18.14 | ALPHA: (98) implies: % 129.84/18.14 | (99) op(e1, e1) = all_46_2 % 129.84/18.14 | (100) ~ (all_46_2 = e0) | ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 & % 129.84/18.14 | $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0) = all_46_1 & % 129.84/18.14 | $i(all_46_1)) % 129.84/18.14 | % 129.84/18.14 | DELTA: instantiating (18) with fresh symbols all_48_0, all_48_1, all_48_2 % 129.84/18.14 | gives: % 129.84/18.14 | (101) op(e2, e2) = all_48_2 & $i(all_48_2) & ( ~ (all_48_2 = e1) | ( ~ % 129.84/18.14 | (all_48_0 = e3) & op(e1, e2) = all_48_0 & $i(all_48_0)) | ( ~ % 129.84/18.14 | (all_48_1 = e0) & op(e1, e1) = all_48_1 & $i(all_48_1))) % 129.84/18.14 | % 129.84/18.14 | ALPHA: (101) implies: % 129.84/18.14 | (102) op(e2, e2) = all_48_2 % 129.84/18.14 | (103) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & % 129.84/18.14 | $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 & % 129.84/18.14 | $i(all_48_1)) % 129.84/18.14 | % 129.84/18.14 | DELTA: instantiating (17) with fresh symbols all_50_0, all_50_1, all_50_2 % 129.84/18.14 | gives: % 129.84/18.14 | (104) op(e3, e3) = all_50_2 & $i(all_50_2) & ( ~ (all_50_2 = e1) | ( ~ % 129.84/18.14 | (all_50_0 = e2) & op(e1, e3) = all_50_0 & $i(all_50_0)) | ( ~ % 129.84/18.14 | (all_50_1 = e0) & op(e1, e1) = all_50_1 & $i(all_50_1))) % 129.84/18.14 | % 129.84/18.14 | ALPHA: (104) implies: % 129.84/18.14 | (105) op(e3, e3) = all_50_2 % 129.84/18.14 | (106) ~ (all_50_2 = e1) | ( ~ (all_50_0 = e2) & op(e1, e3) = all_50_0 & % 129.84/18.14 | $i(all_50_0)) | ( ~ (all_50_1 = e0) & op(e1, e1) = all_50_1 & % 129.84/18.14 | $i(all_50_1)) % 129.84/18.14 | % 129.84/18.14 | DELTA: instantiating (3) with fresh symbols all_52_0, all_52_1, all_52_2, % 129.84/18.14 | all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9, % 129.84/18.14 | all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15 gives: % 129.84/18.14 | (107) ~ (all_52_0 = all_52_1) & ~ (all_52_0 = all_52_2) & ~ (all_52_0 = % 129.84/18.14 | all_52_3) & ~ (all_52_0 = all_52_4) & ~ (all_52_0 = all_52_8) & % 129.84/18.14 | ~ (all_52_0 = all_52_12) & ~ (all_52_1 = all_52_2) & ~ (all_52_1 = % 129.84/18.14 | all_52_3) & ~ (all_52_1 = all_52_5) & ~ (all_52_1 = all_52_9) & % 129.84/18.14 | ~ (all_52_1 = all_52_13) & ~ (all_52_2 = all_52_3) & ~ (all_52_2 = % 129.84/18.14 | all_52_6) & ~ (all_52_2 = all_52_10) & ~ (all_52_2 = all_52_14) & % 129.84/18.14 | ~ (all_52_3 = all_52_7) & ~ (all_52_3 = all_52_11) & ~ (all_52_3 = % 129.84/18.14 | all_52_15) & ~ (all_52_4 = all_52_5) & ~ (all_52_4 = all_52_6) & % 129.84/18.14 | ~ (all_52_4 = all_52_7) & ~ (all_52_4 = all_52_8) & ~ (all_52_4 = % 129.84/18.14 | all_52_12) & ~ (all_52_5 = all_52_6) & ~ (all_52_5 = all_52_7) & % 129.84/18.14 | ~ (all_52_5 = all_52_9) & ~ (all_52_5 = all_52_13) & ~ (all_52_6 = % 129.84/18.14 | all_52_7) & ~ (all_52_6 = all_52_10) & ~ (all_52_6 = all_52_14) & % 129.84/18.14 | ~ (all_52_7 = all_52_11) & ~ (all_52_7 = all_52_15) & ~ (all_52_8 % 129.84/18.14 | = all_52_9) & ~ (all_52_8 = all_52_10) & ~ (all_52_8 = all_52_11) % 129.84/18.14 | & ~ (all_52_8 = all_52_12) & ~ (all_52_9 = all_52_10) & ~ % 129.84/18.14 | (all_52_9 = all_52_11) & ~ (all_52_9 = all_52_13) & ~ (all_52_10 = % 129.84/18.14 | all_52_11) & ~ (all_52_10 = all_52_14) & ~ (all_52_11 = % 129.84/18.14 | all_52_15) & ~ (all_52_12 = all_52_13) & ~ (all_52_12 = % 129.84/18.14 | all_52_14) & ~ (all_52_12 = all_52_15) & ~ (all_52_13 = % 129.84/18.14 | all_52_14) & ~ (all_52_13 = all_52_15) & ~ (all_52_14 = % 129.84/18.14 | all_52_15) & op(e3, e3) = all_52_0 & op(e3, e2) = all_52_4 & op(e3, % 129.84/18.14 | e1) = all_52_8 & op(e3, e0) = all_52_12 & op(e2, e3) = all_52_1 & % 129.84/18.14 | op(e2, e2) = all_52_5 & op(e2, e1) = all_52_9 & op(e2, e0) = % 129.84/18.14 | all_52_13 & op(e1, e3) = all_52_2 & op(e1, e2) = all_52_6 & op(e1, % 129.84/18.14 | e1) = all_52_10 & op(e1, e0) = all_52_14 & op(e0, e3) = all_52_3 & % 129.84/18.14 | op(e0, e2) = all_52_7 & op(e0, e1) = all_52_11 & op(e0, e0) = % 129.84/18.14 | all_52_15 & $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & $i(all_52_3) % 129.84/18.14 | & $i(all_52_4) & $i(all_52_5) & $i(all_52_6) & $i(all_52_7) & % 129.84/18.14 | $i(all_52_8) & $i(all_52_9) & $i(all_52_10) & $i(all_52_11) & % 129.84/18.14 | $i(all_52_12) & $i(all_52_13) & $i(all_52_14) & $i(all_52_15) % 129.84/18.14 | % 129.84/18.14 | ALPHA: (107) implies: % 129.84/18.14 | (108) ~ (all_52_14 = all_52_15) % 129.84/18.14 | (109) ~ (all_52_13 = all_52_15) % 129.84/18.14 | (110) ~ (all_52_13 = all_52_14) % 129.84/18.14 | (111) ~ (all_52_12 = all_52_15) % 129.84/18.14 | (112) ~ (all_52_12 = all_52_14) % 129.84/18.14 | (113) ~ (all_52_12 = all_52_13) % 129.84/18.15 | (114) ~ (all_52_11 = all_52_15) % 129.84/18.15 | (115) ~ (all_52_10 = all_52_14) % 129.84/18.15 | (116) ~ (all_52_10 = all_52_11) % 129.84/18.15 | (117) ~ (all_52_9 = all_52_13) % 129.84/18.15 | (118) ~ (all_52_9 = all_52_11) % 129.84/18.15 | (119) ~ (all_52_9 = all_52_10) % 129.84/18.15 | (120) ~ (all_52_8 = all_52_12) % 129.84/18.15 | (121) ~ (all_52_8 = all_52_11) % 129.84/18.15 | (122) ~ (all_52_8 = all_52_10) % 129.84/18.15 | (123) ~ (all_52_8 = all_52_9) % 129.84/18.15 | (124) ~ (all_52_7 = all_52_15) % 129.84/18.15 | (125) ~ (all_52_7 = all_52_11) % 129.84/18.15 | (126) ~ (all_52_6 = all_52_14) % 129.84/18.15 | (127) ~ (all_52_6 = all_52_10) % 129.84/18.15 | (128) ~ (all_52_6 = all_52_7) % 129.84/18.15 | (129) ~ (all_52_5 = all_52_13) % 129.84/18.15 | (130) ~ (all_52_5 = all_52_9) % 129.84/18.15 | (131) ~ (all_52_5 = all_52_7) % 129.84/18.15 | (132) ~ (all_52_5 = all_52_6) % 129.84/18.15 | (133) ~ (all_52_4 = all_52_12) % 129.84/18.15 | (134) ~ (all_52_4 = all_52_8) % 129.84/18.15 | (135) ~ (all_52_4 = all_52_7) % 129.84/18.15 | (136) ~ (all_52_4 = all_52_6) % 129.84/18.15 | (137) ~ (all_52_4 = all_52_5) % 129.84/18.15 | (138) ~ (all_52_3 = all_52_15) % 129.84/18.15 | (139) ~ (all_52_3 = all_52_11) % 129.84/18.15 | (140) ~ (all_52_3 = all_52_7) % 129.84/18.15 | (141) ~ (all_52_2 = all_52_14) % 129.84/18.15 | (142) ~ (all_52_2 = all_52_10) % 129.84/18.15 | (143) ~ (all_52_2 = all_52_6) % 129.84/18.15 | (144) ~ (all_52_2 = all_52_3) % 129.84/18.15 | (145) ~ (all_52_1 = all_52_13) % 129.84/18.15 | (146) ~ (all_52_1 = all_52_9) % 129.84/18.15 | (147) ~ (all_52_1 = all_52_5) % 129.84/18.15 | (148) ~ (all_52_1 = all_52_3) % 129.84/18.15 | (149) ~ (all_52_1 = all_52_2) % 129.84/18.15 | (150) ~ (all_52_0 = all_52_12) % 129.84/18.15 | (151) ~ (all_52_0 = all_52_8) % 129.84/18.15 | (152) ~ (all_52_0 = all_52_4) % 129.84/18.15 | (153) ~ (all_52_0 = all_52_3) % 129.84/18.15 | (154) ~ (all_52_0 = all_52_2) % 129.84/18.15 | (155) ~ (all_52_0 = all_52_1) % 129.84/18.15 | (156) op(e0, e0) = all_52_15 % 129.84/18.15 | (157) op(e0, e1) = all_52_11 % 129.84/18.15 | (158) op(e0, e2) = all_52_7 % 129.84/18.15 | (159) op(e0, e3) = all_52_3 % 129.84/18.15 | (160) op(e1, e0) = all_52_14 % 129.84/18.15 | (161) op(e1, e1) = all_52_10 % 129.84/18.15 | (162) op(e1, e2) = all_52_6 % 129.84/18.15 | (163) op(e1, e3) = all_52_2 % 129.84/18.15 | (164) op(e2, e0) = all_52_13 % 129.84/18.15 | (165) op(e2, e1) = all_52_9 % 129.84/18.15 | (166) op(e2, e2) = all_52_5 % 129.84/18.15 | (167) op(e2, e3) = all_52_1 % 129.84/18.15 | (168) op(e3, e0) = all_52_12 % 129.84/18.15 | (169) op(e3, e1) = all_52_8 % 129.84/18.15 | (170) op(e3, e2) = all_52_4 % 129.84/18.15 | (171) op(e3, e3) = all_52_0 % 129.84/18.15 | % 129.84/18.15 | DELTA: instantiating (1) with fresh symbols all_54_0, all_54_1, all_54_2, % 129.84/18.15 | all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8, all_54_9, % 129.84/18.15 | all_54_10, all_54_11, all_54_12, all_54_13, all_54_14, all_54_15 gives: % 129.84/18.15 | (172) op(e3, e3) = all_54_0 & op(e3, e2) = all_54_1 & op(e3, e1) = all_54_2 % 129.84/18.15 | & op(e3, e0) = all_54_3 & op(e2, e3) = all_54_4 & op(e2, e2) = % 129.84/18.15 | all_54_5 & op(e2, e1) = all_54_6 & op(e2, e0) = all_54_7 & op(e1, e3) % 129.84/18.15 | = all_54_8 & op(e1, e2) = all_54_9 & op(e1, e1) = all_54_10 & op(e1, % 129.84/18.15 | e0) = all_54_11 & op(e0, e3) = all_54_12 & op(e0, e2) = all_54_13 & % 129.84/18.15 | op(e0, e1) = all_54_14 & op(e0, e0) = all_54_15 & $i(all_54_0) & % 129.84/18.15 | $i(all_54_1) & $i(all_54_2) & $i(all_54_3) & $i(all_54_4) & % 129.84/18.15 | $i(all_54_5) & $i(all_54_6) & $i(all_54_7) & $i(all_54_8) & % 129.84/18.15 | $i(all_54_9) & $i(all_54_10) & $i(all_54_11) & $i(all_54_12) & % 129.84/18.15 | $i(all_54_13) & $i(all_54_14) & $i(all_54_15) & (all_54_0 = e3 | % 129.84/18.15 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0) & (all_54_1 = e3 | % 129.84/18.15 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0) & (all_54_2 = e3 | % 129.84/18.15 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0) & (all_54_3 = e3 | % 129.84/18.15 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0) & (all_54_4 = e3 | % 129.84/18.15 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0) & (all_54_5 = e3 | % 129.84/18.15 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0) & (all_54_6 = e3 | % 129.84/18.15 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0) & (all_54_7 = e3 | % 129.84/18.15 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0) & (all_54_8 = e3 | % 129.84/18.15 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0) & (all_54_9 = e3 | % 129.84/18.15 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0) & (all_54_10 = e3 | % 129.84/18.15 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0) & (all_54_11 = e3 % 129.84/18.15 | | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0) & (all_54_12 = % 129.84/18.15 | e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0) & (all_54_13 % 129.84/18.15 | = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0) & % 129.84/18.15 | (all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0) & % 129.84/18.15 | (all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0) % 129.84/18.15 | % 129.84/18.15 | ALPHA: (172) implies: % 129.84/18.15 | (173) op(e0, e0) = all_54_15 % 129.84/18.15 | (174) op(e0, e1) = all_54_14 % 129.84/18.15 | (175) op(e0, e2) = all_54_13 % 129.84/18.15 | (176) op(e0, e3) = all_54_12 % 129.84/18.15 | (177) op(e1, e0) = all_54_11 % 129.84/18.15 | (178) op(e1, e1) = all_54_10 % 129.84/18.15 | (179) op(e1, e2) = all_54_9 % 129.84/18.15 | (180) op(e1, e3) = all_54_8 % 129.84/18.15 | (181) op(e2, e0) = all_54_7 % 129.84/18.16 | (182) op(e2, e1) = all_54_6 % 129.84/18.16 | (183) op(e2, e2) = all_54_5 % 129.84/18.16 | (184) op(e2, e3) = all_54_4 % 129.84/18.16 | (185) op(e3, e0) = all_54_3 % 129.84/18.16 | (186) op(e3, e1) = all_54_2 % 129.84/18.16 | (187) op(e3, e2) = all_54_1 % 129.84/18.16 | (188) op(e3, e3) = all_54_0 % 129.84/18.16 | (189) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 129.84/18.16 | (190) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 129.84/18.16 | (191) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 129.84/18.16 | (192) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 129.84/18.16 | (193) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 129.84/18.16 | (194) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 129.84/18.16 | (195) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 129.84/18.16 | (196) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 129.84/18.16 | (197) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 129.84/18.16 | (198) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 129.84/18.16 | (199) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 129.84/18.16 | (200) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 129.84/18.16 | (201) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 129.84/18.16 | (202) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 129.84/18.16 | (203) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 129.84/18.16 | (204) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 129.84/18.16 | % 129.84/18.16 | DELTA: instantiating (10) with fresh symbols all_56_0, all_56_1, all_56_2, % 129.84/18.16 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9, % 129.84/18.16 | all_56_10, all_56_11, all_56_12, all_56_13, all_56_14, all_56_15, % 129.84/18.16 | all_56_16, all_56_17, all_56_18, all_56_19, all_56_20, all_56_21, % 129.84/18.16 | all_56_22, all_56_23, all_56_24, all_56_25, all_56_26, all_56_27, % 129.84/18.16 | all_56_28, all_56_29, all_56_30, all_56_31 gives: % 129.84/18.17 | (205) ((all_56_0 = all_56_1 & op(all_56_1, e3) = all_56_1 & op(e3, e3) = % 129.84/18.17 | all_56_1 & $i(all_56_1)) | (all_56_2 = all_56_3 & op(all_56_3, % 129.84/18.17 | e2) = all_56_3 & op(e2, e3) = all_56_3 & $i(all_56_3)) | % 129.84/18.17 | (all_56_4 = all_56_5 & op(all_56_5, e1) = all_56_5 & op(e1, e3) = % 129.84/18.17 | all_56_5 & $i(all_56_5)) | (all_56_6 = all_56_7 & op(all_56_7, % 129.84/18.17 | e0) = all_56_7 & op(e0, e3) = all_56_7 & $i(all_56_7))) & % 129.84/18.17 | ((all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 % 129.84/18.17 | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) % 129.84/18.17 | = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 129.84/18.17 | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 129.84/18.17 | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 129.84/18.17 | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ % 129.84/18.17 | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 129.84/18.17 | op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & % 129.84/18.17 | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 129.84/18.17 | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 129.84/18.17 | $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 129.84/18.17 | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 % 129.84/18.17 | = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 129.84/18.17 | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 129.84/18.17 | op(e0, e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 129.84/18.17 | $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 % 129.84/18.17 | & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 129.84/18.17 | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 129.84/18.17 | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 129.84/18.17 | op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 129.84/18.17 | $i(all_56_17) & $i(all_56_25)) | (all_56_5 = e1 & all_56_21 = e3 % 129.84/18.17 | & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 129.84/18.17 | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 129.84/18.17 | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 129.84/18.17 | op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 129.84/18.17 | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 % 129.84/18.17 | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 129.84/18.17 | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & % 129.84/18.17 | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 129.84/18.17 | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) % 129.84/18.17 | & $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = % 129.84/18.17 | e2 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 129.84/18.17 | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & % 129.84/18.17 | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 129.84/18.17 | all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) % 129.84/18.17 | & $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = % 129.84/18.17 | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 129.84/18.17 | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 129.84/18.17 | = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 129.84/18.17 | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) % 129.84/18.17 | & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 & % 129.84/18.17 | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 129.84/18.17 | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 129.84/18.17 | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 129.84/18.17 | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 129.84/18.17 | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) % 129.84/18.17 | & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 129.84/18.17 | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 129.84/18.17 | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 129.84/18.17 | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 129.84/18.17 | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 129.84/18.17 | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 % 129.84/18.17 | = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ % 129.84/18.17 | (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 129.84/18.17 | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 129.84/18.17 | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 129.84/18.17 | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 129.84/18.17 | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 129.84/18.17 | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 129.84/18.17 | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 129.84/18.17 | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 129.84/18.17 | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))))) & % 129.84/18.17 | ((all_56_8 = all_56_9 & op(all_56_9, e3) = all_56_9 & op(e3, e2) = % 129.84/18.17 | all_56_9 & $i(all_56_9)) | (all_56_10 = all_56_11 & op(all_56_11, % 129.84/18.17 | e2) = all_56_11 & op(e2, e2) = all_56_11 & $i(all_56_11)) | % 129.84/18.17 | (all_56_12 = all_56_13 & op(all_56_13, e1) = all_56_13 & op(e1, e2) % 129.84/18.17 | = all_56_13 & $i(all_56_13)) | (all_56_14 = all_56_15 & % 129.84/18.17 | op(all_56_15, e0) = all_56_15 & op(e0, e2) = all_56_15 & % 129.84/18.17 | $i(all_56_15))) & ((all_56_16 = all_56_17 & op(all_56_17, e3) = % 129.84/18.17 | all_56_17 & op(e3, e1) = all_56_17 & $i(all_56_17)) | (all_56_18 % 129.84/18.17 | = all_56_19 & op(all_56_19, e2) = all_56_19 & op(e2, e1) = % 129.84/18.17 | all_56_19 & $i(all_56_19)) | (all_56_20 = all_56_21 & % 129.84/18.17 | op(all_56_21, e1) = all_56_21 & op(e1, e1) = all_56_21 & % 129.84/18.17 | $i(all_56_21)) | (all_56_22 = all_56_23 & op(all_56_23, e0) = % 129.84/18.17 | all_56_23 & op(e0, e1) = all_56_23 & $i(all_56_23))) & % 129.84/18.17 | ((all_56_24 = all_56_25 & op(all_56_25, e3) = all_56_25 & op(e3, e0) % 129.84/18.17 | = all_56_25 & $i(all_56_25)) | (all_56_26 = all_56_27 & % 129.84/18.17 | op(all_56_27, e2) = all_56_27 & op(e2, e0) = all_56_27 & % 129.84/18.17 | $i(all_56_27)) | (all_56_28 = all_56_29 & op(all_56_29, e1) = % 129.84/18.17 | all_56_29 & op(e1, e0) = all_56_29 & $i(all_56_29)) | (all_56_30 % 129.84/18.17 | = all_56_31 & op(all_56_31, e0) = all_56_31 & op(e0, e0) = % 129.84/18.17 | all_56_31 & $i(all_56_31))) % 129.84/18.17 | % 129.84/18.17 | ALPHA: (205) implies: % 129.98/18.17 | (206) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 129.98/18.17 | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 % 129.98/18.17 | & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 % 129.98/18.17 | & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 129.98/18.17 | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 129.98/18.17 | all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 129.98/18.17 | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 129.98/18.17 | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 129.98/18.17 | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 129.98/18.17 | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & % 129.98/18.17 | all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ % 129.98/18.17 | (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 129.98/18.17 | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 129.98/18.17 | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 129.98/18.17 | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 129.98/18.17 | all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 129.98/18.17 | (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.17 | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = % 129.98/18.17 | all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & % 129.98/18.17 | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_5 = e1 & % 129.98/18.17 | all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 129.98/18.17 | (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.17 | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = % 129.98/18.17 | all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & % 129.98/18.17 | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & % 129.98/18.17 | all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 129.98/18.17 | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 129.98/18.17 | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 129.98/18.17 | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 129.98/18.17 | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & % 129.98/18.17 | all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ % 129.98/18.17 | (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 129.98/18.17 | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 129.98/18.17 | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 129.98/18.17 | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 & % 129.98/18.17 | all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ % 129.98/18.17 | (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 129.98/18.17 | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 129.98/18.17 | all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 129.98/18.17 | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 129.98/18.17 | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 129.98/18.17 | (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 129.98/18.17 | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 129.98/18.17 | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 129.98/18.17 | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 129.98/18.17 | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 129.98/18.17 | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 129.98/18.17 | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 129.98/18.17 | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 129.98/18.17 | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 129.98/18.17 | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 129.98/18.17 | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 129.98/18.17 | ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, % 129.98/18.17 | e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 129.98/18.17 | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 129.98/18.17 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 129.98/18.17 | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 129.98/18.17 | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 129.98/18.17 | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 129.98/18.17 | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)))) % 129.98/18.17 | % 129.98/18.17 | DELTA: instantiating (2) with fresh symbols all_57_0, all_57_1, all_57_2, % 129.98/18.17 | all_57_3, all_57_4, all_57_5, all_57_6, all_57_7, all_57_8, all_57_9, % 129.98/18.17 | all_57_10, all_57_11, all_57_12, all_57_13, all_57_14, all_57_15 gives: % 129.98/18.18 | (207) ((all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = % 129.98/18.18 | e3) | (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, % 129.98/18.18 | e0) = e3)) & ((all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = % 129.98/18.18 | e3 & op(e2, e3) = e3) | (all_57_6 = e3 & op(e1, e3) = e3) | % 129.98/18.18 | (all_57_12 = e3 & op(e0, e3) = e3)) & ((all_57_0 = e2 & op(e3, e3) % 129.98/18.18 | = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_4 = e2 & % 129.98/18.18 | op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)) & % 129.98/18.18 | ((all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = % 129.98/18.18 | e2) | (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & % 129.98/18.18 | op(e0, e3) = e2)) & ((all_57_0 = e1 & op(e3, e3) = e1) | % 129.98/18.18 | (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_4 = e1 & op(e3, e1) = % 129.98/18.18 | e1) | (all_57_9 = e1 & op(e3, e0) = e1)) & ((all_57_0 = e1 & % 129.98/18.18 | op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_6 % 129.98/18.18 | = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)) & % 129.98/18.18 | ((all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = % 129.98/18.18 | e0) | (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, % 129.98/18.18 | e0) = e0)) & ((all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = % 129.98/18.18 | e0 & op(e2, e3) = e0) | (all_57_6 = e0 & op(e1, e3) = e0) | % 129.98/18.18 | (all_57_12 = e0 & op(e0, e3) = e0)) & ((all_57_1 = e3 & op(e3, e2) % 129.98/18.18 | = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | (all_57_7 = e3 & % 129.98/18.18 | op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)) & % 129.98/18.18 | ((all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = % 129.98/18.18 | e2) | (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & % 129.98/18.18 | op(e0, e2) = e2)) & ((all_57_1 = e1 & op(e3, e2) = e1) | % 129.98/18.18 | (all_57_3 = e1 & op(e2, e2) = e1) | (all_57_7 = e1 & op(e1, e2) = % 129.98/18.18 | e1) | (all_57_13 = e1 & op(e0, e2) = e1)) & ((all_57_1 = e0 & % 129.98/18.18 | op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | (all_57_7 % 129.98/18.18 | = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)) & % 129.98/18.18 | ((all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = % 129.98/18.18 | e3) | (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & % 129.98/18.18 | op(e2, e0) = e3)) & ((all_57_2 = e2 & op(e2, e3) = e2) | % 129.98/18.18 | (all_57_3 = e2 & op(e2, e2) = e2) | (all_57_5 = e2 & op(e2, e1) = % 129.98/18.18 | e2) | (all_57_10 = e2 & op(e2, e0) = e2)) & ((all_57_2 = e1 & % 129.98/18.18 | op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | (all_57_5 % 129.98/18.18 | = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)) & % 129.98/18.18 | ((all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = % 129.98/18.18 | e0) | (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & % 129.98/18.18 | op(e2, e0) = e0)) & ((all_57_4 = e3 & op(e3, e1) = e3) | % 129.98/18.18 | (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_8 = e3 & op(e1, e1) = % 129.98/18.18 | e3) | (all_57_14 = e3 & op(e0, e1) = e3)) & ((all_57_4 = e2 & % 129.98/18.18 | op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_8 % 129.98/18.18 | = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)) & % 129.98/18.18 | ((all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = % 129.98/18.18 | e1) | (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & % 129.98/18.18 | op(e0, e1) = e1)) & ((all_57_4 = e0 & op(e3, e1) = e0) | % 129.98/18.18 | (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_8 = e0 & op(e1, e1) = % 129.98/18.18 | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) & ((all_57_6 = e3 & % 129.98/18.18 | op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_8 % 129.98/18.18 | = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)) & % 129.98/18.18 | ((all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = % 129.98/18.18 | e2) | (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & % 129.98/18.18 | op(e1, e0) = e2)) & ((all_57_6 = e1 & op(e1, e3) = e1) | % 129.98/18.18 | (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_8 = e1 & op(e1, e1) = % 129.98/18.18 | e1) | (all_57_11 = e1 & op(e1, e0) = e1)) & ((all_57_6 = e0 & % 129.98/18.18 | op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_8 % 129.98/18.18 | = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & % 129.98/18.18 | ((all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = % 129.98/18.18 | e3) | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & % 129.98/18.18 | op(e0, e0) = e3)) & ((all_57_9 = e2 & op(e3, e0) = e2) | % 129.98/18.18 | (all_57_10 = e2 & op(e2, e0) = e2) | (all_57_11 = e2 & op(e1, e0) = % 129.98/18.18 | e2) | (all_57_15 = e2 & op(e0, e0) = e2)) & ((all_57_9 = e1 & % 129.98/18.18 | op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) | % 129.98/18.18 | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = % 129.98/18.18 | e1)) & ((all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & % 129.98/18.18 | op(e0, e2) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) | % 129.98/18.18 | (all_57_15 = e3 & op(e0, e0) = e3)) & ((all_57_12 = e2 & op(e0, e3) % 129.98/18.18 | = e2) | (all_57_13 = e2 & op(e0, e2) = e2) | (all_57_14 = e2 & % 129.98/18.18 | op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)) & % 129.98/18.18 | ((all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = % 129.98/18.18 | e1) | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & % 129.98/18.18 | op(e0, e0) = e1)) & ((all_57_15 = e0 & op(e0, e0) = e0) | % 129.98/18.18 | (((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) % 129.98/18.18 | = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = % 129.98/18.18 | e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) | % 129.98/18.18 | (all_57_14 = e0 & op(e0, e1) = e0)))) % 129.98/18.18 | % 129.98/18.18 | ALPHA: (207) implies: % 129.98/18.19 | (208) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = % 129.98/18.19 | e0) | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 129.98/18.19 | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | % 129.98/18.19 | (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) % 129.98/18.19 | = e0))) % 129.98/18.19 | (209) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = % 129.98/18.19 | e1) | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, % 129.98/18.19 | e0) = e1) % 129.98/18.19 | (210) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = % 129.98/18.19 | e2) | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, % 129.98/18.19 | e0) = e2) % 129.98/18.19 | (211) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = % 129.98/18.19 | e3) | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, % 129.98/18.19 | e0) = e3) % 129.98/18.19 | (212) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = % 129.98/18.19 | e1) | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, % 129.98/18.19 | e0) = e1) % 129.98/18.19 | (213) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = % 129.98/18.19 | e2) | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, % 129.98/18.19 | e0) = e2) % 129.98/18.19 | (214) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = % 129.98/18.19 | e3) | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, % 129.98/18.19 | e0) = e3) % 129.98/18.19 | (215) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) % 129.98/18.19 | | (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = % 129.98/18.19 | e0) % 129.98/18.19 | (216) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) % 129.98/18.19 | | (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = % 129.98/18.19 | e1) % 129.98/18.19 | (217) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) % 129.98/18.19 | | (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = % 129.98/18.19 | e2) % 129.98/18.19 | (218) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) % 129.98/18.19 | | (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = % 129.98/18.19 | e3) % 129.98/18.19 | (219) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) % 129.98/18.19 | | (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = % 129.98/18.19 | e0) % 129.98/18.19 | (220) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) % 129.98/18.19 | | (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = % 129.98/18.19 | e1) % 129.98/18.19 | (221) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) % 129.98/18.19 | | (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = % 129.98/18.19 | e2) % 129.98/18.19 | (222) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) % 129.98/18.19 | | (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = % 129.98/18.19 | e3) % 129.98/18.19 | (223) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) % 129.98/18.19 | | (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = % 129.98/18.19 | e0) % 129.98/18.19 | (224) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) % 129.98/18.19 | | (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = % 129.98/18.19 | e1) % 129.98/18.19 | (225) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) % 129.98/18.19 | | (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = % 129.98/18.19 | e2) % 129.98/18.19 | (226) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) % 129.98/18.19 | | (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = % 129.98/18.19 | e3) % 129.98/18.19 | (227) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) % 129.98/18.19 | | (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = % 129.98/18.19 | e0) % 129.98/18.19 | (228) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) % 129.98/18.19 | | (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = % 129.98/18.19 | e1) % 129.98/18.19 | (229) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) % 129.98/18.19 | | (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = % 129.98/18.19 | e2) % 129.98/18.20 | (230) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) % 129.98/18.20 | | (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = % 129.98/18.20 | e3) % 129.98/18.20 | (231) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) % 129.98/18.20 | | (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = % 129.98/18.20 | e0) % 129.98/18.20 | (232) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) % 129.98/18.20 | | (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = % 129.98/18.20 | e0) % 129.98/18.20 | (233) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) % 129.98/18.20 | | (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = % 129.98/18.20 | e1) % 129.98/18.20 | (234) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) % 129.98/18.20 | | (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = % 129.98/18.20 | e1) % 129.98/18.20 | (235) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) % 129.98/18.20 | | (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = % 129.98/18.20 | e2) % 129.98/18.20 | (236) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) % 129.98/18.20 | | (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = % 129.98/18.20 | e2) % 129.98/18.20 | (237) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) % 129.98/18.20 | | (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = % 129.98/18.20 | e3) % 129.98/18.20 | (238) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) % 129.98/18.20 | | (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = % 129.98/18.20 | e3) % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_26_2, e0, e0, % 129.98/18.20 | simplifying with (60), (69) gives: % 129.98/18.20 | (239) all_26_2 = all_20_2 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_12_2, all_26_2, e0, e0, % 129.98/18.20 | simplifying with (48), (69) gives: % 129.98/18.20 | (240) all_26_2 = all_12_2 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_34_2, e0, e0, % 129.98/18.20 | simplifying with (60), (81) gives: % 129.98/18.20 | (241) all_34_2 = all_20_2 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_44_2, all_52_15, e0, e0, % 129.98/18.20 | simplifying with (96), (156) gives: % 129.98/18.20 | (242) all_52_15 = all_44_2 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_34_2, all_52_15, e0, e0, % 129.98/18.20 | simplifying with (81), (156) gives: % 129.98/18.20 | (243) all_52_15 = all_34_2 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_15, all_54_15, e0, % 129.98/18.20 | e0, simplifying with (156), (173) gives: % 129.98/18.20 | (244) all_54_15 = all_52_15 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_54_15, e0, e0, % 129.98/18.20 | simplifying with (36), (173) gives: % 129.98/18.20 | (245) all_54_15 = all_4_2 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_11, all_54_14, e1, % 129.98/18.20 | e0, simplifying with (157), (174) gives: % 129.98/18.20 | (246) all_54_14 = all_52_11 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_7, all_54_13, e2, e0, % 129.98/18.20 | simplifying with (158), (175) gives: % 129.98/18.20 | (247) all_54_13 = all_52_7 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_3, all_54_12, e3, e0, % 129.98/18.20 | simplifying with (159), (176) gives: % 129.98/18.20 | (248) all_54_12 = all_52_3 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_14, all_54_11, e0, % 129.98/18.20 | e1, simplifying with (160), (177) gives: % 129.98/18.20 | (249) all_54_11 = all_52_14 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_46_2, all_52_10, e1, e1, % 129.98/18.20 | simplifying with (99), (161) gives: % 129.98/18.20 | (250) all_52_10 = all_46_2 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_36_2, all_52_10, e1, e1, % 129.98/18.20 | simplifying with (84), (161) gives: % 129.98/18.20 | (251) all_52_10 = all_36_2 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_28_2, all_52_10, e1, e1, % 129.98/18.20 | simplifying with (72), (161) gives: % 129.98/18.20 | (252) all_52_10 = all_28_2 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_6_2, all_52_10, e1, e1, % 129.98/18.20 | simplifying with (39), (161) gives: % 129.98/18.20 | (253) all_52_10 = all_6_2 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_10, all_54_10, e1, % 129.98/18.20 | e1, simplifying with (161), (178) gives: % 129.98/18.20 | (254) all_54_10 = all_52_10 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_40_2, all_54_10, e1, e1, % 129.98/18.20 | simplifying with (90), (178) gives: % 129.98/18.20 | (255) all_54_10 = all_40_2 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_18_2, all_54_10, e1, e1, % 129.98/18.20 | simplifying with (57), (178) gives: % 129.98/18.20 | (256) all_54_10 = all_18_2 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_6, all_54_9, e2, e1, % 129.98/18.20 | simplifying with (162), (179) gives: % 129.98/18.20 | (257) all_54_9 = all_52_6 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_2, all_54_8, e3, e1, % 129.98/18.20 | simplifying with (163), (180) gives: % 129.98/18.20 | (258) all_54_8 = all_52_2 % 129.98/18.20 | % 129.98/18.20 | GROUND_INST: instantiating (function-axioms) with all_52_13, all_54_7, e0, e2, % 129.98/18.20 | simplifying with (164), (181) gives: % 129.98/18.20 | (259) all_54_7 = all_52_13 % 129.98/18.20 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_52_9, all_54_6, e1, e2, % 129.98/18.21 | simplifying with (165), (182) gives: % 129.98/18.21 | (260) all_54_6 = all_52_9 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_14_2, all_22_2, e2, e2, % 129.98/18.21 | simplifying with (51), (63) gives: % 129.98/18.21 | (261) all_22_2 = all_14_2 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_30_2, e2, e2, % 129.98/18.21 | simplifying with (63), (75) gives: % 129.98/18.21 | (262) all_30_2 = all_22_2 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_30_2, all_42_2, e2, e2, % 129.98/18.21 | simplifying with (75), (93) gives: % 129.98/18.21 | (263) all_42_2 = all_30_2 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_48_2, all_52_5, e2, e2, % 129.98/18.21 | simplifying with (102), (166) gives: % 129.98/18.21 | (264) all_52_5 = all_48_2 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_52_5, e2, e2, % 129.98/18.21 | simplifying with (93), (166) gives: % 129.98/18.21 | (265) all_52_5 = all_42_2 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_52_5, all_54_5, e2, e2, % 129.98/18.21 | simplifying with (166), (183) gives: % 129.98/18.21 | (266) all_54_5 = all_52_5 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_8_2, all_54_5, e2, e2, % 129.98/18.21 | simplifying with (42), (183) gives: % 129.98/18.21 | (267) all_54_5 = all_8_2 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_52_1, all_54_4, e3, e2, % 129.98/18.21 | simplifying with (167), (184) gives: % 129.98/18.21 | (268) all_54_4 = all_52_1 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_52_12, all_54_3, e0, e3, % 129.98/18.21 | simplifying with (168), (185) gives: % 129.98/18.21 | (269) all_54_3 = all_52_12 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_52_8, all_54_2, e1, e3, % 129.98/18.21 | simplifying with (169), (186) gives: % 129.98/18.21 | (270) all_54_2 = all_52_8 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_52_4, all_54_1, e2, e3, % 129.98/18.21 | simplifying with (170), (187) gives: % 129.98/18.21 | (271) all_54_1 = all_52_4 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_32_2, all_38_2, e3, e3, % 129.98/18.21 | simplifying with (78), (87) gives: % 129.98/18.21 | (272) all_38_2 = all_32_2 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_38_2, e3, e3, % 129.98/18.21 | simplifying with (66), (87) gives: % 129.98/18.21 | (273) all_38_2 = all_24_2 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_50_2, e3, e3, % 129.98/18.21 | simplifying with (87), (105) gives: % 129.98/18.21 | (274) all_50_2 = all_38_2 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_52_0, e3, e3, % 129.98/18.21 | simplifying with (87), (171) gives: % 129.98/18.21 | (275) all_52_0 = all_38_2 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_16_2, all_52_0, e3, e3, % 129.98/18.21 | simplifying with (54), (171) gives: % 129.98/18.21 | (276) all_52_0 = all_16_2 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_50_2, all_54_0, e3, e3, % 129.98/18.21 | simplifying with (105), (188) gives: % 129.98/18.21 | (277) all_54_0 = all_50_2 % 129.98/18.21 | % 129.98/18.21 | GROUND_INST: instantiating (function-axioms) with all_10_2, all_54_0, e3, e3, % 129.98/18.21 | simplifying with (45), (188) gives: % 129.98/18.21 | (278) all_54_0 = all_10_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (277), (278) imply: % 129.98/18.21 | (279) all_50_2 = all_10_2 % 129.98/18.21 | % 129.98/18.21 | SIMP: (279) implies: % 129.98/18.21 | (280) all_50_2 = all_10_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (266), (267) imply: % 129.98/18.21 | (281) all_52_5 = all_8_2 % 129.98/18.21 | % 129.98/18.21 | SIMP: (281) implies: % 129.98/18.21 | (282) all_52_5 = all_8_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (255), (256) imply: % 129.98/18.21 | (283) all_40_2 = all_18_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (254), (255) imply: % 129.98/18.21 | (284) all_52_10 = all_40_2 % 129.98/18.21 | % 129.98/18.21 | SIMP: (284) implies: % 129.98/18.21 | (285) all_52_10 = all_40_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (244), (245) imply: % 129.98/18.21 | (286) all_52_15 = all_4_2 % 129.98/18.21 | % 129.98/18.21 | SIMP: (286) implies: % 129.98/18.21 | (287) all_52_15 = all_4_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (275), (276) imply: % 129.98/18.21 | (288) all_38_2 = all_16_2 % 129.98/18.21 | % 129.98/18.21 | SIMP: (288) implies: % 129.98/18.21 | (289) all_38_2 = all_16_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (264), (265) imply: % 129.98/18.21 | (290) all_48_2 = all_42_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (264), (282) imply: % 129.98/18.21 | (291) all_48_2 = all_8_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (250), (251) imply: % 129.98/18.21 | (292) all_46_2 = all_36_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (250), (252) imply: % 129.98/18.21 | (293) all_46_2 = all_28_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (250), (285) imply: % 129.98/18.21 | (294) all_46_2 = all_40_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (250), (253) imply: % 129.98/18.21 | (295) all_46_2 = all_6_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (242), (243) imply: % 129.98/18.21 | (296) all_44_2 = all_34_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (242), (287) imply: % 129.98/18.21 | (297) all_44_2 = all_4_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (274), (280) imply: % 129.98/18.21 | (298) all_38_2 = all_10_2 % 129.98/18.21 | % 129.98/18.21 | SIMP: (298) implies: % 129.98/18.21 | (299) all_38_2 = all_10_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (290), (291) imply: % 129.98/18.21 | (300) all_42_2 = all_8_2 % 129.98/18.21 | % 129.98/18.21 | SIMP: (300) implies: % 129.98/18.21 | (301) all_42_2 = all_8_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (292), (295) imply: % 129.98/18.21 | (302) all_36_2 = all_6_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (292), (293) imply: % 129.98/18.21 | (303) all_36_2 = all_28_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (292), (294) imply: % 129.98/18.21 | (304) all_40_2 = all_36_2 % 129.98/18.21 | % 129.98/18.21 | SIMP: (304) implies: % 129.98/18.21 | (305) all_40_2 = all_36_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (296), (297) imply: % 129.98/18.21 | (306) all_34_2 = all_4_2 % 129.98/18.21 | % 129.98/18.21 | SIMP: (306) implies: % 129.98/18.21 | (307) all_34_2 = all_4_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (263), (301) imply: % 129.98/18.21 | (308) all_30_2 = all_8_2 % 129.98/18.21 | % 129.98/18.21 | SIMP: (308) implies: % 129.98/18.21 | (309) all_30_2 = all_8_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (283), (305) imply: % 129.98/18.21 | (310) all_36_2 = all_18_2 % 129.98/18.21 | % 129.98/18.21 | SIMP: (310) implies: % 129.98/18.21 | (311) all_36_2 = all_18_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (272), (299) imply: % 129.98/18.21 | (312) all_32_2 = all_10_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (272), (273) imply: % 129.98/18.21 | (313) all_32_2 = all_24_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (272), (289) imply: % 129.98/18.21 | (314) all_32_2 = all_16_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (303), (311) imply: % 129.98/18.21 | (315) all_28_2 = all_18_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (302), (303) imply: % 129.98/18.21 | (316) all_28_2 = all_6_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (241), (307) imply: % 129.98/18.21 | (317) all_20_2 = all_4_2 % 129.98/18.21 | % 129.98/18.21 | SIMP: (317) implies: % 129.98/18.21 | (318) all_20_2 = all_4_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (312), (313) imply: % 129.98/18.21 | (319) all_24_2 = all_10_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (313), (314) imply: % 129.98/18.21 | (320) all_24_2 = all_16_2 % 129.98/18.21 | % 129.98/18.21 | COMBINE_EQS: (262), (309) imply: % 129.98/18.21 | (321) all_22_2 = all_8_2 % 129.98/18.21 | % 129.98/18.22 | SIMP: (321) implies: % 129.98/18.22 | (322) all_22_2 = all_8_2 % 129.98/18.22 | % 129.98/18.22 | COMBINE_EQS: (315), (316) imply: % 129.98/18.22 | (323) all_18_2 = all_6_2 % 129.98/18.22 | % 129.98/18.22 | SIMP: (323) implies: % 129.98/18.22 | (324) all_18_2 = all_6_2 % 129.98/18.22 | % 129.98/18.22 | COMBINE_EQS: (239), (240) imply: % 129.98/18.22 | (325) all_20_2 = all_12_2 % 129.98/18.22 | % 129.98/18.22 | SIMP: (325) implies: % 129.98/18.22 | (326) all_20_2 = all_12_2 % 129.98/18.22 | % 129.98/18.22 | COMBINE_EQS: (319), (320) imply: % 129.98/18.22 | (327) all_16_2 = all_10_2 % 129.98/18.22 | % 129.98/18.22 | COMBINE_EQS: (261), (322) imply: % 129.98/18.22 | (328) all_14_2 = all_8_2 % 129.98/18.22 | % 129.98/18.22 | SIMP: (328) implies: % 129.98/18.22 | (329) all_14_2 = all_8_2 % 129.98/18.22 | % 129.98/18.22 | COMBINE_EQS: (318), (326) imply: % 129.98/18.22 | (330) all_12_2 = all_4_2 % 129.98/18.22 | % 129.98/18.22 | COMBINE_EQS: (240), (330) imply: % 129.98/18.22 | (331) all_26_2 = all_4_2 % 129.98/18.22 | % 129.98/18.22 | COMBINE_EQS: (283), (324) imply: % 129.98/18.22 | (332) all_40_2 = all_6_2 % 129.98/18.22 | % 129.98/18.22 | COMBINE_EQS: (276), (327) imply: % 129.98/18.22 | (333) all_52_0 = all_10_2 % 129.98/18.22 | % 129.98/18.22 | COMBINE_EQS: (255), (332) imply: % 129.98/18.22 | (334) all_54_10 = all_6_2 % 129.98/18.22 | % 129.98/18.22 | REDUCE: (155), (333) imply: % 129.98/18.22 | (335) ~ (all_52_1 = all_10_2) % 129.98/18.22 | % 129.98/18.22 | SIMP: (335) implies: % 129.98/18.22 | (336) ~ (all_52_1 = all_10_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (154), (333) imply: % 129.98/18.22 | (337) ~ (all_52_2 = all_10_2) % 129.98/18.22 | % 129.98/18.22 | SIMP: (337) implies: % 129.98/18.22 | (338) ~ (all_52_2 = all_10_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (153), (333) imply: % 129.98/18.22 | (339) ~ (all_52_3 = all_10_2) % 129.98/18.22 | % 129.98/18.22 | SIMP: (339) implies: % 129.98/18.22 | (340) ~ (all_52_3 = all_10_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (152), (333) imply: % 129.98/18.22 | (341) ~ (all_52_4 = all_10_2) % 129.98/18.22 | % 129.98/18.22 | SIMP: (341) implies: % 129.98/18.22 | (342) ~ (all_52_4 = all_10_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (151), (333) imply: % 129.98/18.22 | (343) ~ (all_52_8 = all_10_2) % 129.98/18.22 | % 129.98/18.22 | SIMP: (343) implies: % 129.98/18.22 | (344) ~ (all_52_8 = all_10_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (150), (333) imply: % 129.98/18.22 | (345) ~ (all_52_12 = all_10_2) % 129.98/18.22 | % 129.98/18.22 | SIMP: (345) implies: % 129.98/18.22 | (346) ~ (all_52_12 = all_10_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (147), (282) imply: % 129.98/18.22 | (347) ~ (all_52_1 = all_8_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (142), (253) imply: % 129.98/18.22 | (348) ~ (all_52_2 = all_6_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (138), (287) imply: % 129.98/18.22 | (349) ~ (all_52_3 = all_4_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (137), (282) imply: % 129.98/18.22 | (350) ~ (all_52_4 = all_8_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (132), (282) imply: % 129.98/18.22 | (351) ~ (all_52_6 = all_8_2) % 129.98/18.22 | % 129.98/18.22 | SIMP: (351) implies: % 129.98/18.22 | (352) ~ (all_52_6 = all_8_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (131), (282) imply: % 129.98/18.22 | (353) ~ (all_52_7 = all_8_2) % 129.98/18.22 | % 129.98/18.22 | SIMP: (353) implies: % 129.98/18.22 | (354) ~ (all_52_7 = all_8_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (130), (282) imply: % 129.98/18.22 | (355) ~ (all_52_9 = all_8_2) % 129.98/18.22 | % 129.98/18.22 | SIMP: (355) implies: % 129.98/18.22 | (356) ~ (all_52_9 = all_8_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (129), (282) imply: % 129.98/18.22 | (357) ~ (all_52_13 = all_8_2) % 129.98/18.22 | % 129.98/18.22 | SIMP: (357) implies: % 129.98/18.22 | (358) ~ (all_52_13 = all_8_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (127), (253) imply: % 129.98/18.22 | (359) ~ (all_52_6 = all_6_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (124), (287) imply: % 129.98/18.22 | (360) ~ (all_52_7 = all_4_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (122), (253) imply: % 129.98/18.22 | (361) ~ (all_52_8 = all_6_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (119), (253) imply: % 129.98/18.22 | (362) ~ (all_52_9 = all_6_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (116), (253) imply: % 129.98/18.22 | (363) ~ (all_52_11 = all_6_2) % 129.98/18.22 | % 129.98/18.22 | SIMP: (363) implies: % 129.98/18.22 | (364) ~ (all_52_11 = all_6_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (115), (253) imply: % 129.98/18.22 | (365) ~ (all_52_14 = all_6_2) % 129.98/18.22 | % 129.98/18.22 | SIMP: (365) implies: % 129.98/18.22 | (366) ~ (all_52_14 = all_6_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (114), (287) imply: % 129.98/18.22 | (367) ~ (all_52_11 = all_4_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (111), (287) imply: % 129.98/18.22 | (368) ~ (all_52_12 = all_4_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (109), (287) imply: % 129.98/18.22 | (369) ~ (all_52_13 = all_4_2) % 129.98/18.22 | % 129.98/18.22 | REDUCE: (108), (287) imply: % 129.98/18.22 | (370) ~ (all_52_14 = all_4_2) % 129.98/18.22 | % 129.98/18.22 | BETA: splitting (37) gives: % 129.98/18.22 | % 129.98/18.22 | Case 1: % 129.98/18.22 | | % 129.98/18.22 | | (371) ~ (all_4_2 = e1) % 129.98/18.22 | | % 129.98/18.22 | | BETA: splitting (40) gives: % 129.98/18.22 | | % 129.98/18.22 | | Case 1: % 129.98/18.22 | | | % 129.98/18.22 | | | (372) ~ (all_6_2 = e2) % 129.98/18.22 | | | % 129.98/18.22 | | | BETA: splitting (43) gives: % 129.98/18.22 | | | % 129.98/18.22 | | | Case 1: % 129.98/18.22 | | | | % 129.98/18.22 | | | | (373) ~ (all_8_2 = e1) % 129.98/18.22 | | | | % 129.98/18.22 | | | | BETA: splitting (46) gives: % 129.98/18.22 | | | | % 129.98/18.22 | | | | Case 1: % 129.98/18.22 | | | | | % 129.98/18.22 | | | | | (374) ~ (all_10_2 = e0) % 129.98/18.22 | | | | | % 129.98/18.22 | | | | | BETA: splitting (52) gives: % 129.98/18.22 | | | | | % 129.98/18.22 | | | | | Case 1: % 129.98/18.22 | | | | | | % 129.98/18.22 | | | | | | (375) ~ (all_14_2 = e3) % 129.98/18.22 | | | | | | % 129.98/18.22 | | | | | | REDUCE: (329), (375) imply: % 129.98/18.22 | | | | | | (376) ~ (all_8_2 = e3) % 129.98/18.22 | | | | | | % 129.98/18.22 | | | | | | BETA: splitting (55) gives: % 129.98/18.22 | | | | | | % 129.98/18.22 | | | | | | Case 1: % 129.98/18.22 | | | | | | | % 129.98/18.22 | | | | | | | (377) ~ (all_16_2 = e2) % 129.98/18.22 | | | | | | | % 129.98/18.22 | | | | | | | REDUCE: (327), (377) imply: % 129.98/18.22 | | | | | | | (378) ~ (all_10_2 = e2) % 129.98/18.22 | | | | | | | % 129.98/18.22 | | | | | | | BETA: splitting (61) gives: % 129.98/18.22 | | | | | | | % 129.98/18.22 | | | | | | | Case 1: % 129.98/18.22 | | | | | | | | % 129.98/18.22 | | | | | | | | (379) ~ (all_20_2 = e2) % 129.98/18.22 | | | | | | | | % 129.98/18.22 | | | | | | | | REDUCE: (318), (379) imply: % 129.98/18.22 | | | | | | | | (380) ~ (all_4_2 = e2) % 129.98/18.22 | | | | | | | | % 129.98/18.22 | | | | | | | | BETA: splitting (73) gives: % 129.98/18.22 | | | | | | | | % 129.98/18.22 | | | | | | | | Case 1: % 129.98/18.22 | | | | | | | | | % 129.98/18.22 | | | | | | | | | (381) ~ (all_28_2 = e3) % 129.98/18.22 | | | | | | | | | % 129.98/18.22 | | | | | | | | | REDUCE: (316), (381) imply: % 129.98/18.22 | | | | | | | | | (382) ~ (all_6_2 = e3) % 129.98/18.22 | | | | | | | | | % 129.98/18.22 | | | | | | | | | BETA: splitting (76) gives: % 129.98/18.22 | | | | | | | | | % 129.98/18.22 | | | | | | | | | Case 1: % 129.98/18.22 | | | | | | | | | | % 129.98/18.22 | | | | | | | | | | (383) ~ (all_30_2 = e0) % 129.98/18.22 | | | | | | | | | | % 129.98/18.22 | | | | | | | | | | REDUCE: (309), (383) imply: % 129.98/18.22 | | | | | | | | | | (384) ~ (all_8_2 = e0) % 129.98/18.22 | | | | | | | | | | % 129.98/18.22 | | | | | | | | | | BETA: splitting (199) gives: % 129.98/18.22 | | | | | | | | | | % 129.98/18.22 | | | | | | | | | | Case 1: % 129.98/18.22 | | | | | | | | | | | % 129.98/18.22 | | | | | | | | | | | (385) all_54_5 = e3 % 129.98/18.22 | | | | | | | | | | | % 129.98/18.22 | | | | | | | | | | | COMBINE_EQS: (267), (385) imply: % 129.98/18.22 | | | | | | | | | | | (386) all_8_2 = e3 % 129.98/18.22 | | | | | | | | | | | % 129.98/18.22 | | | | | | | | | | | REDUCE: (376), (386) imply: % 129.98/18.22 | | | | | | | | | | | (387) $false % 129.98/18.23 | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | CLOSE: (387) is inconsistent. % 129.98/18.23 | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | Case 2: % 129.98/18.23 | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | (388) ~ (all_54_5 = e3) % 129.98/18.23 | | | | | | | | | | | (389) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 129.98/18.23 | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | BETA: splitting (389) gives: % 129.98/18.23 | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | Case 1: % 129.98/18.23 | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | (390) all_54_5 = e2 % 129.98/18.23 | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | COMBINE_EQS: (267), (390) imply: % 129.98/18.23 | | | | | | | | | | | | (391) all_8_2 = e2 % 129.98/18.23 | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | REDUCE: (347), (391) imply: % 129.98/18.23 | | | | | | | | | | | | (392) ~ (all_52_1 = e2) % 129.98/18.23 | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | REDUCE: (350), (391) imply: % 129.98/18.23 | | | | | | | | | | | | (393) ~ (all_52_4 = e2) % 129.98/18.23 | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | REDUCE: (356), (391) imply: % 129.98/18.23 | | | | | | | | | | | | (394) ~ (all_52_9 = e2) % 129.98/18.23 | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | REDUCE: (358), (391) imply: % 129.98/18.23 | | | | | | | | | | | | (395) ~ (all_52_13 = e2) % 129.98/18.23 | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | REDUCE: (376), (391) imply: % 129.98/18.23 | | | | | | | | | | | | (396) ~ (e3 = e2) % 129.98/18.23 | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | BETA: splitting (225) gives: % 129.98/18.23 | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | Case 1: % 129.98/18.23 | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | (397) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 129.98/18.23 | | | | | | | | | | | | | & op(e2, e2) = e2) % 129.98/18.23 | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | BETA: splitting (397) gives: % 129.98/18.23 | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | Case 1: % 129.98/18.23 | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | (398) all_57_2 = e2 & op(e2, e3) = e2 % 129.98/18.23 | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | ALPHA: (398) implies: % 129.98/18.23 | | | | | | | | | | | | | | (399) op(e2, e3) = e2 % 129.98/18.23 | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | REF_CLOSE: (167), (392), (399), (function-axioms) are % 129.98/18.23 | | | | | | | | | | | | | | inconsistent by sub-proof #779. % 129.98/18.23 | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | Case 2: % 129.98/18.23 | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | (400) all_57_3 = e2 & op(e2, e2) = e2 % 129.98/18.23 | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | ALPHA: (400) implies: % 129.98/18.23 | | | | | | | | | | | | | | (401) all_57_3 = e2 % 129.98/18.23 | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | BETA: splitting (79) gives: % 129.98/18.23 | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | Case 1: % 129.98/18.23 | | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | | (402) ~ (all_32_2 = e1) % 129.98/18.23 | | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | | REDUCE: (312), (402) imply: % 129.98/18.23 | | | | | | | | | | | | | | | (403) ~ (all_10_2 = e1) % 129.98/18.23 | | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 129.98/18.23 | | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | | Case 1: % 129.98/18.23 | | | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | | | (404) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 129.98/18.23 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 129.98/18.23 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 129.98/18.23 | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 129.98/18.23 | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 129.98/18.23 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 129.98/18.23 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 129.98/18.23 | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 129.98/18.23 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 129.98/18.23 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 129.98/18.23 | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 129.98/18.23 | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 129.98/18.23 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 129.98/18.23 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 129.98/18.23 | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 129.98/18.23 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 129.98/18.23 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 129.98/18.23 | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 129.98/18.23 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 129.98/18.23 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 129.98/18.23 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 129.98/18.23 | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 129.98/18.23 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 129.98/18.23 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.23 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 129.98/18.23 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 129.98/18.23 | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 129.98/18.23 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 129.98/18.23 | | | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | | | BETA: splitting (404) gives: % 129.98/18.23 | | | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | | | Case 1: % 129.98/18.23 | | | | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | | | | (405) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 129.98/18.23 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 129.98/18.23 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 129.98/18.23 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 129.98/18.23 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 129.98/18.23 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 129.98/18.23 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 129.98/18.23 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 129.98/18.23 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 129.98/18.23 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 129.98/18.23 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 129.98/18.23 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 129.98/18.23 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 129.98/18.23 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 129.98/18.23 | | | | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | | | | BETA: splitting (405) gives: % 129.98/18.23 | | | | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.23 | | | | | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | | | | | (406) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 129.98/18.23 | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 129.98/18.23 | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 129.98/18.23 | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 129.98/18.23 | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 129.98/18.23 | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 129.98/18.23 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 129.98/18.23 | | | | | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | | | | | ALPHA: (406) implies: % 129.98/18.23 | | | | | | | | | | | | | | | | | | (407) op(e3, e3) = e2 % 129.98/18.23 | | | | | | | | | | | | | | | | | | % 129.98/18.23 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (204), (278), (374), (378), (403), (407), % 129.98/18.23 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.23 | | | | | | | | | | | | | | | | | | #776. % 129.98/18.23 | | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.24 | | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | | | (408) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 129.98/18.24 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 129.98/18.24 | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 129.98/18.24 | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 129.98/18.24 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 129.98/18.24 | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 129.98/18.24 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 129.98/18.24 | | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | | | ALPHA: (408) implies: % 129.98/18.24 | | | | | | | | | | | | | | | | | | (409) op(e3, e3) = e1 % 129.98/18.24 | | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (204), (278), (374), (378), (403), (409), % 129.98/18.24 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.24 | | | | | | | | | | | | | | | | | | #774. % 129.98/18.24 | | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | | End of split % 129.98/18.24 | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | Case 2: % 129.98/18.24 | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | | (410) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 129.98/18.24 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 129.98/18.24 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 129.98/18.24 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 129.98/18.24 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 129.98/18.24 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 129.98/18.24 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 129.98/18.24 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 129.98/18.24 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 129.98/18.24 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.24 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 129.98/18.24 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 129.98/18.24 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 129.98/18.24 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 129.98/18.24 | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | | BETA: splitting (410) gives: % 129.98/18.24 | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.24 | | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | | | (411) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 129.98/18.24 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 129.98/18.24 | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 129.98/18.24 | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 129.98/18.24 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 129.98/18.24 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 129.98/18.24 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 129.98/18.24 | | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | | | ALPHA: (411) implies: % 129.98/18.24 | | | | | | | | | | | | | | | | | | (412) op(e3, e3) = e0 % 129.98/18.24 | | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (204), (278), (374), (378), (403), (412), % 129.98/18.24 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.24 | | | | | | | | | | | | | | | | | | #772. % 129.98/18.24 | | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.24 | | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | | | (413) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 129.98/18.24 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 129.98/18.24 | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.24 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 129.98/18.24 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 129.98/18.24 | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 129.98/18.24 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 129.98/18.24 | | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | | | ALPHA: (413) implies: % 129.98/18.24 | | | | | | | | | | | | | | | | | | (414) op(e2, e3) = e2 % 129.98/18.24 | | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (392), (414), (function-axioms) are % 129.98/18.24 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #779. % 129.98/18.24 | | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | | End of split % 129.98/18.24 | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | End of split % 129.98/18.24 | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | Case 2: % 129.98/18.24 | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | (415) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 129.98/18.24 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 129.98/18.24 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.24 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 129.98/18.24 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 129.98/18.24 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 129.98/18.24 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 129.98/18.24 | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 129.98/18.24 | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 129.98/18.24 | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 129.98/18.24 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 129.98/18.24 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 129.98/18.24 | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 129.98/18.24 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 129.98/18.24 | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 129.98/18.24 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 129.98/18.24 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 129.98/18.24 | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 129.98/18.24 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 129.98/18.24 | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 129.98/18.24 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 129.98/18.24 | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 129.98/18.24 | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 129.98/18.24 | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 129.98/18.24 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 129.98/18.24 | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 129.98/18.24 | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 129.98/18.24 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 129.98/18.24 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 129.98/18.24 | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 129.98/18.24 | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 129.98/18.24 | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.24 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 129.98/18.24 | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 129.98/18.24 | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 129.98/18.24 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 129.98/18.24 | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 129.98/18.24 | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 129.98/18.24 | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 129.98/18.24 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 129.98/18.24 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 129.98/18.24 | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 129.98/18.24 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 129.98/18.24 | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 129.98/18.24 | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 129.98/18.24 | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 129.98/18.24 | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 129.98/18.24 | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 129.98/18.24 | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 129.98/18.24 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 129.98/18.24 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 129.98/18.24 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 129.98/18.24 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 129.98/18.24 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 129.98/18.24 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 129.98/18.24 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 129.98/18.24 | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 129.98/18.24 | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | BETA: splitting (415) gives: % 129.98/18.24 | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | Case 1: % 129.98/18.24 | | | | | | | | | | | | | | | | | % 129.98/18.24 | | | | | | | | | | | | | | | | | (416) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 129.98/18.24 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 129.98/18.24 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.24 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 129.98/18.24 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 129.98/18.24 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 129.98/18.24 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 129.98/18.24 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 129.98/18.24 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 129.98/18.24 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 129.98/18.24 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 129.98/18.25 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 129.98/18.25 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 129.98/18.25 | | | | | | | | | | | | | | | | | % 129.98/18.25 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (165), (382), (394), (416), % 129.98/18.25 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.25 | | | | | | | | | | | | | | | | | #769. % 129.98/18.25 | | | | | | | | | | | | | | | | | % 129.98/18.25 | | | | | | | | | | | | | | | | Case 2: % 129.98/18.25 | | | | | | | | | | | | | | | | | % 129.98/18.25 | | | | | | | | | | | | | | | | | (417) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 129.98/18.25 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 129.98/18.25 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 129.98/18.25 | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 129.98/18.25 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 129.98/18.25 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 129.98/18.25 | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 129.98/18.25 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 129.98/18.25 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 129.98/18.25 | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 129.98/18.25 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 129.98/18.25 | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 129.98/18.25 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 129.98/18.25 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 129.98/18.25 | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 129.98/18.25 | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 129.98/18.25 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 129.98/18.25 | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 129.98/18.25 | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 129.98/18.25 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 129.98/18.25 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 129.98/18.25 | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 129.98/18.25 | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 129.98/18.25 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 129.98/18.25 | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 129.98/18.25 | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 129.98/18.25 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 129.98/18.25 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 129.98/18.25 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 129.98/18.25 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 129.98/18.25 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 129.98/18.25 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 129.98/18.25 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 129.98/18.25 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 129.98/18.25 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 129.98/18.25 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 129.98/18.25 | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 129.98/18.25 | | | | | | | | | | | | | | | | | % 129.98/18.25 | | | | | | | | | | | | | | | | | BETA: splitting (417) gives: % 129.98/18.25 | | | | | | | | | | | | | | | | | % 129.98/18.25 | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.25 | | | | | | | | | | | | | | | | | | % 129.98/18.25 | | | | | | | | | | | | | | | | | | (418) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 129.98/18.25 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 129.98/18.25 | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 129.98/18.25 | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 129.98/18.25 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 129.98/18.25 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 129.98/18.25 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 129.98/18.25 | | | | | | | | | | | | | | | | | | % 129.98/18.25 | | | | | | | | | | | | | | | | | | ALPHA: (418) implies: % 129.98/18.25 | | | | | | | | | | | | | | | | | | (419) op(e2, e0) = e2 % 129.98/18.25 | | | | | | | | | | | | | | | | | | % 129.98/18.25 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (395), (419), (function-axioms) are % 129.98/18.25 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 129.98/18.25 | | | | | | | | | | | | | | | | | | % 129.98/18.25 | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.25 | | | | | | | | | | | | | | | | | | % 129.98/18.25 | | | | | | | | | | | | | | | | | | (420) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 129.98/18.25 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 129.98/18.25 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 129.98/18.25 | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 129.98/18.25 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 129.98/18.25 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 129.98/18.25 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 129.98/18.25 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 129.98/18.25 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 129.98/18.25 | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 129.98/18.25 | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 129.98/18.25 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 129.98/18.25 | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 129.98/18.25 | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 129.98/18.25 | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 129.98/18.25 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 129.98/18.25 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 129.98/18.25 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 129.98/18.25 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 129.98/18.25 | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 129.98/18.25 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 129.98/18.25 | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 129.98/18.25 | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 129.98/18.25 | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 129.98/18.25 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 129.98/18.25 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 129.98/18.25 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 129.98/18.25 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 129.98/18.25 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 129.98/18.25 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 129.98/18.25 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 129.98/18.25 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 129.98/18.25 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 129.98/18.25 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 129.98/18.25 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 129.98/18.25 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 129.98/18.25 | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 129.98/18.25 | | | | | | | | | | | | | | | | | | % 129.98/18.25 | | | | | | | | | | | | | | | | | | BETA: splitting (420) gives: % 129.98/18.25 | | | | | | | | | | | | | | | | | | % 129.98/18.25 | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.25 | | | | | | | | | | | | | | | | | | | % 129.98/18.25 | | | | | | | | | | | | | | | | | | | (421) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 129.98/18.25 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 129.98/18.25 | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 129.98/18.25 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 129.98/18.25 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 129.98/18.25 | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 129.98/18.25 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 129.98/18.25 | | | | | | | | | | | | | | | | | | | % 129.98/18.25 | | | | | | | | | | | | | | | | | | | ALPHA: (421) implies: % 129.98/18.25 | | | | | | | | | | | | | | | | | | | (422) op(e1, e1) = e2 % 129.98/18.25 | | | | | | | | | | | | | | | | | | | % 129.98/18.25 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (422), (function-axioms) are % 129.98/18.25 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 129.98/18.25 | | | | | | | | | | | | | | | | | | | % 129.98/18.25 | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.25 | | | | | | | | | | | | | | | | | | | % 129.98/18.25 | | | | | | | | | | | | | | | | | | | (423) op(e0, e0) = all_56_31 & $i(all_56_31) & % 129.98/18.25 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 129.98/18.25 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 129.98/18.25 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 129.98/18.25 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 129.98/18.25 | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 129.98/18.25 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 129.98/18.25 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 129.98/18.25 | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 129.98/18.26 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 129.98/18.26 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 129.98/18.26 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 129.98/18.26 | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 129.98/18.26 | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | ALPHA: (423) implies: % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (424) op(e0, e0) = all_56_31 % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (425) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 129.98/18.26 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 129.98/18.26 | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 129.98/18.26 | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 129.98/18.26 | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 129.98/18.26 | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 129.98/18.26 | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (39), (45), (100), (118), (157), (160), % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (163), (164), (165), (167), (189), (190), (204), % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (218), (226), (245), (246), (278), (295), (336), % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (338), (364), (369), (370), (371), (374), (378), % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (380), (401), (403), (424), (425), % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.26 | | | | | | | | | | | | | | | | | | | #744. % 129.98/18.26 | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | End of split % 129.98/18.26 | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | End of split % 129.98/18.26 | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | End of split % 129.98/18.26 | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | End of split % 129.98/18.26 | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | Case 2: % 129.98/18.26 | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | (426) all_32_2 = e1 % 129.98/18.26 | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | COMBINE_EQS: (312), (426) imply: % 129.98/18.26 | | | | | | | | | | | | | | | (427) all_10_2 = e1 % 129.98/18.26 | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | SIMP: (427) implies: % 129.98/18.26 | | | | | | | | | | | | | | | (428) all_10_2 = e1 % 129.98/18.26 | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | COMBINE_EQS: (280), (428) imply: % 129.98/18.26 | | | | | | | | | | | | | | | (429) all_50_2 = e1 % 129.98/18.26 | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | REDUCE: (336), (428) imply: % 129.98/18.26 | | | | | | | | | | | | | | | (430) ~ (all_52_1 = e1) % 129.98/18.26 | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | REDUCE: (338), (428) imply: % 129.98/18.26 | | | | | | | | | | | | | | | (431) ~ (all_52_2 = e1) % 129.98/18.26 | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | REDUCE: (342), (428) imply: % 129.98/18.26 | | | | | | | | | | | | | | | (432) ~ (all_52_4 = e1) % 129.98/18.26 | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | REDUCE: (344), (428) imply: % 129.98/18.26 | | | | | | | | | | | | | | | (433) ~ (all_52_8 = e1) % 129.98/18.26 | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | REDUCE: (346), (428) imply: % 129.98/18.26 | | | | | | | | | | | | | | | (434) ~ (all_52_12 = e1) % 129.98/18.26 | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | REDUCE: (378), (428) imply: % 129.98/18.26 | | | | | | | | | | | | | | | (435) ~ (e2 = e1) % 129.98/18.26 | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | REDUCE: (45), (428) imply: % 129.98/18.26 | | | | | | | | | | | | | | | (436) op(e3, e3) = e1 % 129.98/18.26 | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 129.98/18.26 | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | Case 1: % 129.98/18.26 | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | (437) ~ (all_34_2 = e3) % 129.98/18.26 | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | REDUCE: (307), (437) imply: % 129.98/18.26 | | | | | | | | | | | | | | | | (438) ~ (all_4_2 = e3) % 129.98/18.26 | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 129.98/18.26 | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | Case 1: % 129.98/18.26 | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | (439) all_54_15 = e3 % 129.98/18.26 | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (439) imply: % 129.98/18.26 | | | | | | | | | | | | | | | | | (440) all_4_2 = e3 % 129.98/18.26 | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | REDUCE: (438), (440) imply: % 129.98/18.26 | | | | | | | | | | | | | | | | | (441) $false % 129.98/18.26 | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | CLOSE: (441) is inconsistent. % 129.98/18.26 | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | Case 2: % 129.98/18.26 | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | (442) ~ (all_54_15 = e3) % 129.98/18.26 | | | | | | | | | | | | | | | | | (443) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 129.98/18.26 | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | BETA: splitting (443) gives: % 129.98/18.26 | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.26 | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | (444) all_54_15 = e2 % 129.98/18.26 | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (444) imply: % 129.98/18.26 | | | | | | | | | | | | | | | | | | (445) all_4_2 = e2 % 129.98/18.26 | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | REDUCE: (380), (445) imply: % 129.98/18.26 | | | | | | | | | | | | | | | | | | (446) $false % 129.98/18.26 | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | CLOSE: (446) is inconsistent. % 129.98/18.26 | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.26 | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | (447) ~ (all_54_15 = e2) % 129.98/18.26 | | | | | | | | | | | | | | | | | | (448) all_54_15 = e1 | all_54_15 = e0 % 129.98/18.26 | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | BETA: splitting (448) gives: % 129.98/18.26 | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.26 | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (449) all_54_15 = e1 % 129.98/18.26 | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (449) imply: % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (450) all_4_2 = e1 % 129.98/18.26 | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | REDUCE: (371), (450) imply: % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (451) $false % 129.98/18.26 | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | CLOSE: (451) is inconsistent. % 129.98/18.26 | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.26 | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (452) all_54_15 = e0 % 129.98/18.26 | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (452) imply: % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (453) all_4_2 = e0 % 129.98/18.26 | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | REDUCE: (438), (453) imply: % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (454) ~ (e3 = e0) % 129.98/18.26 | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | REDUCE: (380), (453) imply: % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (455) ~ (e2 = e0) % 129.98/18.26 | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | REDUCE: (371), (453) imply: % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (456) ~ (e1 = e0) % 129.98/18.26 | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | REDUCE: (36), (453) imply: % 129.98/18.26 | | | | | | | | | | | | | | | | | | | (457) op(e0, e0) = e0 % 129.98/18.26 | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 129.98/18.26 | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | (458) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | BETA: splitting (458) gives: % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.26 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | (459) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (459) gives: % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (460) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (460) implies: % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (461) op(e3, e3) = e2 % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (436), (461), (function-axioms) are % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743. % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (462) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (462) implies: % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (463) ~ (all_56_21 = e1) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (464) ~ (all_56_5 = e3) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (465) op(e1, e1) = all_56_21 % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (466) op(e1, e3) = all_56_5 % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (467) op(e3, e1) = e3 % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | all_56_21, e1, e1, simplifying with (39), (465) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | gives: % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (468) all_56_21 = all_6_2 % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | all_56_5, e3, e1, simplifying with (163), (466) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | gives: % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (469) all_56_5 = all_52_2 % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3, % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (467) gives: % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (470) all_52_8 = e3 % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (463), (468) imply: % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (471) ~ (all_6_2 = e1) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (470) imply: % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (472) ~ (all_52_4 = e3) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (470) imply: % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (473) ~ (all_52_12 = e3) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | SIMP: (473) implies: % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (474) ~ (all_52_12 = e3) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (470) imply: % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (475) ~ (all_6_2 = e3) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (39), (106), (163), (168), (170), % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (194), (203), (216), (217), (218), (228), (230), % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (238), (271), (334), (372), (382), (393), (401), % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (429), (431), (432), (436), (464), (466), (471), % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | (472), (474), (function-axioms) are inconsistent % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #718. % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | (476) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (392), (436), (476), (function-axioms) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #716. % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (477) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (164), (165), (372), (382), % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | (394), (395), (457), (477), (function-axioms) are % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #708. % 129.98/18.27 | | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.27 | | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | | End of split % 129.98/18.27 | | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | | End of split % 129.98/18.27 | | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | | End of split % 129.98/18.27 | | | | | | | | | | | | | | | | % 129.98/18.27 | | | | | | | | | | | | | | | Case 2: % 129.98/18.27 | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | (478) all_34_2 = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | (479) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & % 129.98/18.28 | | | | | | | | | | | | | | | | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3) % 129.98/18.28 | | | | | | | | | | | | | | | | = all_34_1 & $i(all_34_1)) % 129.98/18.28 | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (478) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | (480) all_4_2 = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | SIMP: (480) implies: % 129.98/18.28 | | | | | | | | | | | | | | | | (481) all_4_2 = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | REDUCE: (349), (481) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | (482) ~ (all_52_3 = e3) % 129.98/18.28 | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | REDUCE: (367), (481) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | (483) ~ (all_52_11 = e3) % 129.98/18.28 | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | REDUCE: (368), (481) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | (484) ~ (all_52_12 = e3) % 129.98/18.28 | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | REDUCE: (369), (481) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | (485) ~ (all_52_13 = e3) % 129.98/18.28 | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | REDUCE: (370), (481) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | (486) ~ (all_52_14 = e3) % 129.98/18.28 | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | REDUCE: (36), (481) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | (487) op(e0, e0) = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | BETA: splitting (479) gives: % 129.98/18.28 | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | Case 1: % 129.98/18.28 | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | (488) ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & % 129.98/18.28 | | | | | | | | | | | | | | | | | $i(all_34_0) % 129.98/18.28 | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | ALPHA: (488) implies: % 129.98/18.28 | | | | | | | | | | | | | | | | | (489) ~ (all_34_0 = e2) % 129.98/18.28 | | | | | | | | | | | | | | | | | (490) op(e3, e0) = all_34_0 % 129.98/18.28 | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 129.98/18.28 | | | | | | | | | | | | | | | | | all_34_0, e0, e3, simplifying with (168), (490) % 129.98/18.28 | | | | | | | | | | | | | | | | | gives: % 129.98/18.28 | | | | | | | | | | | | | | | | | (491) all_52_12 = all_34_0 % 129.98/18.28 | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (491) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | (492) all_54_3 = all_34_0 % 129.98/18.28 | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | REDUCE: (133), (491) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | (493) ~ (all_52_4 = all_34_0) % 129.98/18.28 | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | REDUCE: (113), (491) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | (494) ~ (all_52_13 = all_34_0) % 129.98/18.28 | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | SIMP: (494) implies: % 129.98/18.28 | | | | | | | | | | | | | | | | | (495) ~ (all_52_13 = all_34_0) % 129.98/18.28 | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | REDUCE: (484), (491) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | (496) ~ (all_34_0 = e3) % 129.98/18.28 | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | REDUCE: (434), (491) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | (497) ~ (all_34_0 = e1) % 129.98/18.28 | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 129.98/18.28 | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.28 | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | (498) all_54_3 = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (492), (498) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | | (499) all_34_0 = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | REDUCE: (496), (499) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | | (500) $false % 129.98/18.28 | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | CLOSE: (500) is inconsistent. % 129.98/18.28 | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.28 | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | (501) ~ (all_54_3 = e3) % 129.98/18.28 | | | | | | | | | | | | | | | | | | (502) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 129.98/18.28 | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 129.98/18.28 | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | (503) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 129.98/18.28 | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 129.98/18.28 | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | BETA: splitting (503) gives: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | (504) all_57_9 = e2 & op(e3, e0) = e2 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | ALPHA: (504) implies: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | (505) all_57_9 = e2 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | BETA: splitting (502) gives: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | (506) all_54_3 = e2 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (489), (492), (506) are inconsistent by sub-proof % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | #707. % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | (507) ~ (all_54_3 = e2) % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | (508) all_54_3 = e1 | all_54_3 = e0 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (508) gives: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | (509) all_54_3 = e1 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (492), (497), (509) are inconsistent by sub-proof % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | #706. % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | (510) all_54_3 = e0 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (492), (510) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | (511) all_34_0 = e0 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | SIMP: (511) implies: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | (512) all_34_0 = e0 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (493), (512) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | (513) ~ (all_52_4 = e0) % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (495), (512) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | (514) ~ (all_52_13 = e0) % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (489), (512) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | (515) ~ (e2 = e0) % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (497), (512) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | (516) ~ (e1 = e0) % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | (517) all_54_1 = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (517) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | (518) all_52_4 = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (518) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | (519) ~ (all_52_6 = e3) % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (519) implies: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | (520) ~ (all_52_6 = e3) % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (518) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | (521) ~ (all_52_8 = e3) % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (521) implies: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | (522) ~ (all_52_8 = e3) % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | (523) all_54_7 = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (523) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | (524) all_52_13 = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (485), (524) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | (525) $false % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (525) is inconsistent. % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | (526) ~ (all_54_7 = e3) % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | (527) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | (528) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (528) gives: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (529) all_57_0 = e3 & op(e3, e3) = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (529) implies: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (530) op(e3, e3) = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (436), (530), (function-axioms) are % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #775. % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (531) all_57_1 = e3 & op(e3, e2) = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (531) implies: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (532) all_57_1 = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (533) gives: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) all_57_4 = e3 & op(e3, e1) = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (534) implies: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) op(e3, e1) = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (522), (535), (function-axioms) are % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #705. % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) all_57_5 = e3 & op(e2, e1) = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (536) implies: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) all_57_5 = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (538) gives: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) all_57_6 = e3 & op(e1, e3) = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (539) implies: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) all_57_6 = e3 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (527) gives: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) all_54_7 = e2 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (541) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) all_52_13 = e2 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (395), (542) imply: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) $false % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (543) is inconsistent. % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) ~ (all_54_7 = e2) % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) all_54_7 = e1 | all_54_7 = e0 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (546) gives: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) all_57_6 = e2 & op(e1, e3) = e2 % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (134), (168), (169), (203), (238), % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271), (393), (432), (436), (484), (489), (492), % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493), (497), (502), (532), (540), (547), % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #697. % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) all_57_7 = e2 & op(e1, e2) = e2 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (548) implies: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) all_57_7 = e2 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) all_57_15 = e0 & op(e0, e0) = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (550) implies: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) op(e0, e0) = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (487), (551), (function-axioms) are % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #715. % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (552) implies: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0) % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (554) gives: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) all_57_9 = e0 & op(e3, e0) = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (555) implies: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) all_57_9 = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (505), (556) are inconsistent by sub-proof % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #696. % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (557) gives: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) all_57_10 = e0 & op(e2, e0) = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (558) implies: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) op(e2, e0) = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (259), (514), (545), (559), % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #694. % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) all_57_11 = e0 & op(e1, e0) = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (560) implies: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) all_57_11 = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1) % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (562) gives: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563) all_57_6 = e1 & op(e1, e3) = e1 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (563) implies: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (564) op(e1, e3) = e1 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (431), (564), (function-axioms) are % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #725. % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) all_57_7 = e1 & op(e1, e2) = e1 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236), % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (436), (505), (513), (549), (565), % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #685. % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (566) gives: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) all_57_8 = e1 & op(e1, e1) = e1 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (567) implies: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) op(e1, e1) = e1 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (569) gives: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (570) all_57_2 = e0 & op(e2, e3) = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (570) implies: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (571) all_57_2 = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (572) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (572) gives: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) all_57_1 = e1 & op(e3, e2) = e1 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (432), (573), (function-axioms) are % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #684. % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (574) all_57_3 = e1 & op(e2, e2) = e1 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (574) implies: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (575) all_57_3 = e1 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (575) imply: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (576) e2 = e1 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (505), (576) imply: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (577) all_57_9 = e1 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236), % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (436), (513), (577), (function-axioms) are % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #686. % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (578) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (578) gives: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (579) all_57_7 = e1 & op(e1, e2) = e1 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236), % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (436), (505), (513), (549), (579), % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #685. % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) all_57_13 = e1 & op(e0, e2) = e1 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (580) implies: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) all_57_13 = e1 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2) % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (392), (436), (582), (function-axioms) % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #683. % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (583) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (583) gives: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (584) all_57_6 = e2 & op(e1, e3) = e2 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (134), (168), (169), (203), (238), % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271), (393), (432), (436), (484), (489), (492), % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493), (497), (502), (532), (540), (584), % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #697. % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (585) all_57_12 = e2 & op(e0, e3) = e2 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (585) implies: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586) all_57_12 = e2 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (553) gives: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587) all_57_12 = e0 & op(e0, e3) = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (587) implies: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (588) all_57_12 = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (586), (588) are inconsistent by sub-proof % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #682. % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (589) gives: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (590) all_57_13 = e0 & op(e0, e2) = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (590) implies: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (591) all_57_13 = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (581), (591) are inconsistent by sub-proof % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #681. % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (592) all_57_14 = e0 & op(e0, e1) = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (592) implies: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (593) all_57_14 = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (594) op(e0, e1) = e0 % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (595) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (595) gives: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (596) all_57_4 = e2 & op(e3, e1) = e2 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (596) implies: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (597) all_57_4 = e2 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (598) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (598) gives: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (599) all_57_1 = e0 & op(e3, e2) = e0 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (513), (599), (function-axioms) are % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #693. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (600) all_57_3 = e0 & op(e2, e2) = e0 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (600) implies: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601) all_57_3 = e0 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602) op(e2, e2) = e0 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (170), (224), % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (232), (236), (238), (430), (436), (513), % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537), (571), (597), (601), (602), % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #665. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (603) gives: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (604) all_57_7 = e0 & op(e1, e2) = e0 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (549), (604) are inconsistent by sub-proof % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #664. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605) all_57_13 = e0 & op(e0, e2) = e0 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (605) implies: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (606) all_57_13 = e0 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (581), (606) are inconsistent by sub-proof % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #681. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (607) all_57_5 = e2 & op(e2, e1) = e2 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (607) implies: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (608) all_57_5 = e2 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (533) gives: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (609) all_57_4 = e3 & op(e3, e1) = e3 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (609) implies: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (610) op(e3, e1) = e3 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (522), (610), (function-axioms) are % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #705. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (536), (608) are inconsistent by sub-proof % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #663. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (611) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (611) gives: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (612) all_57_8 = e3 & op(e1, e1) = e3 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (612) implies: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (613) op(e1, e1) = e3 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (568), (613), (function-axioms) are % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) all_57_14 = e3 & op(e0, e1) = e3 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (593), (614) are inconsistent by sub-proof % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #661. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (615) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (39), (372), (594), (615), (function-axioms) % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #659. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) all_57_3 = e0 & op(e2, e2) = e0 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (616) implies: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) all_57_3 = e0 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (401), (617) are inconsistent by sub-proof % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #679. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (618) gives: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619) all_57_5 = e0 & op(e2, e1) = e0 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (537), (619) are inconsistent by sub-proof % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #658. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (620) all_57_10 = e0 & op(e2, e0) = e0 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (620) implies: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (621) op(e2, e0) = e0 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (259), (514), (545), (621), % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #694. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) all_57_11 = e1 & op(e1, e0) = e1 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (622) implies: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (623) all_57_11 = e1 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (561), (623) imply: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (624) e1 = e0 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (624) imply: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (625) $false % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (625) is inconsistent. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (626) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (626) gives: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627) all_57_8 = e2 & op(e1, e1) = e2 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (627) implies: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (628) op(e1, e1) = e2 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (628), (function-axioms) are % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629) all_57_11 = e2 & op(e1, e0) = e2 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (629) implies: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (630) all_57_11 = e2 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (164), (197), (208), (259), (395), % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485), (487), (489), (492), (495), (497), (502), % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505), (630), (function-axioms) are inconsistent % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #655. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (631) all_57_7 = e3 & op(e1, e2) = e3 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (631) implies: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632) op(e1, e2) = e3 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (520), (632), (function-axioms) are % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (633) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (382), (486), (633), % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #653. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (634) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (382), (483), (634), % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | #651. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | (635) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (484), (522), (635), % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | #650. % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.30 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | (636) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (393), (432), (513), (636) are inconsistent % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #701. % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | (637) all_57_10 = e2 & op(e2, e0) = e2 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (637) implies: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | (638) op(e2, e0) = e2 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (395), (638), (function-axioms) are % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.31 | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | (639) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 129.98/18.31 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 129.98/18.31 | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (639) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | (640) all_57_11 = e2 & op(e1, e0) = e2 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (640) implies: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | (641) all_57_11 = e2 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | (642) op(e1, e0) = e2 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | (643) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (643) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | (644) all_57_0 = e2 & op(e3, e3) = e2 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (644) implies: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | (645) op(e3, e3) = e2 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (436), (645), (function-axioms) are % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743. % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | (646) all_57_1 = e2 & op(e3, e2) = e2 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (646) implies: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | (647) all_57_1 = e2 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | (648) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (436), (647), (648), (function-axioms) % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #703. % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | (649) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (168), (169), (203), (271), (393), (432), % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | (484), (489), (492), (493), (497), (502), (649), % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | #698. % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | (650) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (650) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | (651) all_57_4 = e2 & op(e3, e1) = e2 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (651) implies: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | (652) all_57_4 = e2 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | (653) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (653) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | (654) all_57_0 = e3 & op(e3, e3) = e3 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (654) implies: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | (655) op(e3, e3) = e3 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (436), (655), (function-axioms) are % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #775. % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | (656) all_57_1 = e3 & op(e3, e2) = e3 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (656) implies: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | (657) all_57_1 = e3 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | (658) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (658) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (659) all_57_4 = e3 & op(e3, e1) = e3 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (169), (203), (271), (393), (432), (489), % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (492), (493), (497), (502), (659), % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | #699. % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (660) all_57_5 = e3 & op(e2, e1) = e3 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (660) implies: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (661) all_57_5 = e3 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (502) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) all_54_3 = e2 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (492), (662) imply: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) all_34_0 = e2 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (489), (663) imply: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) $false % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (664) is inconsistent. % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) ~ (all_54_3 = e2) % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) all_54_3 = e1 | all_54_3 = e0 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (667) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (436), (657), (667), (function-axioms) % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #648. % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (668) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (668) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (669) all_57_4 = e0 & op(e3, e1) = e0 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (652), (669) are inconsistent by sub-proof % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #647. % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (670) all_57_9 = e0 & op(e3, e0) = e0 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (670) implies: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671) all_57_9 = e0 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (672) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (672) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673) all_57_2 = e1 & op(e2, e3) = e1 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (430), (673), (function-axioms) are % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #676. % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (674) all_57_3 = e1 & op(e2, e2) = e1 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (674) implies: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (675) all_57_3 = e1 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (675) imply: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (676) e2 = e1 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (652), (676) imply: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (677) all_57_4 = e1 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (236), (238), (436), % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671), (677), (function-axioms) are inconsistent % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #668. % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (678) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (678) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (679) all_57_5 = e1 & op(e2, e1) = e1 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (661), (679) are inconsistent by sub-proof % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #673. % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (680) all_57_10 = e1 & op(e2, e0) = e1 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (680) implies: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (681) op(e2, e0) = e1 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (682) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (683) all_57_2 = e0 & op(e2, e3) = e0 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (683) implies: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (684) all_57_2 = e0 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (685) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (685) gives: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (686) all_57_0 = e3 & op(e3, e3) = e3 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (686) implies: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (687) op(e3, e3) = e3 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (436), (687), (function-axioms) are % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #775. % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (688) all_57_2 = e3 & op(e2, e3) = e3 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (688) implies: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (689) all_57_2 = e3 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (684), (689) imply: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (690) e3 = e0 % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (690) imply: % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (691) $false % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (691) is inconsistent. % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (692) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (692) gives: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (693) all_57_6 = e3 & op(e1, e3) = e3 % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (693) implies: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (694) all_57_6 = e3 % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (695) op(e1, e3) = e3 % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (696) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (392), (436), (696), (function-axioms) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #683. % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (697) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (697) gives: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (698) all_57_6 = e2 & op(e1, e3) = e2 % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (134), (168), (169), (203), (238), % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271), (393), (432), (436), (484), (489), (492), % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493), (497), (502), (657), (694), (698), % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #697. % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (699) all_57_12 = e2 & op(e0, e3) = e2 % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (699) implies: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (700) all_57_12 = e2 % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (666) gives: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (701) all_54_3 = e1 % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (492), (497), (701) are inconsistent by sub-proof % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #706. % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (702) all_54_3 = e0 % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (492), (702) imply: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (703) all_34_0 = e0 % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (703) implies: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (704) all_34_0 = e0 % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (495), (704) imply: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (705) ~ (all_52_13 = e0) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (496), (704) imply: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (706) ~ (e3 = e0) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (489), (704) imply: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (707) ~ (e2 = e0) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (497), (704) imply: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (708) ~ (e1 = e0) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (490), (704) imply: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (709) op(e3, e0) = e0 % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (710) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (710) gives: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (711) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (711) gives: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (712) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (712) implies: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (713) op(e3, e3) = e2 % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (233), (684), (694), (700), (713), % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #643. % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (714) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (714) implies: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (715) ~ (all_56_5 = e3) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (716) op(e1, e3) = all_56_5 % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (695), (715), (716), (function-axioms) are % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #724. % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (717) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (110), (160), (163), (164), (168), % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (208), (212), (214), (366), (436), (484), % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485), (486), (489), (490), (641), (642), (681), % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (695), (705), (709), (717), (function-axioms) are % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #630. % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 129.98/18.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (718) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (718) gives: % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (719) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (719) gives: % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (720) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 129.98/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (720) implies: % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (721) ~ (all_56_25 = e0) % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (722) op(e3, e0) = all_56_25 % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (709), (721), (722), (function-axioms) are % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #642. % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (723) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (723) implies: % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (724) op(e2, e1) = e2 % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (394), (724), (function-axioms) are % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770. % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (725) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (725) gives: % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (726) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (726) implies: % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (727) op(e2, e0) = e2 % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (395), (727), (function-axioms) are % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.63/18.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (728) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (164), (208), % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (214), (372), (485), (641), (642), (695), % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (709), (728), (function-axioms) are inconsistent % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #629. % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729) all_57_12 = e3 & op(e0, e3) = e3 % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (482), (729), (function-axioms) are % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #628. % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (730) all_57_3 = e0 & op(e2, e2) = e0 % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (401), (730) are inconsistent by sub-proof % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #627. % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (731) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (731) gives: % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (732) all_57_5 = e0 & op(e2, e1) = e0 % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (661), (732) are inconsistent by sub-proof % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #658. % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (733) all_57_10 = e0 & op(e2, e0) = e0 % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (733) implies: % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (734) op(e2, e0) = e0 % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (681), (734), (function-axioms) are % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #695. % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | (735) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (382), (483), (735), % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | #651. % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | (736) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (168), (169), (203), (271), (393), (432), % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | (484), (489), (492), (493), (497), (502), (736), % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | #698. % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | (737) all_57_9 = e2 & op(e3, e0) = e2 % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (737) implies: % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | (738) all_57_9 = e2 % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (164), (197), (208), (259), (395), % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | (485), (487), (489), (492), (495), (497), (502), % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | (641), (738), (function-axioms) are inconsistent % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #655. % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | Case 2: % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | (739) all_57_15 = e2 & op(e0, e0) = e2 % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | ALPHA: (739) implies: % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | (740) op(e0, e0) = e2 % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (487), (740), (function-axioms) are % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634. % 130.63/18.34 | | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | Case 2: % 130.63/18.34 | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | (741) ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 & % 130.63/18.34 | | | | | | | | | | | | | | | | | $i(all_34_1) % 130.63/18.34 | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | ALPHA: (741) implies: % 130.63/18.34 | | | | | | | | | | | | | | | | | (742) ~ (all_34_1 = e1) % 130.63/18.34 | | | | | | | | | | | | | | | | | (743) op(e3, e3) = all_34_1 % 130.63/18.34 | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | | REF_CLOSE: (436), (742), (743), (function-axioms) are % 130.63/18.34 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #626. % 130.63/18.34 | | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | Case 2: % 130.63/18.34 | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | (744) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 130.63/18.34 | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 130.63/18.34 | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | REF_CLOSE: (164), (165), (394), (395), (744), % 130.63/18.34 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.63/18.34 | | | | | | | | | | | | | #625. % 130.63/18.34 | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | Case 2: % 130.63/18.34 | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | (745) all_54_5 = e1 | all_54_5 = e0 % 130.63/18.34 | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | REF_CLOSE: (267), (373), (384), (745) are inconsistent by % 130.63/18.34 | | | | | | | | | | | | sub-proof #624. % 130.63/18.34 | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | End of split % 130.63/18.34 | | | | | | | | | | % 130.63/18.34 | | | | | | | | | Case 2: % 130.63/18.34 | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | (746) all_30_2 = e0 % 130.63/18.34 | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | COMBINE_EQS: (309), (746) imply: % 130.63/18.34 | | | | | | | | | | (747) all_8_2 = e0 % 130.63/18.34 | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | SIMP: (747) implies: % 130.63/18.34 | | | | | | | | | | (748) all_8_2 = e0 % 130.63/18.34 | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | COMBINE_EQS: (301), (748) imply: % 130.63/18.34 | | | | | | | | | | (749) all_42_2 = e0 % 130.63/18.34 | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | REDUCE: (350), (748) imply: % 130.63/18.34 | | | | | | | | | | (750) ~ (all_52_4 = e0) % 130.63/18.34 | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | REDUCE: (352), (748) imply: % 130.63/18.34 | | | | | | | | | | (751) ~ (all_52_6 = e0) % 130.63/18.34 | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | REDUCE: (354), (748) imply: % 130.63/18.34 | | | | | | | | | | (752) ~ (all_52_7 = e0) % 130.63/18.34 | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | REDUCE: (356), (748) imply: % 130.63/18.34 | | | | | | | | | | (753) ~ (all_52_9 = e0) % 130.63/18.34 | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | REDUCE: (358), (748) imply: % 130.63/18.34 | | | | | | | | | | (754) ~ (all_52_13 = e0) % 130.63/18.34 | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | REDUCE: (376), (748) imply: % 130.63/18.34 | | | | | | | | | | (755) ~ (e3 = e0) % 130.63/18.34 | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | REDUCE: (373), (748) imply: % 130.63/18.34 | | | | | | | | | | (756) ~ (e1 = e0) % 130.63/18.34 | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | BETA: splitting (227) gives: % 130.63/18.34 | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | Case 1: % 130.63/18.34 | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | (757) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 130.63/18.34 | | | | | | | | | | | & op(e2, e2) = e0) % 130.63/18.34 | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | BETA: splitting (757) gives: % 130.63/18.34 | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | Case 1: % 130.63/18.34 | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | (758) all_57_1 = e0 & op(e3, e2) = e0 % 130.63/18.34 | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | REF_CLOSE: (170), (750), (758), (function-axioms) are % 130.63/18.34 | | | | | | | | | | | | inconsistent by sub-proof #693. % 130.63/18.34 | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | Case 2: % 130.63/18.34 | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | (759) all_57_3 = e0 & op(e2, e2) = e0 % 130.63/18.34 | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | ALPHA: (759) implies: % 130.63/18.34 | | | | | | | | | | | | (760) all_57_3 = e0 % 130.63/18.34 | | | | | | | | | | | | (761) op(e2, e2) = e0 % 130.63/18.34 | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | BETA: splitting (79) gives: % 130.63/18.34 | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | Case 1: % 130.63/18.34 | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | (762) ~ (all_32_2 = e1) % 130.63/18.34 | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | REDUCE: (312), (762) imply: % 130.63/18.34 | | | | | | | | | | | | | (763) ~ (all_10_2 = e1) % 130.63/18.34 | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | BETA: splitting (204) gives: % 130.63/18.34 | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | Case 1: % 130.63/18.34 | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | (764) all_54_0 = e3 % 130.63/18.34 | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | COMBINE_EQS: (278), (764) imply: % 130.63/18.34 | | | | | | | | | | | | | | (765) all_10_2 = e3 % 130.63/18.34 | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | REDUCE: (338), (765) imply: % 130.63/18.34 | | | | | | | | | | | | | | (766) ~ (all_52_2 = e3) % 130.63/18.34 | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | REDUCE: (344), (765) imply: % 130.63/18.34 | | | | | | | | | | | | | | (767) ~ (all_52_8 = e3) % 130.63/18.34 | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | REDUCE: (346), (765) imply: % 130.63/18.34 | | | | | | | | | | | | | | (768) ~ (all_52_12 = e3) % 130.63/18.34 | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | REDUCE: (45), (765) imply: % 130.63/18.34 | | | | | | | | | | | | | | (769) op(e3, e3) = e3 % 130.63/18.34 | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | BETA: splitting (82) gives: % 130.63/18.34 | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | Case 1: % 130.63/18.34 | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | (770) ~ (all_34_2 = e3) % 130.63/18.34 | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | REDUCE: (307), (770) imply: % 130.63/18.34 | | | | | | | | | | | | | | | (771) ~ (all_4_2 = e3) % 130.63/18.34 | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 130.63/18.34 | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | Case 1: % 130.63/18.34 | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | (772) all_54_15 = e3 % 130.63/18.34 | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (772) imply: % 130.63/18.34 | | | | | | | | | | | | | | | | (773) all_4_2 = e3 % 130.63/18.34 | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | REDUCE: (771), (773) imply: % 130.63/18.34 | | | | | | | | | | | | | | | | (774) $false % 130.63/18.34 | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | CLOSE: (774) is inconsistent. % 130.63/18.34 | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | Case 2: % 130.63/18.34 | | | | | | | | | | | | | | | | % 130.63/18.34 | | | | | | | | | | | | | | | | (775) ~ (all_54_15 = e3) % 130.63/18.35 | | | | | | | | | | | | | | | | (776) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 130.63/18.35 | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | BETA: splitting (776) gives: % 130.63/18.35 | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | Case 1: % 130.63/18.35 | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | (777) all_54_15 = e2 % 130.63/18.35 | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (777) imply: % 130.63/18.35 | | | | | | | | | | | | | | | | | (778) all_4_2 = e2 % 130.63/18.35 | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | REDUCE: (380), (778) imply: % 130.63/18.35 | | | | | | | | | | | | | | | | | (779) $false % 130.63/18.35 | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | CLOSE: (779) is inconsistent. % 130.63/18.35 | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | Case 2: % 130.63/18.35 | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | (780) ~ (all_54_15 = e2) % 130.63/18.35 | | | | | | | | | | | | | | | | | (781) all_54_15 = e1 | all_54_15 = e0 % 130.63/18.35 | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | BETA: splitting (781) gives: % 130.63/18.35 | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | Case 1: % 130.63/18.35 | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | (782) all_54_15 = e1 % 130.63/18.35 | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (782) imply: % 130.63/18.35 | | | | | | | | | | | | | | | | | | (783) all_4_2 = e1 % 130.63/18.35 | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | REDUCE: (371), (783) imply: % 130.63/18.35 | | | | | | | | | | | | | | | | | | (784) $false % 130.63/18.35 | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | CLOSE: (784) is inconsistent. % 130.63/18.35 | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | Case 2: % 130.63/18.35 | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | (785) all_54_15 = e0 % 130.63/18.35 | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (785) imply: % 130.63/18.35 | | | | | | | | | | | | | | | | | | (786) all_4_2 = e0 % 130.63/18.35 | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | REDUCE: (349), (786) imply: % 130.63/18.35 | | | | | | | | | | | | | | | | | | (787) ~ (all_52_3 = e0) % 130.63/18.35 | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | REDUCE: (368), (786) imply: % 130.63/18.35 | | | | | | | | | | | | | | | | | | (788) ~ (all_52_12 = e0) % 130.63/18.35 | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | REDUCE: (380), (786) imply: % 130.63/18.35 | | | | | | | | | | | | | | | | | | (789) ~ (e2 = e0) % 130.63/18.35 | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | REDUCE: (36), (786) imply: % 130.63/18.35 | | | | | | | | | | | | | | | | | | (790) op(e0, e0) = e0 % 130.63/18.35 | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 130.63/18.35 | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | Case 1: % 130.63/18.35 | | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | | (791) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 130.63/18.35 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 130.63/18.35 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 130.63/18.35 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 130.63/18.35 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 130.63/18.35 | | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (791) gives: % 130.63/18.35 | | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | | Case 1: % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | (792) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (769), (792), (function-axioms) are % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623. % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | | Case 2: % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | (793) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (761), (768), (793), (function-axioms) % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #622. % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | | End of split % 130.63/18.35 | | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | Case 2: % 130.63/18.35 | | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | | (794) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 130.63/18.35 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 130.63/18.35 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 130.63/18.35 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 130.63/18.35 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 130.63/18.35 | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 130.63/18.35 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 130.63/18.35 | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 130.63/18.35 | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 130.63/18.35 | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 130.63/18.35 | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 130.63/18.35 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 130.63/18.35 | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 130.63/18.35 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 130.63/18.35 | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 130.63/18.35 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 130.63/18.35 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 130.63/18.35 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 130.63/18.35 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 130.63/18.35 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 130.63/18.35 | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 130.63/18.35 | | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (794) gives: % 130.63/18.35 | | | | | | | | | | | | | | | | | | | % 130.63/18.35 | | | | | | | | | | | | | | | | | | | Case 1: % 130.63/18.35 | | | | | | | | | | | | | | | | | | | | % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | (795) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (382), (761), (795), (function-axioms) % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #621. % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | % 130.63/18.36 | | | | | | | | | | | | | | | | | | | Case 2: % 130.63/18.36 | | | | | | | | | | | | | | | | | | | | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | (796) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | BETA: splitting (796) gives: % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | (797) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | ALPHA: (797) implies: % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | (798) ~ (all_56_31 = e0) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | (799) op(e0, e0) = all_56_31 % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (790), (798), (799), (function-axioms) are % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #712. % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | (800) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (800) gives: % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (801) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (801) implies: % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (802) op(e1, e1) = e2 % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (802), (function-axioms) are % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (803) op(e0, e0) = all_56_31 & $i(all_56_31) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (803) implies: % 130.78/18.36 | | | | | | | | | | | | | | | | | | | | | | (804) op(e0, e0) = all_56_31 % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | (805) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (805) gives: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | (806) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (806) gives: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | (807) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (807) implies: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | (808) op(e0, e3) = e0 % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (805) gives: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (806) gives: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (807) implies: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (809) ~ (all_56_1 = e3) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (810) op(e3, e3) = all_56_1 % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (769), (809), (810), (function-axioms) are % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #766. % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (811) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (811) implies: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (812) all_56_31 = e2 % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (804), (812) imply: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (813) op(e0, e0) = e2 % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (790), (813), (function-axioms) are % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #714. % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | (814) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (814) gives: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (815) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (815) implies: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (816) op(e0, e3) = all_56_7 % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (787), (808), (816), (function-axioms) are % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #620. % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (817) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (790), (804), (817), (function-axioms) are % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #711. % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | (818) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (818) implies: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | (819) all_56_31 = e2 % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (804), (819) imply: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | (820) op(e0, e0) = e2 % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (790), (820), (function-axioms) are % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #714. % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | (821) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (821) gives: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | (822) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (822) implies: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | (823) op(e1, e1) = e0 % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | (824) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (824) gives: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (825) all_57_0 = e0 & op(e3, e3) = e0 % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (825) implies: % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (826) op(e3, e3) = e0 % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (769), (826), (function-axioms) are % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #773. % 130.78/18.37 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (827) all_57_1 = e0 & op(e3, e2) = e0 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (827) implies: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (828) op(e3, e2) = e0 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e0, % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (828) gives: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (829) all_52_4 = e0 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (750), (829) imply: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (830) $false % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (830) is inconsistent. % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | (831) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (831) gives: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (832) all_57_4 = e0 & op(e3, e1) = e0 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (832) implies: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (833) op(e3, e1) = e0 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (169), (361), (823), (833), % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | #619. % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (834) all_57_9 = e0 & op(e3, e0) = e0 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (788), (834), (function-axioms) are % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #618. % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | (835) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (790), (804), (835), (function-axioms) are % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #711. % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.38 | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | End of split % 130.78/18.38 | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | End of split % 130.78/18.38 | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | End of split % 130.78/18.38 | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | End of split % 130.78/18.38 | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | Case 2: % 130.78/18.38 | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | (836) all_34_2 = e3 % 130.78/18.38 | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | COMBINE_EQS: (307), (836) imply: % 130.78/18.38 | | | | | | | | | | | | | | | (837) all_4_2 = e3 % 130.78/18.38 | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | SIMP: (837) implies: % 130.78/18.38 | | | | | | | | | | | | | | | (838) all_4_2 = e3 % 130.78/18.38 | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | REDUCE: (360), (838) imply: % 130.78/18.38 | | | | | | | | | | | | | | | (839) ~ (all_52_7 = e3) % 130.78/18.38 | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | REDUCE: (367), (838) imply: % 130.78/18.38 | | | | | | | | | | | | | | | (840) ~ (all_52_11 = e3) % 130.78/18.38 | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | REDUCE: (370), (838) imply: % 130.78/18.38 | | | | | | | | | | | | | | | (841) ~ (all_52_14 = e3) % 130.78/18.38 | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | REDUCE: (36), (838) imply: % 130.78/18.38 | | | | | | | | | | | | | | | (842) op(e0, e0) = e3 % 130.78/18.38 | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 130.78/18.38 | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | Case 1: % 130.78/18.38 | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | (843) ~ (all_42_2 = e0) % 130.78/18.38 | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | REDUCE: (749), (843) imply: % 130.78/18.38 | | | | | | | | | | | | | | | | (844) $false % 130.78/18.38 | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | CLOSE: (844) is inconsistent. % 130.78/18.38 | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | Case 2: % 130.78/18.38 | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | (845) ( ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 & % 130.78/18.38 | | | | | | | | | | | | | | | | $i(all_42_0)) | ( ~ (all_42_1 = e3) & op(e0, e0) % 130.78/18.38 | | | | | | | | | | | | | | | | = all_42_1 & $i(all_42_1)) % 130.78/18.38 | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 130.78/18.38 | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | Case 1: % 130.78/18.38 | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | (846) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 130.78/18.38 | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 130.78/18.38 | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | BETA: splitting (846) gives: % 130.78/18.38 | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.38 | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | (847) all_57_6 = e3 & op(e1, e3) = e3 % 130.78/18.38 | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (766), (847), (function-axioms) are % 130.78/18.38 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #761. % 130.78/18.38 | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.38 | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | (848) all_57_7 = e3 & op(e1, e2) = e3 % 130.78/18.38 | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | ALPHA: (848) implies: % 130.78/18.38 | | | | | | | | | | | | | | | | | | (849) all_57_7 = e3 % 130.78/18.38 | | | | | | | | | | | | | | | | | | (850) op(e1, e2) = e3 % 130.78/18.38 | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | BETA: splitting (845) gives: % 130.78/18.38 | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | (851) ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 & % 130.78/18.38 | | | | | | | | | | | | | | | | | | | $i(all_42_0) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | ALPHA: (851) implies: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | (852) ~ (all_42_0 = e1) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | (853) op(e0, e2) = all_42_0 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | (854) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | BETA: splitting (854) gives: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (855) all_57_4 = e3 & op(e3, e1) = e3 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | ALPHA: (855) implies: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (856) op(e3, e1) = e3 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (767), (856), (function-axioms) are % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #705. % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (857) all_57_5 = e3 & op(e2, e1) = e3 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | ALPHA: (857) implies: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (858) op(e2, e1) = e3 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | all_42_0, e2, e0, simplifying with (158), (853) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | gives: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (859) all_52_7 = all_42_0 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e3, % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (162), (850) gives: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (860) all_52_6 = e3 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e3, % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (858) gives: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (861) all_52_9 = e3 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (859) imply: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (862) all_54_13 = all_42_0 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (860) imply: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (863) ~ (all_52_4 = e3) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (859) imply: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (864) ~ (all_52_4 = all_42_0) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | REDUCE: (839), (859) imply: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (865) ~ (all_42_0 = e3) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | REDUCE: (752), (859) imply: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (866) ~ (all_42_0 = e0) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (861) imply: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (867) ~ (all_52_11 = e3) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (861) imply: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | (868) ~ (all_6_2 = e3) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | (869) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (869) gives: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | (870) all_57_1 = e1 & op(e3, e2) = e1 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (870) implies: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | (871) all_57_1 = e1 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | (872) op(e3, e2) = e1 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | (873) all_54_13 = e3 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (862), (865), (873) are inconsistent by sub-proof % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | #617. % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | (874) ~ (all_54_13 = e3) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | (875) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (875) gives: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | (876) all_54_13 = e2 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (862), (876) imply: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | (877) all_42_0 = e2 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (877) implies: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | (878) all_42_0 = e2 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (864), (878) imply: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | (879) ~ (all_52_4 = e2) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (865), (878) imply: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | (880) ~ (e3 = e2) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (853), (878) imply: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | (881) op(e0, e2) = e2 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (882) all_54_1 = e3 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (882) imply: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (883) all_52_4 = e3 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (863), (883) imply: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (884) $false % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (884) is inconsistent. % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (885) ~ (all_54_1 = e3) % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (886) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (887) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (887) gives: % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (888) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (888) gives: % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (889) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (889) implies: % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (890) op(e3, e3) = e2 % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (769), (890), (function-axioms) are % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #778. % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (891) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (891) implies: % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (892) op(e3, e3) = e1 % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236), % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (863), (871), (872), (892), % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #610. % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (893) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (761), (768), (893), (function-axioms) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #622. % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (894) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (894) gives: % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (895) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (382), (761), (895), (function-axioms) % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #621. % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (896) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (896) gives: % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (897) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (897) implies: % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (898) ~ (all_56_15 = e2) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (899) op(e0, e2) = all_56_15 % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (881), (898), (899), (function-axioms) are % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609. % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (900) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (900) gives: % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (901) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (901) implies: % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (902) op(e1, e1) = e2 % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (902), (function-axioms) are % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (903) op(e0, e0) = all_56_31 & $i(all_56_31) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (903) implies: % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (904) op(e0, e0) = all_56_31 % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (905) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 130.78/18.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (39), (100), (157), (190), (246), (271), % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295), (364), (750), (769), (840), (842), (879), % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (886), (904), (905), (function-axioms) are % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #605. % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | (906) all_54_13 = e1 | all_54_13 = e0 % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (852), (862), (866), (906) are inconsistent by % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #604. % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | (907) all_57_3 = e1 & op(e2, e2) = e1 % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (907) implies: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | (908) op(e2, e2) = e1 % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (761), (908), (function-axioms) are % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | (909) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (909) gives: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | (910) all_57_7 = e1 & op(e1, e2) = e1 % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (849), (910) are inconsistent by sub-proof % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | #603. % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | (911) all_57_13 = e1 & op(e0, e2) = e1 % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (911) implies: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | (912) op(e0, e2) = e1 % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | (913) all_54_13 = e3 % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (862), (865), (913) are inconsistent by sub-proof % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | #617. % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | (914) ~ (all_54_13 = e3) % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | (915) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (915) gives: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | (916) all_54_13 = e2 % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (862), (916) imply: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | (917) all_42_0 = e2 % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (917) implies: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | (918) all_42_0 = e2 % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (864), (918) imply: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | (919) ~ (all_52_4 = e2) % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (865), (918) imply: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | (920) ~ (e3 = e2) % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (853), (918) imply: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | (921) op(e0, e2) = e2 % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (922) all_54_1 = e3 % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (922) imply: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (923) all_52_4 = e3 % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (863), (923) imply: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (924) $false % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (924) is inconsistent. % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (925) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (926) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (926) gives: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (927) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (769), (927), (function-axioms) are % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623. % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (928) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (761), (768), (928), (function-axioms) % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #622. % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (929) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (929) gives: % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (930) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (382), (761), (930), (function-axioms) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #621. % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (931) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (931) gives: % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (932) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (932) implies: % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (933) op(e0, e2) = all_56_15 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e2, e0, simplifying with (921), (933) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (934) all_56_15 = e2 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e2, e0, simplifying with (912), (933) % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (935) all_56_15 = e1 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (934), (935) imply: % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (936) e2 = e1 % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (936) imply: % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (937) $false % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (937) is inconsistent. % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 130.78/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (938) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (938) gives: % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (939) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (939) implies: % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (940) op(e1, e1) = e2 % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (940), (function-axioms) are % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (941) op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (941) implies: % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (942) op(e0, e0) = all_56_31 % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (943) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (39), (100), (157), (190), (246), (271), % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295), (364), (750), (769), (840), (842), (919), % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (925), (942), (943), (function-axioms) are % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #605. % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | (944) all_54_13 = e1 | all_54_13 = e0 % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (852), (862), (866), (944) are inconsistent by % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #604. % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | (945) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (382), (840), (945), % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | #651. % 131.07/18.43 | | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.43 | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | (946) ~ (all_42_1 = e3) & op(e0, e0) = all_42_1 & % 131.07/18.43 | | | | | | | | | | | | | | | | | | | $i(all_42_1) % 131.07/18.43 | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (842), (946), (function-axioms) are inconsistent % 131.07/18.43 | | | | | | | | | | | | | | | | | | | by sub-proof #602. % 131.07/18.43 | | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | Case 2: % 131.07/18.43 | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | (947) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 131.07/18.43 | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 131.07/18.43 | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (382), (841), (947), % 131.07/18.43 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.07/18.43 | | | | | | | | | | | | | | | | | #653. % 131.07/18.43 | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | Case 2: % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | (948) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | REF_CLOSE: (278), (374), (378), (763), (948) are inconsistent % 131.07/18.43 | | | | | | | | | | | | | | by sub-proof #777. % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | Case 2: % 131.07/18.43 | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | (949) all_32_2 = e1 % 131.07/18.43 | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | COMBINE_EQS: (312), (949) imply: % 131.07/18.43 | | | | | | | | | | | | | (950) all_10_2 = e1 % 131.07/18.43 | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | REDUCE: (336), (950) imply: % 131.07/18.43 | | | | | | | | | | | | | (951) ~ (all_52_1 = e1) % 131.07/18.43 | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | REDUCE: (342), (950) imply: % 131.07/18.43 | | | | | | | | | | | | | (952) ~ (all_52_4 = e1) % 131.07/18.43 | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | REDUCE: (378), (950) imply: % 131.07/18.43 | | | | | | | | | | | | | (953) ~ (e2 = e1) % 131.07/18.43 | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | REDUCE: (45), (950) imply: % 131.07/18.43 | | | | | | | | | | | | | (954) op(e3, e3) = e1 % 131.07/18.43 | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | BETA: splitting (82) gives: % 131.07/18.43 | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | Case 1: % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | (955) ~ (all_34_2 = e3) % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | REDUCE: (307), (955) imply: % 131.07/18.43 | | | | | | | | | | | | | | (956) ~ (all_4_2 = e3) % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | BETA: splitting (189) gives: % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | Case 1: % 131.07/18.43 | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | (957) all_54_15 = e3 % 131.07/18.43 | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | REF_CLOSE: (245), (956), (957) are inconsistent by sub-proof % 131.07/18.43 | | | | | | | | | | | | | | | #601. % 131.07/18.43 | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | Case 2: % 131.07/18.43 | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | (958) ~ (all_54_15 = e3) % 131.07/18.43 | | | | | | | | | | | | | | | (959) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 131.07/18.43 | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (39), (168), (169), (170), (206), % 131.07/18.43 | | | | | | | | | | | | | | | (232), (245), (368), (371), (372), (380), (382), % 131.07/18.43 | | | | | | | | | | | | | | | (750), (761), (954), (956), (959), % 131.07/18.43 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.07/18.43 | | | | | | | | | | | | | | | #594. % 131.07/18.43 | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | End of split % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | Case 2: % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | (960) all_34_2 = e3 % 131.07/18.43 | | | | | | | | | | | | | | (961) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & % 131.07/18.43 | | | | | | | | | | | | | | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3) % 131.07/18.43 | | | | | | | | | | | | | | = all_34_1 & $i(all_34_1)) % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | COMBINE_EQS: (307), (960) imply: % 131.07/18.43 | | | | | | | | | | | | | | (962) all_4_2 = e3 % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | SIMP: (962) implies: % 131.07/18.43 | | | | | | | | | | | | | | (963) all_4_2 = e3 % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | REDUCE: (360), (963) imply: % 131.07/18.43 | | | | | | | | | | | | | | (964) ~ (all_52_7 = e3) % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | REDUCE: (367), (963) imply: % 131.07/18.43 | | | | | | | | | | | | | | (965) ~ (all_52_11 = e3) % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | REDUCE: (368), (963) imply: % 131.07/18.43 | | | | | | | | | | | | | | (966) ~ (all_52_12 = e3) % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | REDUCE: (369), (963) imply: % 131.07/18.43 | | | | | | | | | | | | | | (967) ~ (all_52_13 = e3) % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | REDUCE: (370), (963) imply: % 131.07/18.43 | | | | | | | | | | | | | | (968) ~ (all_52_14 = e3) % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | REDUCE: (36), (963) imply: % 131.07/18.43 | | | | | | | | | | | | | | (969) op(e0, e0) = e3 % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | BETA: splitting (94) gives: % 131.07/18.43 | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | Case 1: % 131.07/18.43 | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | (970) ~ (all_42_2 = e0) % 131.07/18.43 | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | REDUCE: (749), (970) imply: % 131.07/18.43 | | | | | | | | | | | | | | | (971) $false % 131.07/18.43 | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | CLOSE: (971) is inconsistent. % 131.07/18.43 | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | Case 2: % 131.07/18.43 | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | (972) ( ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 & % 131.07/18.43 | | | | | | | | | | | | | | | $i(all_42_0)) | ( ~ (all_42_1 = e3) & op(e0, e0) % 131.07/18.43 | | | | | | | | | | | | | | | = all_42_1 & $i(all_42_1)) % 131.07/18.43 | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | BETA: splitting (972) gives: % 131.07/18.43 | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | Case 1: % 131.07/18.43 | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | (973) ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 & % 131.07/18.43 | | | | | | | | | | | | | | | | $i(all_42_0) % 131.07/18.43 | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | ALPHA: (973) implies: % 131.07/18.43 | | | | | | | | | | | | | | | | (974) ~ (all_42_0 = e1) % 131.07/18.43 | | | | | | | | | | | | | | | | (975) op(e0, e2) = all_42_0 % 131.07/18.43 | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | BETA: splitting (961) gives: % 131.07/18.43 | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | Case 1: % 131.07/18.43 | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | (976) ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & % 131.07/18.43 | | | | | | | | | | | | | | | | | $i(all_34_0) % 131.07/18.43 | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | ALPHA: (976) implies: % 131.07/18.43 | | | | | | | | | | | | | | | | | (977) ~ (all_34_0 = e2) % 131.07/18.43 | | | | | | | | | | | | | | | | | (978) op(e3, e0) = all_34_0 % 131.07/18.43 | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, % 131.07/18.43 | | | | | | | | | | | | | | | | | all_42_0, e2, e0, simplifying with (158), (975) % 131.07/18.43 | | | | | | | | | | | | | | | | | gives: % 131.07/18.43 | | | | | | | | | | | | | | | | | (979) all_52_7 = all_42_0 % 131.07/18.43 | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 131.07/18.43 | | | | | | | | | | | | | | | | | all_34_0, e0, e3, simplifying with (168), (978) % 131.07/18.43 | | | | | | | | | | | | | | | | | gives: % 131.07/18.43 | | | | | | | | | | | | | | | | | (980) all_52_12 = all_34_0 % 131.07/18.43 | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (979) imply: % 131.07/18.43 | | | | | | | | | | | | | | | | | (981) all_54_13 = all_42_0 % 131.07/18.43 | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | REDUCE: (135), (979) imply: % 131.07/18.43 | | | | | | | | | | | | | | | | | (982) ~ (all_52_4 = all_42_0) % 131.07/18.43 | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | REDUCE: (128), (979) imply: % 131.07/18.43 | | | | | | | | | | | | | | | | | (983) ~ (all_52_6 = all_42_0) % 131.07/18.43 | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | REDUCE: (964), (979) imply: % 131.07/18.43 | | | | | | | | | | | | | | | | | (984) ~ (all_42_0 = e3) % 131.07/18.43 | | | | | | | | | | | | | | | | | % 131.07/18.43 | | | | | | | | | | | | | | | | | REDUCE: (752), (979) imply: % 131.07/18.43 | | | | | | | | | | | | | | | | | (985) ~ (all_42_0 = e0) % 131.07/18.43 | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | (986) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 131.07/18.44 | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 131.07/18.44 | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | BETA: splitting (986) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | (987) all_57_12 = e1 & op(e0, e3) = e1 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | ALPHA: (987) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | (988) all_57_12 = e1 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (235), (237), % 131.07/18.44 | | | | | | | | | | | | | | | | | | | (954), (988), (function-axioms) are inconsistent % 131.07/18.44 | | | | | | | | | | | | | | | | | | | by sub-proof #583. % 131.07/18.44 | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | (989) all_57_13 = e1 & op(e0, e2) = e1 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | ALPHA: (989) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | (990) all_57_13 = e1 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | (991) all_54_13 = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (981), (984), (991) are inconsistent by sub-proof % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | #617. % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | (992) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (992) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (993) all_54_13 = e2 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (981), (993) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (994) all_42_0 = e2 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | SIMP: (994) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (995) all_42_0 = e2 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (982), (995) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (996) ~ (all_52_4 = e2) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (983), (995) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (997) ~ (all_52_6 = e2) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (998) all_54_1 = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (998) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (999) all_52_4 = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (999) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1000) ~ (all_52_6 = e3) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1000) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1001) ~ (all_52_6 = e3) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (999) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1002) ~ (all_52_8 = e3) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1002) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1003) ~ (all_52_8 = e3) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1004) all_54_9 = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (1004) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1005) all_52_6 = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1001), (1005) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1006) $false % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1006) is inconsistent. % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1007) ~ (all_54_9 = e3) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1008) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (39), (100), (157), (160), % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (162), (167), (169), (170), (194), (208), (210), % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (213), (215), (216), (218), (221), (222), (224), % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (225), (231), (232), (236), (238), (257), (295), % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (334), (359), (361), (372), (382), (750), (751), % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (760), (761), (951), (954), (965), (968), (969), % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (990), (997), (1001), (1003), (1008), % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | #565. % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1009) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (750), (952), (996), (1009) are % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #701. % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (1010) all_54_13 = e1 | all_54_13 = e0 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (974), (981), (985), (1010) are inconsistent by % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | sub-proof #604. % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.44 | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | End of split % 131.07/18.44 | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.44 | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | (1011) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 131.07/18.44 | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 131.07/18.44 | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | BETA: splitting (1011) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | (1012) all_57_14 = e1 & op(e0, e1) = e1 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | ALPHA: (1012) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | (1013) all_57_14 = e1 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | (1014) all_54_13 = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (981), (984), (1014) are inconsistent by sub-proof % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | #617. % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | (1015) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1015) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (1016) all_54_13 = e2 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (981), (1016) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (1017) all_42_0 = e2 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | SIMP: (1017) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (1018) all_42_0 = e2 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (982), (1018) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (1019) ~ (all_52_4 = e2) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (983), (1018) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (1020) ~ (all_52_6 = e2) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (975), (1018) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | (1021) op(e0, e2) = e2 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1022) all_54_1 = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (1022) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1023) all_52_4 = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (1023) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1024) ~ (all_52_6 = e3) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1024) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1025) ~ (all_52_6 = e3) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (1023) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1026) ~ (all_52_8 = e3) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1026) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | (1027) ~ (all_52_8 = e3) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1028) all_54_9 = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (1028) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1029) all_52_6 = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1025), (1029) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1030) $false % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1030) is inconsistent. % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1031) ~ (all_54_9 = e3) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | (1032) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | (1033) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1033) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | (1034) all_57_4 = e3 & op(e3, e1) = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1034) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | (1035) op(e3, e1) = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1027), (1035), (function-axioms) are % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #705. % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | (1036) all_57_5 = e3 & op(e2, e1) = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1036) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | (1037) all_57_5 = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (1038) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1038) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1039) all_57_6 = e3 & op(e1, e3) = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1039) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1040) all_57_6 = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1041) op(e1, e3) = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1042) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (761), (952), (1042), % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #564. % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1043) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1043) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1044) all_57_7 = e1 & op(e1, e2) = e1 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1044) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1045) all_57_7 = e1 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1046) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1046) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1047) all_57_1 = e3 & op(e3, e2) = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1047) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1048) all_57_1 = e3 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1049) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (954), (1048), (1049), (function-axioms) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #562. % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1050) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1050) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1051) all_57_4 = e2 & op(e3, e1) = e2 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1051) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1052) all_57_4 = e2 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1053) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (750), (954), (1053), % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #692. % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1054) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1054) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1055) all_57_4 = e0 & op(e3, e1) = e0 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1055) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1056) all_57_4 = e0 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (221), (222), % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (382), (1013), (1056), (function-axioms) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #558. % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1057) all_57_9 = e0 & op(e3, e0) = e0 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1057) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1058) all_57_9 = e0 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1059) op(e3, e0) = e0 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1060) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1060) gives: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1061) all_57_6 = e2 & op(e1, e3) = e2 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1061) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1062) all_57_6 = e2 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1040), (1062) are inconsistent by sub-proof % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #592. % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1063) all_57_7 = e2 & op(e1, e2) = e2 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1063) implies: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1064) all_57_7 = e2 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1045), (1064) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1065) e2 = e1 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1052), (1065) imply: % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1066) all_57_4 = e1 % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (236), (238), (954), % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1058), (1066), (function-axioms) are inconsistent % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #668. % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1067) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1067) gives: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1068) all_57_8 = e2 & op(e1, e1) = e2 % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1068) implies: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1069) op(e1, e1) = e2 % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1069), (function-axioms) are % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1070) all_57_11 = e2 & op(e1, e0) = e2 % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1070) implies: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1071) all_57_11 = e2 % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1072) op(e1, e0) = e2 % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1073) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1073) gives: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1074) all_57_9 = e1 & op(e3, e0) = e1 % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1074) implies: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1075) all_57_9 = e1 % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236), % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (750), (954), (1075), (function-axioms) are % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #686. % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1076) all_57_10 = e1 & op(e2, e0) = e1 % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1076) implies: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1077) op(e2, e0) = e1 % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1078) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1078) gives: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1079) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1079) gives: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1080) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1080) implies: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1081) op(e3, e3) = e2 % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (954), (1081), (function-axioms) are % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743. % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1082) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1082) implies: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1083) ~ (all_56_5 = e3) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1084) op(e1, e3) = all_56_5 % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (39), (218), (382), (1045), (1071), % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1083), (1084), (function-axioms) are inconsistent % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #722. % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1085) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (110), (160), (163), (164), (168), % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (208), (212), (214), (366), (754), (954), % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (966), (967), (968), (977), (978), (1041), (1059), % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1071), (1072), (1077), (1085), (function-axioms) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #630. % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1086) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.07/18.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1086) gives: % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1087) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1087) gives: % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1088) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1088) implies: % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1089) ~ (all_56_25 = e0) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1090) op(e3, e0) = all_56_25 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1059), (1089), (1090), (function-axioms) are % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #642. % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1091) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1091) implies: % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1092) ~ (all_56_5 = e3) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1093) op(e1, e3) = all_56_5 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (39), (218), (382), (1045), (1071), % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1092), (1093), (function-axioms) are inconsistent % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #722. % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1094) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1094) gives: % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1095) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1095) implies: % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1096) ~ (all_56_15 = e2) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1097) op(e0, e2) = all_56_15 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1021), (1096), (1097), (function-axioms) are % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609. % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1098) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.07/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (164), (208), % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (214), (372), (967), (1041), (1059), % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1071), (1072), (1098), (function-axioms) are % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #629. % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1099) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (969), (1072), (1099), (function-axioms) % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #557. % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1100) all_57_9 = e2 & op(e3, e0) = e2 % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1100) implies: % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1101) all_57_9 = e2 % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1102) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1102) gives: % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1103) all_57_4 = e2 & op(e3, e1) = e2 % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1103) implies: % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1104) all_57_4 = e2 % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1105) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (750), (954), (1105), % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #692. % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1106) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1106) gives: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1107) all_57_4 = e0 & op(e3, e1) = e0 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1107) implies: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1108) all_57_4 = e0 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (221), (222), % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (382), (1013), (1108), (function-axioms) % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #558. % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1109) all_57_9 = e0 & op(e3, e0) = e0 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1109) implies: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1110) all_57_9 = e0 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1101), (1110) imply: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1111) e2 = e0 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1104), (1111) imply: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1112) all_57_4 = e0 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (221), (222), % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (382), (1013), (1112), (function-axioms) % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #558. % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1113) all_57_5 = e2 & op(e2, e1) = e2 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1037), (1113) are inconsistent by sub-proof % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #677. % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1114) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1114) gives: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1115) all_57_8 = e2 & op(e1, e1) = e2 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1115) implies: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1116) op(e1, e1) = e2 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1116), (function-axioms) are % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1117) all_57_14 = e2 & op(e0, e1) = e2 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1117) implies: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1118) op(e0, e1) = e2 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (194), (257), (295), (334), (359), (372), % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382), (751), (969), (1020), (1032), (1118), % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #566. % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1119) all_57_3 = e3 & op(e2, e2) = e3 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1119) implies: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1120) op(e2, e2) = e3 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (761), (1120), (function-axioms) are % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1121) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (964), (1025), (1121), % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #555. % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1122) all_57_13 = e1 & op(e0, e2) = e1 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1122) implies: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1123) all_57_13 = e1 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (39), (100), (157), (160), % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (167), (169), (170), (194), (208), (210), % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (215), (216), (218), (221), (222), (224), % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (231), (232), (236), (238), (257), (295), % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334), (359), (361), (372), (382), (750), (751), % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (760), (761), (951), (954), (965), (968), (969), % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1020), (1025), (1027), (1032), (1123), % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #565. % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1124) all_57_7 = e3 & op(e1, e2) = e3 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1124) implies: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125) op(e1, e2) = e3 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (1025), (1125), (function-axioms) are % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654. % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (1126) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (382), (968), (1126), % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | #653. % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | (1127) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (382), (965), (1127), % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | #651. % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | (1128) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (750), (952), (1019), (1128) are % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #701. % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | (1129) all_54_13 = e1 | all_54_13 = e0 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (974), (981), (985), (1129) are inconsistent by % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | sub-proof #604. % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | (1130) all_57_15 = e1 & op(e0, e0) = e1 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | ALPHA: (1130) implies: % 131.23/18.47 | | | | | | | | | | | | | | | | | | | (1131) op(e0, e0) = e1 % 131.23/18.47 | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (969), (1131), (function-axioms) are % 131.23/18.47 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606. % 131.23/18.47 | | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | (1132) ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 & % 131.23/18.47 | | | | | | | | | | | | | | | | | $i(all_34_1) % 131.23/18.47 | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | ALPHA: (1132) implies: % 131.23/18.47 | | | | | | | | | | | | | | | | | (1133) ~ (all_34_1 = e1) % 131.23/18.47 | | | | | | | | | | | | | | | | | (1134) op(e3, e3) = all_34_1 % 131.23/18.47 | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | | REF_CLOSE: (954), (1133), (1134), (function-axioms) are % 131.23/18.47 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #626. % 131.23/18.47 | | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | (1135) ~ (all_42_1 = e3) & op(e0, e0) = all_42_1 & % 131.23/18.47 | | | | | | | | | | | | | | | | $i(all_42_1) % 131.23/18.47 | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | REF_CLOSE: (969), (1135), (function-axioms) are inconsistent % 131.23/18.47 | | | | | | | | | | | | | | | | by sub-proof #602. % 131.23/18.47 | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | (1136) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 131.23/18.47 | | | | | | | | | | | e0 & op(e0, e2) = e0) % 131.23/18.47 | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | BETA: splitting (1136) gives: % 131.23/18.47 | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | Case 1: % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | (1137) all_57_7 = e0 & op(e1, e2) = e0 % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | ALPHA: (1137) implies: % 131.23/18.47 | | | | | | | | | | | | (1138) op(e1, e2) = e0 % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e0, % 131.23/18.47 | | | | | | | | | | | | e2, e1, simplifying with (162), (1138) gives: % 131.23/18.47 | | | | | | | | | | | | (1139) all_52_6 = e0 % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | REDUCE: (751), (1139) imply: % 131.23/18.47 | | | | | | | | | | | | (1140) $false % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | CLOSE: (1140) is inconsistent. % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | (1141) all_57_13 = e0 & op(e0, e2) = e0 % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | ALPHA: (1141) implies: % 131.23/18.47 | | | | | | | | | | | | (1142) op(e0, e2) = e0 % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0, % 131.23/18.47 | | | | | | | | | | | | e2, e0, simplifying with (158), (1142) gives: % 131.23/18.47 | | | | | | | | | | | | (1143) all_52_7 = e0 % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | REDUCE: (752), (1143) imply: % 131.23/18.47 | | | | | | | | | | | | (1144) $false % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | CLOSE: (1144) is inconsistent. % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | | % 131.23/18.47 | | | | | | | | | End of split % 131.23/18.47 | | | | | | | | | % 131.23/18.47 | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | % 131.23/18.47 | | | | | | | | | (1145) all_28_2 = e3 % 131.23/18.47 | | | | | | | | | % 131.23/18.47 | | | | | | | | | COMBINE_EQS: (316), (1145) imply: % 131.23/18.47 | | | | | | | | | (1146) all_6_2 = e3 % 131.23/18.47 | | | | | | | | | % 131.23/18.47 | | | | | | | | | SIMP: (1146) implies: % 131.23/18.47 | | | | | | | | | (1147) all_6_2 = e3 % 131.23/18.47 | | | | | | | | | % 131.23/18.47 | | | | | | | | | REDUCE: (359), (1147) imply: % 131.23/18.47 | | | | | | | | | (1148) ~ (all_52_6 = e3) % 131.23/18.47 | | | | | | | | | % 131.23/18.47 | | | | | | | | | REDUCE: (361), (1147) imply: % 131.23/18.47 | | | | | | | | | (1149) ~ (all_52_8 = e3) % 131.23/18.47 | | | | | | | | | % 131.23/18.47 | | | | | | | | | REDUCE: (362), (1147) imply: % 131.23/18.47 | | | | | | | | | (1150) ~ (all_52_9 = e3) % 131.23/18.47 | | | | | | | | | % 131.23/18.47 | | | | | | | | | REDUCE: (39), (1147) imply: % 131.23/18.47 | | | | | | | | | (1151) op(e1, e1) = e3 % 131.23/18.47 | | | | | | | | | % 131.23/18.47 | | | | | | | | | BETA: splitting (76) gives: % 131.23/18.47 | | | | | | | | | % 131.23/18.47 | | | | | | | | | Case 1: % 131.23/18.47 | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | (1152) ~ (all_30_2 = e0) % 131.23/18.47 | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | REDUCE: (309), (1152) imply: % 131.23/18.47 | | | | | | | | | | (1153) ~ (all_8_2 = e0) % 131.23/18.47 | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | BETA: splitting (199) gives: % 131.23/18.47 | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | Case 1: % 131.23/18.47 | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | (1154) all_54_5 = e3 % 131.23/18.47 | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | REF_CLOSE: (267), (376), (1154) are inconsistent by sub-proof % 131.23/18.47 | | | | | | | | | | | #554. % 131.23/18.47 | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | (1155) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 131.23/18.47 | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | BETA: splitting (1155) gives: % 131.23/18.47 | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | Case 1: % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | (1156) all_54_5 = e2 % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | COMBINE_EQS: (267), (1156) imply: % 131.23/18.47 | | | | | | | | | | | | (1157) all_8_2 = e2 % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | SIMP: (1157) implies: % 131.23/18.47 | | | | | | | | | | | | (1158) all_8_2 = e2 % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | REDUCE: (347), (1158) imply: % 131.23/18.47 | | | | | | | | | | | | (1159) ~ (all_52_1 = e2) % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | REDUCE: (350), (1158) imply: % 131.23/18.47 | | | | | | | | | | | | (1160) ~ (all_52_4 = e2) % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | REDUCE: (356), (1158) imply: % 131.23/18.47 | | | | | | | | | | | | (1161) ~ (all_52_9 = e2) % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | REDUCE: (358), (1158) imply: % 131.23/18.47 | | | | | | | | | | | | (1162) ~ (all_52_13 = e2) % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | BETA: splitting (225) gives: % 131.23/18.47 | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | Case 1: % 131.23/18.47 | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | (1163) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 131.23/18.47 | | | | | | | | | | | | | & op(e2, e2) = e2) % 131.23/18.47 | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | BETA: splitting (1163) gives: % 131.23/18.47 | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | Case 1: % 131.23/18.47 | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | (1164) all_57_2 = e2 & op(e2, e3) = e2 % 131.23/18.47 | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | ALPHA: (1164) implies: % 131.23/18.47 | | | | | | | | | | | | | | (1165) op(e2, e3) = e2 % 131.23/18.47 | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | REF_CLOSE: (167), (1159), (1165), (function-axioms) are % 131.23/18.47 | | | | | | | | | | | | | | inconsistent by sub-proof #779. % 131.23/18.47 | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | Case 2: % 131.23/18.47 | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | (1166) all_57_3 = e2 & op(e2, e2) = e2 % 131.23/18.47 | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | ALPHA: (1166) implies: % 131.23/18.47 | | | | | | | | | | | | | | (1167) all_57_3 = e2 % 131.23/18.47 | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | BETA: splitting (79) gives: % 131.23/18.47 | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | Case 1: % 131.23/18.47 | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | (1168) ~ (all_32_2 = e1) % 131.23/18.47 | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | REDUCE: (312), (1168) imply: % 131.23/18.47 | | | | | | | | | | | | | | | (1169) ~ (all_10_2 = e1) % 131.23/18.47 | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 131.23/18.47 | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | Case 1: % 131.23/18.47 | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | (1170) all_54_0 = e3 % 131.23/18.47 | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (1170) imply: % 131.23/18.47 | | | | | | | | | | | | | | | | (1171) all_10_2 = e3 % 131.23/18.47 | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | SIMP: (1171) implies: % 131.23/18.47 | | | | | | | | | | | | | | | | (1172) all_10_2 = e3 % 131.23/18.47 | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | REDUCE: (346), (1172) imply: % 131.23/18.47 | | | | | | | | | | | | | | | | (1173) ~ (all_52_12 = e3) % 131.23/18.47 | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | REDUCE: (45), (1172) imply: % 131.23/18.47 | | | | | | | | | | | | | | | | (1174) op(e3, e3) = e3 % 131.23/18.47 | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 131.23/18.47 | | | | | | | | | | | | | | | | % 131.23/18.47 | | | | | | | | | | | | | | | | Case 1: % 131.23/18.47 | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | (1175) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.23/18.48 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.23/18.48 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.23/18.48 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.23/18.48 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.23/18.48 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.23/18.48 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.23/18.48 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.23/18.48 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.23/18.48 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.23/18.48 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.23/18.48 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.23/18.48 | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | BETA: splitting (1175) gives: % 131.23/18.48 | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.48 | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | | (1176) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.23/18.48 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.23/18.48 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.23/18.48 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.23/18.48 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.23/18.48 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.23/18.48 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.23/18.48 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.23/18.48 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.23/18.48 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 131.23/18.48 | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (1174), (1176), (function-axioms) are % 131.23/18.48 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623. % 131.23/18.48 | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.48 | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | | (1177) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.23/18.48 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.23/18.48 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.23/18.48 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.23/18.48 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.23/18.48 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.23/18.48 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.23/18.48 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.48 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.23/18.48 | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1173), (1174), (1177), (function-axioms) % 131.23/18.48 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #553. % 131.23/18.48 | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | End of split % 131.23/18.48 | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | Case 2: % 131.23/18.48 | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | (1178) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.23/18.48 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.23/18.48 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.23/18.48 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.23/18.48 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.23/18.48 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.23/18.48 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 131.23/18.48 | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 131.23/18.48 | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.23/18.48 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 131.23/18.48 | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 131.23/18.48 | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 131.23/18.48 | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 131.23/18.48 | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 131.23/18.48 | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 131.23/18.48 | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 131.23/18.48 | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.23/18.48 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 131.23/18.48 | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 131.23/18.48 | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 131.23/18.48 | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.23/18.48 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.23/18.48 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 131.23/18.48 | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 131.23/18.48 | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 131.23/18.48 | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 131.23/18.48 | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.23/18.48 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.23/18.48 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.23/18.48 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.23/18.48 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.23/18.48 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.23/18.48 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.23/18.48 | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.23/18.48 | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | BETA: splitting (1178) gives: % 131.23/18.48 | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.48 | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | | (1179) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.23/18.48 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.23/18.48 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.23/18.48 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.48 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.23/18.48 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.23/18.48 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.23/18.48 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.23/18.48 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.23/18.48 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.23/18.48 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.23/18.48 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.23/18.48 | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | | BETA: splitting (1179) gives: % 131.23/18.48 | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.48 | | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | | | (1180) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.23/18.48 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 131.23/18.48 | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.48 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.23/18.48 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 131.23/18.48 | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.48 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 131.23/18.48 | | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | | | ALPHA: (1180) implies: % 131.23/18.48 | | | | | | | | | | | | | | | | | | | (1181) ~ (all_56_1 = e3) % 131.23/18.48 | | | | | | | | | | | | | | | | | | | (1182) op(e3, e3) = all_56_1 % 131.23/18.48 | | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1174), (1181), (1182), (function-axioms) are % 131.23/18.48 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #766. % 131.23/18.48 | | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.48 | | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | | | (1183) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 131.23/18.48 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 131.23/18.48 | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 131.23/18.48 | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.23/18.48 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 131.23/18.48 | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.23/18.48 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 131.23/18.48 | | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | | | ALPHA: (1183) implies: % 131.23/18.48 | | | | | | | | | | | | | | | | | | | (1184) op(e2, e1) = e2 % 131.23/18.48 | | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (1161), (1184), (function-axioms) are % 131.23/18.48 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770. % 131.23/18.48 | | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | | End of split % 131.23/18.48 | | | | | | | | | | | | | | | | | | % 131.23/18.48 | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.48 | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | (1185) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 131.23/18.49 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.23/18.49 | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.23/18.49 | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.23/18.49 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.23/18.49 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.23/18.49 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.23/18.49 | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.23/18.49 | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.23/18.49 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.23/18.49 | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.23/18.49 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.23/18.49 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.23/18.49 | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.23/18.49 | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.23/18.49 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.23/18.49 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.23/18.49 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.23/18.49 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.23/18.49 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.23/18.49 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.23/18.49 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.23/18.49 | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.23/18.49 | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | BETA: splitting (1185) gives: % 131.23/18.49 | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.49 | | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | | (1186) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 131.23/18.49 | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | | ALPHA: (1186) implies: % 131.23/18.49 | | | | | | | | | | | | | | | | | | | (1187) op(e2, e0) = e2 % 131.23/18.49 | | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1162), (1187), (function-axioms) are % 131.23/18.49 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 131.23/18.49 | | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.49 | | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | | (1188) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.23/18.49 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.23/18.49 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.23/18.49 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.23/18.49 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.23/18.49 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.23/18.49 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.23/18.49 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.23/18.49 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.23/18.49 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.23/18.49 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.23/18.49 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.23/18.49 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | | BETA: splitting (1188) gives: % 131.23/18.49 | | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (1189) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | ALPHA: (1189) implies: % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (1190) op(e1, e1) = e2 % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1190), (function-axioms) are % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (1191) op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | ALPHA: (1191) implies: % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (1192) op(e0, e0) = all_56_31 % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (1193) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (39), (45), (100), (118), (157), (160), % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (163), (164), (165), (167), (189), (190), (204), % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (218), (226), (245), (246), (278), (295), (336), % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (338), (364), (369), (370), (371), (374), (378), % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (380), (1167), (1169), (1192), (1193), % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | #744. % 131.23/18.49 | | | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | | End of split % 131.23/18.49 | | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | | End of split % 131.23/18.49 | | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | | End of split % 131.23/18.49 | | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | End of split % 131.23/18.49 | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | Case 2: % 131.23/18.49 | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | (1194) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 131.23/18.49 | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | | REF_CLOSE: (278), (374), (378), (1169), (1194) are % 131.23/18.49 | | | | | | | | | | | | | | | | inconsistent by sub-proof #777. % 131.23/18.49 | | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | End of split % 131.23/18.49 | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | Case 2: % 131.23/18.49 | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | (1195) all_32_2 = e1 % 131.23/18.49 | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | COMBINE_EQS: (312), (1195) imply: % 131.23/18.49 | | | | | | | | | | | | | | | (1196) all_10_2 = e1 % 131.23/18.49 | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | SIMP: (1196) implies: % 131.23/18.49 | | | | | | | | | | | | | | | (1197) all_10_2 = e1 % 131.23/18.49 | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | REDUCE: (338), (1197) imply: % 131.23/18.49 | | | | | | | | | | | | | | | (1198) ~ (all_52_2 = e1) % 131.23/18.49 | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | REDUCE: (340), (1197) imply: % 131.23/18.49 | | | | | | | | | | | | | | | (1199) ~ (all_52_3 = e1) % 131.23/18.49 | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | REDUCE: (378), (1197) imply: % 131.23/18.49 | | | | | | | | | | | | | | | (1200) ~ (e2 = e1) % 131.23/18.49 | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | REDUCE: (45), (1197) imply: % 131.23/18.49 | | | | | | | | | | | | | | | (1201) op(e3, e3) = e1 % 131.23/18.49 | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 131.23/18.49 | | | | | | | | | | | | | | | % 131.23/18.49 | | | | | | | | | | | | | | | Case 1: % 131.23/18.49 | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | (1202) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.23/18.50 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.23/18.50 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.23/18.50 | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.23/18.50 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.23/18.50 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.23/18.50 | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.23/18.50 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.23/18.50 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.23/18.50 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.23/18.50 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.23/18.50 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.23/18.50 | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | BETA: splitting (1202) gives: % 131.23/18.50 | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | Case 1: % 131.23/18.50 | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | | (1203) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.23/18.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.23/18.50 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.23/18.50 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.23/18.50 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.23/18.50 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.23/18.50 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.23/18.50 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.23/18.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.23/18.50 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.23/18.50 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.23/18.50 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.23/18.50 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.23/18.50 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 131.23/18.50 | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (1149), (1201), (1203), % 131.23/18.50 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.23/18.50 | | | | | | | | | | | | | | | | | #552. % 131.23/18.50 | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | Case 2: % 131.23/18.50 | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | | (1204) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.23/18.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.23/18.50 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.23/18.50 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.23/18.50 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.50 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.23/18.50 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.23/18.50 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.23/18.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.23/18.50 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.50 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.23/18.50 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.23/18.50 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.50 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.23/18.50 | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (1159), (1201), (1204), % 131.23/18.50 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.23/18.50 | | | | | | | | | | | | | | | | | #716. % 131.23/18.50 | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | End of split % 131.23/18.50 | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | Case 2: % 131.23/18.50 | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | (1205) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.23/18.50 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.23/18.50 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.23/18.50 | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.23/18.50 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.23/18.50 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.23/18.50 | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 131.23/18.50 | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 131.23/18.50 | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.23/18.50 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 131.23/18.50 | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 131.23/18.50 | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 131.23/18.50 | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 131.23/18.50 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 131.23/18.50 | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 131.23/18.50 | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 131.23/18.50 | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.23/18.50 | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 131.23/18.50 | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 131.23/18.50 | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 131.23/18.50 | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.23/18.50 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.23/18.50 | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 131.23/18.50 | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 131.23/18.50 | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 131.23/18.50 | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 131.23/18.50 | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.23/18.50 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.23/18.50 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.23/18.50 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.23/18.50 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.23/18.50 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.23/18.50 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.23/18.50 | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.23/18.50 | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | BETA: splitting (1205) gives: % 131.23/18.50 | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | Case 1: % 131.23/18.50 | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | | (1206) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.23/18.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.23/18.50 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.50 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.23/18.50 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.23/18.50 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.50 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.23/18.50 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.23/18.50 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.23/18.50 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.23/18.50 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.23/18.50 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.23/18.50 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.23/18.50 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.23/18.50 | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | | BETA: splitting (1206) gives: % 131.23/18.50 | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.50 | | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | | | (1207) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.23/18.50 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 131.23/18.50 | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.50 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.23/18.50 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 131.23/18.50 | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.50 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 131.23/18.50 | | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | | | ALPHA: (1207) implies: % 131.23/18.50 | | | | | | | | | | | | | | | | | | (1208) op(e1, e3) = e1 % 131.23/18.50 | | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1198), (1208), (function-axioms) are % 131.23/18.50 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #725. % 131.23/18.50 | | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.50 | | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | | | (1209) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 131.23/18.50 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 131.23/18.50 | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 131.23/18.50 | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.23/18.50 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 131.23/18.50 | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.23/18.50 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 131.23/18.50 | | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | | | ALPHA: (1209) implies: % 131.23/18.50 | | | | | | | | | | | | | | | | | | (1210) op(e2, e1) = e2 % 131.23/18.50 | | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (1161), (1210), (function-axioms) are % 131.23/18.50 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770. % 131.23/18.50 | | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | | End of split % 131.23/18.50 | | | | | | | | | | | | | | | | | % 131.23/18.50 | | | | | | | | | | | | | | | | Case 2: % 131.23/18.50 | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | (1211) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.23/18.51 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.23/18.51 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 131.23/18.51 | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 131.23/18.51 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.51 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.23/18.51 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.23/18.51 | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.23/18.51 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.23/18.51 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.23/18.51 | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.23/18.51 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.23/18.51 | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.23/18.51 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.23/18.51 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.23/18.51 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.23/18.51 | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.23/18.51 | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.23/18.51 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.23/18.51 | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.23/18.51 | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.23/18.51 | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.23/18.51 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.23/18.51 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.23/18.51 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.23/18.51 | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.23/18.51 | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.23/18.51 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.23/18.51 | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.23/18.51 | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.23/18.51 | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.23/18.51 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.23/18.51 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.23/18.51 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.23/18.51 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.51 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.23/18.51 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.23/18.51 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.23/18.51 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.23/18.51 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.23/18.51 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.23/18.51 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.23/18.51 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.23/18.51 | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.23/18.51 | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | BETA: splitting (1211) gives: % 131.23/18.51 | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.51 | | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | | (1212) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.23/18.51 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 131.23/18.51 | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 131.23/18.51 | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.23/18.51 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 131.23/18.51 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.23/18.51 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 131.23/18.51 | | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | | ALPHA: (1212) implies: % 131.23/18.51 | | | | | | | | | | | | | | | | | | (1213) op(e2, e0) = e2 % 131.23/18.51 | | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1162), (1213), (function-axioms) are % 131.23/18.51 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 131.23/18.51 | | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.51 | | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | | (1214) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.23/18.51 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.23/18.51 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.23/18.51 | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.23/18.51 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.23/18.51 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.23/18.51 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.23/18.51 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.23/18.51 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.23/18.51 | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.23/18.51 | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.23/18.51 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.23/18.51 | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.23/18.51 | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.23/18.51 | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.23/18.51 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.23/18.51 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.23/18.51 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.23/18.51 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.23/18.51 | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.23/18.51 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.23/18.51 | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.23/18.51 | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.23/18.51 | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.23/18.51 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.23/18.51 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.23/18.51 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.23/18.51 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.51 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.23/18.51 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.23/18.51 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.23/18.51 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.23/18.51 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.23/18.51 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.23/18.51 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.23/18.51 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.23/18.51 | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.23/18.51 | | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | | BETA: splitting (1214) gives: % 131.23/18.51 | | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.51 | | | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | | | (1215) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.23/18.51 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 131.23/18.51 | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 131.23/18.51 | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 131.23/18.51 | | | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | | | ALPHA: (1215) implies: % 131.23/18.51 | | | | | | | | | | | | | | | | | | | (1216) op(e1, e1) = e2 % 131.23/18.51 | | | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1216), (function-axioms) are % 131.23/18.51 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 131.23/18.51 | | | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.51 | | | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | | | (1217) op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.23/18.51 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 131.23/18.51 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.23/18.51 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 131.23/18.51 | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.23/18.51 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 131.23/18.51 | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.23/18.51 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.23/18.51 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 131.23/18.51 | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.23/18.51 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.23/18.51 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 131.23/18.51 | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 131.23/18.51 | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 131.23/18.51 | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 131.23/18.51 | | | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | | | ALPHA: (1217) implies: % 131.23/18.51 | | | | | | | | | | | | | | | | | | | (1218) op(e0, e0) = all_56_31 % 131.23/18.51 | | | | | | | | | | | | | | | | | | | (1219) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.23/18.51 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.23/18.51 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 131.23/18.51 | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 131.23/18.51 | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 131.23/18.51 | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 131.23/18.51 | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 131.23/18.51 | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.23/18.51 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 131.23/18.51 | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 131.23/18.51 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.23/18.51 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 131.23/18.51 | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 131.23/18.51 | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 131.23/18.51 | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 131.23/18.51 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.23/18.51 | | | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (36), (82), (159), (168), (169), % 131.23/18.51 | | | | | | | | | | | | | | | | | | | (170), (232), (236), (238), (307), (349), (368), % 131.23/18.51 | | | | | | | | | | | | | | | | | | | (371), (380), (1149), (1151), (1160), (1199), % 131.23/18.51 | | | | | | | | | | | | | | | | | | | (1201), (1218), (1219), (function-axioms) are % 131.23/18.51 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #548. % 131.23/18.51 | | | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | | End of split % 131.23/18.51 | | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | | End of split % 131.23/18.51 | | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | | End of split % 131.23/18.51 | | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | | End of split % 131.23/18.51 | | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | | End of split % 131.23/18.51 | | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | End of split % 131.23/18.51 | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | Case 2: % 131.23/18.51 | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | (1220) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 131.23/18.51 | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 131.23/18.51 | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | | REF_CLOSE: (164), (165), (1161), (1162), (1220), % 131.23/18.51 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.23/18.51 | | | | | | | | | | | | | #625. % 131.23/18.51 | | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | End of split % 131.23/18.51 | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | Case 2: % 131.23/18.51 | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | (1221) all_54_5 = e1 | all_54_5 = e0 % 131.23/18.51 | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | | REF_CLOSE: (267), (373), (1153), (1221) are inconsistent by % 131.23/18.51 | | | | | | | | | | | | sub-proof #624. % 131.23/18.51 | | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | | End of split % 131.23/18.51 | | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | End of split % 131.23/18.51 | | | | | | | | | | % 131.23/18.51 | | | | | | | | | Case 2: % 131.23/18.51 | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | (1222) all_30_2 = e0 % 131.23/18.51 | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | COMBINE_EQS: (309), (1222) imply: % 131.23/18.51 | | | | | | | | | | (1223) all_8_2 = e0 % 131.23/18.51 | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | COMBINE_EQS: (301), (1223) imply: % 131.23/18.51 | | | | | | | | | | (1224) all_42_2 = e0 % 131.23/18.51 | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | REDUCE: (350), (1223) imply: % 131.23/18.51 | | | | | | | | | | (1225) ~ (all_52_4 = e0) % 131.23/18.51 | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | REDUCE: (354), (1223) imply: % 131.23/18.51 | | | | | | | | | | (1226) ~ (all_52_7 = e0) % 131.23/18.51 | | | | | | | | | | % 131.23/18.51 | | | | | | | | | | REDUCE: (376), (1223) imply: % 131.23/18.52 | | | | | | | | | | (1227) ~ (e3 = e0) % 131.23/18.52 | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | REDUCE: (373), (1223) imply: % 131.23/18.52 | | | | | | | | | | (1228) ~ (e1 = e0) % 131.23/18.52 | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | REDUCE: (42), (1223) imply: % 131.23/18.52 | | | | | | | | | | (1229) op(e2, e2) = e0 % 131.23/18.52 | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | BETA: splitting (79) gives: % 131.23/18.52 | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | Case 1: % 131.23/18.52 | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | (1230) ~ (all_32_2 = e1) % 131.23/18.52 | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | REDUCE: (312), (1230) imply: % 131.23/18.52 | | | | | | | | | | | (1231) ~ (all_10_2 = e1) % 131.23/18.52 | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | REF_CLOSE: (4), (36), (39), (45), (158), (164), (165), (167), % 131.23/18.52 | | | | | | | | | | | (168), (204), (206), (226), (278), (336), (346), % 131.23/18.52 | | | | | | | | | | | (371), (372), (374), (378), (1150), (1151), % 131.23/18.52 | | | | | | | | | | | (1226), (1229), (1231), (function-axioms) are % 131.23/18.52 | | | | | | | | | | | inconsistent by sub-proof #541. % 131.23/18.52 | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | Case 2: % 131.23/18.52 | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | (1232) all_32_2 = e1 % 131.23/18.52 | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | COMBINE_EQS: (312), (1232) imply: % 131.23/18.52 | | | | | | | | | | | (1233) all_10_2 = e1 % 131.23/18.52 | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | SIMP: (1233) implies: % 131.23/18.52 | | | | | | | | | | | (1234) all_10_2 = e1 % 131.23/18.52 | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | REDUCE: (338), (1234) imply: % 131.23/18.52 | | | | | | | | | | | (1235) ~ (all_52_2 = e1) % 131.23/18.52 | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | REDUCE: (342), (1234) imply: % 131.23/18.52 | | | | | | | | | | | (1236) ~ (all_52_4 = e1) % 131.23/18.52 | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | REDUCE: (346), (1234) imply: % 131.23/18.52 | | | | | | | | | | | (1237) ~ (all_52_12 = e1) % 131.23/18.52 | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | REDUCE: (378), (1234) imply: % 131.23/18.52 | | | | | | | | | | | (1238) ~ (e2 = e1) % 131.23/18.52 | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | REDUCE: (45), (1234) imply: % 131.23/18.52 | | | | | | | | | | | (1239) op(e3, e3) = e1 % 131.23/18.52 | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | BETA: splitting (82) gives: % 131.23/18.52 | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | Case 1: % 131.23/18.52 | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | (1240) ~ (all_34_2 = e3) % 131.23/18.52 | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | REDUCE: (307), (1240) imply: % 131.23/18.52 | | | | | | | | | | | | (1241) ~ (all_4_2 = e3) % 131.23/18.52 | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | BETA: splitting (189) gives: % 131.23/18.52 | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | Case 1: % 131.23/18.52 | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | (1242) all_54_15 = e3 % 131.23/18.52 | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | COMBINE_EQS: (245), (1242) imply: % 131.23/18.52 | | | | | | | | | | | | | (1243) all_4_2 = e3 % 131.23/18.52 | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | REDUCE: (1241), (1243) imply: % 131.23/18.52 | | | | | | | | | | | | | (1244) $false % 131.23/18.52 | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | CLOSE: (1244) is inconsistent. % 131.23/18.52 | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | Case 2: % 131.23/18.52 | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | (1245) ~ (all_54_15 = e3) % 131.23/18.52 | | | | | | | | | | | | | (1246) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 131.23/18.52 | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | BETA: splitting (1246) gives: % 131.23/18.52 | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | Case 1: % 131.23/18.52 | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | (1247) all_54_15 = e2 % 131.23/18.52 | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | COMBINE_EQS: (245), (1247) imply: % 131.23/18.52 | | | | | | | | | | | | | | (1248) all_4_2 = e2 % 131.23/18.52 | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | REDUCE: (380), (1248) imply: % 131.23/18.52 | | | | | | | | | | | | | | (1249) $false % 131.23/18.52 | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | CLOSE: (1249) is inconsistent. % 131.23/18.52 | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | Case 2: % 131.23/18.52 | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | (1250) ~ (all_54_15 = e2) % 131.23/18.52 | | | | | | | | | | | | | | (1251) all_54_15 = e1 | all_54_15 = e0 % 131.23/18.52 | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | BETA: splitting (1251) gives: % 131.23/18.52 | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | Case 1: % 131.23/18.52 | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | (1252) all_54_15 = e1 % 131.23/18.52 | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | COMBINE_EQS: (245), (1252) imply: % 131.23/18.52 | | | | | | | | | | | | | | | (1253) all_4_2 = e1 % 131.23/18.52 | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | REDUCE: (371), (1253) imply: % 131.23/18.52 | | | | | | | | | | | | | | | (1254) $false % 131.23/18.52 | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | CLOSE: (1254) is inconsistent. % 131.23/18.52 | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | Case 2: % 131.23/18.52 | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | (1255) all_54_15 = e0 % 131.23/18.52 | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | COMBINE_EQS: (245), (1255) imply: % 131.23/18.52 | | | | | | | | | | | | | | | (1256) all_4_2 = e0 % 131.23/18.52 | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | REDUCE: (368), (1256) imply: % 131.23/18.52 | | | | | | | | | | | | | | | (1257) ~ (all_52_12 = e0) % 131.23/18.52 | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | REDUCE: (380), (1256) imply: % 131.23/18.52 | | | | | | | | | | | | | | | (1258) ~ (e2 = e0) % 131.23/18.52 | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | REDUCE: (36), (1256) imply: % 131.23/18.52 | | | | | | | | | | | | | | | (1259) op(e0, e0) = e0 % 131.23/18.52 | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 131.23/18.52 | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | Case 1: % 131.23/18.52 | | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | | (1260) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.23/18.52 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.23/18.52 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.23/18.52 | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.23/18.52 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.23/18.52 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.23/18.52 | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.23/18.52 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.23/18.52 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.23/18.52 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.23/18.52 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.23/18.52 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.23/18.52 | | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (168), (169), (170), (232), (1225), % 131.23/18.52 | | | | | | | | | | | | | | | | (1229), (1239), (1257), (1260), (function-axioms) % 131.23/18.52 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #597. % 131.23/18.52 | | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | Case 2: % 131.23/18.52 | | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | | (1261) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.23/18.52 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.23/18.52 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.23/18.52 | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.23/18.52 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.23/18.52 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.23/18.52 | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 131.23/18.52 | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 131.23/18.52 | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.23/18.52 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 131.23/18.52 | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 131.23/18.52 | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 131.23/18.52 | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 131.23/18.52 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 131.23/18.52 | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 131.23/18.52 | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 131.23/18.52 | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.23/18.52 | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 131.23/18.52 | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 131.23/18.52 | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 131.23/18.52 | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.23/18.52 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.23/18.52 | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 131.23/18.52 | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 131.23/18.52 | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 131.23/18.52 | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 131.23/18.52 | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.23/18.52 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.23/18.52 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.23/18.52 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.23/18.52 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.23/18.52 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.23/18.52 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.23/18.52 | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.23/18.52 | | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | | BETA: splitting (1261) gives: % 131.23/18.52 | | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | | Case 1: % 131.23/18.52 | | | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | | | (1262) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.23/18.52 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.23/18.52 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.52 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.23/18.52 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.23/18.52 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.52 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.23/18.52 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.23/18.52 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.23/18.52 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.23/18.52 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.23/18.52 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.23/18.52 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.23/18.52 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.23/18.52 | | | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | | | BETA: splitting (1262) gives: % 131.23/18.52 | | | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.52 | | | | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | | | | (1263) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.23/18.52 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 131.23/18.52 | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.52 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.23/18.52 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 131.23/18.52 | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.52 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 131.23/18.52 | | | | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | | | | ALPHA: (1263) implies: % 131.23/18.52 | | | | | | | | | | | | | | | | | | (1264) op(e1, e3) = e1 % 131.23/18.52 | | | | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1235), (1264), (function-axioms) are % 131.23/18.52 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #725. % 131.23/18.52 | | | | | | | | | | | | | | | | | | % 131.23/18.52 | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.52 | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | (1265) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 131.23/18.53 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 131.23/18.53 | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 131.23/18.53 | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.23/18.53 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 131.23/18.53 | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.23/18.53 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 131.23/18.53 | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | ALPHA: (1265) implies: % 131.23/18.53 | | | | | | | | | | | | | | | | | | (1266) op(e2, e2) = e1 % 131.23/18.53 | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1229), (1266), (function-axioms) are % 131.23/18.53 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 131.23/18.53 | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | End of split % 131.23/18.53 | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | Case 2: % 131.23/18.53 | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | (1267) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.23/18.53 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.23/18.53 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 131.23/18.53 | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 131.23/18.53 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.53 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.23/18.53 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.23/18.53 | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.23/18.53 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.23/18.53 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.23/18.53 | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.23/18.53 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.23/18.53 | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.23/18.53 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.23/18.53 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.23/18.53 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.23/18.53 | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.23/18.53 | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.23/18.53 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.23/18.53 | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.23/18.53 | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.23/18.53 | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.23/18.53 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.23/18.53 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.23/18.53 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.23/18.53 | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.23/18.53 | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.23/18.53 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.23/18.53 | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.23/18.53 | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.23/18.53 | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.23/18.53 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.23/18.53 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.23/18.53 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.23/18.53 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.53 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.23/18.53 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.23/18.53 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.23/18.53 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.23/18.53 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.23/18.53 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.23/18.53 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.23/18.53 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.23/18.53 | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.23/18.53 | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (372), (1259), (1267), % 131.23/18.53 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.23/18.53 | | | | | | | | | | | | | | | | | #596. % 131.23/18.53 | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | End of split % 131.23/18.53 | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | End of split % 131.23/18.53 | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | End of split % 131.23/18.53 | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | End of split % 131.23/18.53 | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | End of split % 131.23/18.53 | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | Case 2: % 131.23/18.53 | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | (1268) all_34_2 = e3 % 131.23/18.53 | | | | | | | | | | | | (1269) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & % 131.23/18.53 | | | | | | | | | | | | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3) % 131.23/18.53 | | | | | | | | | | | | = all_34_1 & $i(all_34_1)) % 131.23/18.53 | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | COMBINE_EQS: (307), (1268) imply: % 131.23/18.53 | | | | | | | | | | | | (1270) all_4_2 = e3 % 131.23/18.53 | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | SIMP: (1270) implies: % 131.23/18.53 | | | | | | | | | | | | (1271) all_4_2 = e3 % 131.23/18.53 | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | REDUCE: (349), (1271) imply: % 131.23/18.53 | | | | | | | | | | | | (1272) ~ (all_52_3 = e3) % 131.23/18.53 | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | REDUCE: (360), (1271) imply: % 131.23/18.53 | | | | | | | | | | | | (1273) ~ (all_52_7 = e3) % 131.23/18.53 | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | REDUCE: (367), (1271) imply: % 131.23/18.53 | | | | | | | | | | | | (1274) ~ (all_52_11 = e3) % 131.23/18.53 | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | REDUCE: (368), (1271) imply: % 131.23/18.53 | | | | | | | | | | | | (1275) ~ (all_52_12 = e3) % 131.23/18.53 | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | REDUCE: (36), (1271) imply: % 131.23/18.53 | | | | | | | | | | | | (1276) op(e0, e0) = e3 % 131.23/18.53 | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | BETA: splitting (1269) gives: % 131.23/18.53 | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | Case 1: % 131.23/18.53 | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | (1277) ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & % 131.23/18.53 | | | | | | | | | | | | | $i(all_34_0) % 131.23/18.53 | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | ALPHA: (1277) implies: % 131.23/18.53 | | | | | | | | | | | | | (1278) ~ (all_34_0 = e2) % 131.23/18.53 | | | | | | | | | | | | | (1279) op(e3, e0) = all_34_0 % 131.23/18.53 | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | BETA: splitting (94) gives: % 131.23/18.53 | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | Case 1: % 131.23/18.53 | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | (1280) ~ (all_42_2 = e0) % 131.23/18.53 | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | REDUCE: (1224), (1280) imply: % 131.23/18.53 | | | | | | | | | | | | | | (1281) $false % 131.23/18.53 | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | CLOSE: (1281) is inconsistent. % 131.23/18.53 | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | Case 2: % 131.23/18.53 | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | (1282) ( ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 & % 131.23/18.53 | | | | | | | | | | | | | | $i(all_42_0)) | ( ~ (all_42_1 = e3) & op(e0, e0) % 131.23/18.53 | | | | | | | | | | | | | | = all_42_1 & $i(all_42_1)) % 131.23/18.53 | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | BETA: splitting (1282) gives: % 131.23/18.53 | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | Case 1: % 131.23/18.53 | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | (1283) ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 & % 131.23/18.53 | | | | | | | | | | | | | | | $i(all_42_0) % 131.23/18.53 | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | ALPHA: (1283) implies: % 131.23/18.53 | | | | | | | | | | | | | | | (1284) ~ (all_42_0 = e1) % 131.23/18.53 | | | | | | | | | | | | | | | (1285) op(e0, e2) = all_42_0 % 131.23/18.53 | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 131.23/18.53 | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | Case 1: % 131.23/18.53 | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | (1286) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 131.23/18.53 | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 131.23/18.53 | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | BETA: splitting (1286) gives: % 131.23/18.53 | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | Case 1: % 131.23/18.53 | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | (1287) all_57_1 = e3 & op(e3, e2) = e3 % 131.23/18.53 | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | ALPHA: (1287) implies: % 131.23/18.53 | | | | | | | | | | | | | | | | | (1288) op(e3, e2) = e3 % 131.23/18.53 | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 131.23/18.53 | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.53 | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | (1289) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 131.23/18.53 | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 131.23/18.53 | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | BETA: splitting (1289) gives: % 131.23/18.53 | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1290) all_57_12 = e3 & op(e0, e3) = e3 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1272), (1290), (function-axioms) are % 131.23/18.53 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #628. % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1291) all_57_13 = e3 & op(e0, e2) = e3 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1273), (1291), (function-axioms) are % 131.23/18.53 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #556. % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | End of split % 131.23/18.53 | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.53 | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | (1292) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 131.23/18.53 | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 131.23/18.53 | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | BETA: splitting (1292) gives: % 131.23/18.53 | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1293) all_57_14 = e3 & op(e0, e1) = e3 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (1274), (1293), (function-axioms) are % 131.23/18.53 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #652. % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1294) all_57_15 = e3 & op(e0, e0) = e3 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, % 131.23/18.53 | | | | | | | | | | | | | | | | | | | all_42_0, e2, e0, simplifying with (158), (1285) % 131.23/18.53 | | | | | | | | | | | | | | | | | | | gives: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1295) all_52_7 = all_42_0 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 131.23/18.53 | | | | | | | | | | | | | | | | | | | all_34_0, e0, e3, simplifying with (168), (1279) % 131.23/18.53 | | | | | | | | | | | | | | | | | | | gives: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1296) all_52_12 = all_34_0 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3, % 131.23/18.53 | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (1288) gives: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1297) all_52_4 = e3 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (1295) imply: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1298) all_54_13 = all_42_0 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (1296) imply: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1299) all_54_3 = all_34_0 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | REDUCE: (134), (1297) imply: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1300) ~ (all_52_8 = e3) % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | REDUCE: (1273), (1295) imply: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1301) ~ (all_42_0 = e3) % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | REDUCE: (1226), (1295) imply: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1302) ~ (all_42_0 = e0) % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | REDUCE: (1275), (1296) imply: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1303) ~ (all_34_0 = e3) % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | REDUCE: (1237), (1296) imply: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | (1304) ~ (all_34_0 = e1) % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | (1305) all_54_13 = e3 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1298), (1301), (1305) are inconsistent by % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | sub-proof #617. % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | (1306) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | (1307) all_54_3 = e3 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1299), (1307) imply: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | (1308) all_34_0 = e3 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | SIMP: (1308) implies: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | (1309) all_34_0 = e3 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1303), (1309) imply: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | (1310) $false % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1310) is inconsistent. % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | (1311) ~ (all_54_3 = e3) % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | (1312) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1312) gives: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | (1313) all_54_3 = e2 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1278), (1299), (1313) are inconsistent by % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | sub-proof #707. % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | (1314) all_54_3 = e1 | all_54_3 = e0 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1314) gives: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | (1315) all_54_3 = e1 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1299), (1304), (1315) are inconsistent by % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #706. % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | (1316) all_54_3 = e0 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1299), (1316) imply: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | (1317) all_34_0 = e0 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1317) implies: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | (1318) all_34_0 = e0 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1279), (1318) imply: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | (1319) op(e3, e0) = e0 % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.53 | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (1320) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1320) gives: % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (1321) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (1149), (1239), (1321), % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | #552. % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (1322) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.23/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (1229), (1275), (1322), % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | #622. % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (1323) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1323) gives: % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (1324) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1229), (1319), (1324), (function-axioms) are % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #540. % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (1325) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1325) gives: % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (1326) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1326) implies: % 131.54/18.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (1327) ~ (all_56_15 = e2) % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (1328) op(e0, e2) = all_56_15 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1284), (1285), (1298), (1302), (1306), (1327), % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (1328), (function-axioms) are inconsistent by % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #539. % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (1329) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (39), (158), (372), (1151), (1226), % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (1276), (1319), (1329), (function-axioms) are % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #537. % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | Case 2: % 131.54/18.55 | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | (1330) all_57_3 = e3 & op(e2, e2) = e3 % 131.54/18.55 | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | ALPHA: (1330) implies: % 131.54/18.55 | | | | | | | | | | | | | | | | | (1331) op(e2, e2) = e3 % 131.54/18.55 | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1229), (1331), (function-axioms) are % 131.54/18.55 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 131.54/18.55 | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | Case 2: % 131.54/18.55 | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | (1332) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 131.54/18.55 | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 131.54/18.55 | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (1148), (1273), (1332), % 131.54/18.55 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.54/18.55 | | | | | | | | | | | | | | | | #555. % 131.54/18.55 | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | Case 2: % 131.54/18.55 | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | (1333) ~ (all_42_1 = e3) & op(e0, e0) = all_42_1 & % 131.54/18.55 | | | | | | | | | | | | | | | $i(all_42_1) % 131.54/18.55 | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | REF_CLOSE: (1276), (1333), (function-axioms) are inconsistent % 131.54/18.55 | | | | | | | | | | | | | | | by sub-proof #602. % 131.54/18.55 | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | Case 2: % 131.54/18.55 | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | (1334) ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 & % 131.54/18.55 | | | | | | | | | | | | | $i(all_34_1) % 131.54/18.55 | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | ALPHA: (1334) implies: % 131.54/18.55 | | | | | | | | | | | | | (1335) ~ (all_34_1 = e1) % 131.54/18.55 | | | | | | | | | | | | | (1336) op(e3, e3) = all_34_1 % 131.54/18.55 | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | REF_CLOSE: (1239), (1335), (1336), (function-axioms) are % 131.54/18.55 | | | | | | | | | | | | | inconsistent by sub-proof #626. % 131.54/18.55 | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | | % 131.54/18.55 | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | % 131.54/18.55 | | | | | | | | End of split % 131.54/18.55 | | | | | | | | % 131.54/18.55 | | | | | | | Case 2: % 131.54/18.55 | | | | | | | | % 131.54/18.55 | | | | | | | | (1337) all_20_2 = e2 % 131.54/18.55 | | | | | | | | % 131.54/18.55 | | | | | | | | COMBINE_EQS: (318), (1337) imply: % 131.54/18.55 | | | | | | | | (1338) all_4_2 = e2 % 131.54/18.55 | | | | | | | | % 131.54/18.55 | | | | | | | | SIMP: (1338) implies: % 131.54/18.55 | | | | | | | | (1339) all_4_2 = e2 % 131.54/18.55 | | | | | | | | % 131.54/18.55 | | | | | | | | REDUCE: (360), (1339) imply: % 131.54/18.55 | | | | | | | | (1340) ~ (all_52_7 = e2) % 131.54/18.55 | | | | | | | | % 131.54/18.55 | | | | | | | | REDUCE: (367), (1339) imply: % 131.54/18.55 | | | | | | | | (1341) ~ (all_52_11 = e2) % 131.54/18.55 | | | | | | | | % 131.54/18.55 | | | | | | | | REDUCE: (368), (1339) imply: % 131.54/18.55 | | | | | | | | (1342) ~ (all_52_12 = e2) % 131.54/18.55 | | | | | | | | % 131.54/18.55 | | | | | | | | REDUCE: (369), (1339) imply: % 131.54/18.55 | | | | | | | | (1343) ~ (all_52_13 = e2) % 131.54/18.55 | | | | | | | | % 131.54/18.55 | | | | | | | | REDUCE: (370), (1339) imply: % 131.54/18.55 | | | | | | | | (1344) ~ (all_52_14 = e2) % 131.54/18.55 | | | | | | | | % 131.54/18.55 | | | | | | | | REDUCE: (36), (1339) imply: % 131.54/18.55 | | | | | | | | (1345) op(e0, e0) = e2 % 131.54/18.55 | | | | | | | | % 131.54/18.55 | | | | | | | | BETA: splitting (73) gives: % 131.54/18.55 | | | | | | | | % 131.54/18.55 | | | | | | | | Case 1: % 131.54/18.55 | | | | | | | | | % 131.54/18.55 | | | | | | | | | (1346) ~ (all_28_2 = e3) % 131.54/18.55 | | | | | | | | | % 131.54/18.55 | | | | | | | | | REDUCE: (316), (1346) imply: % 131.54/18.55 | | | | | | | | | (1347) ~ (all_6_2 = e3) % 131.54/18.55 | | | | | | | | | % 131.54/18.55 | | | | | | | | | BETA: splitting (76) gives: % 131.54/18.55 | | | | | | | | | % 131.54/18.55 | | | | | | | | | Case 1: % 131.54/18.55 | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | (1348) ~ (all_30_2 = e0) % 131.54/18.55 | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | REDUCE: (309), (1348) imply: % 131.54/18.55 | | | | | | | | | | (1349) ~ (all_8_2 = e0) % 131.54/18.55 | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | BETA: splitting (199) gives: % 131.54/18.55 | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | Case 1: % 131.54/18.55 | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | (1350) all_54_5 = e3 % 131.54/18.55 | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | REF_CLOSE: (267), (376), (1350) are inconsistent by sub-proof % 131.54/18.55 | | | | | | | | | | | #554. % 131.54/18.55 | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | Case 2: % 131.54/18.55 | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | (1351) ~ (all_54_5 = e3) % 131.54/18.55 | | | | | | | | | | | (1352) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 131.54/18.55 | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | BETA: splitting (1352) gives: % 131.54/18.55 | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | Case 1: % 131.54/18.55 | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | (1353) all_54_5 = e2 % 131.54/18.55 | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | COMBINE_EQS: (267), (1353) imply: % 131.54/18.55 | | | | | | | | | | | | (1354) all_8_2 = e2 % 131.54/18.55 | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | SIMP: (1354) implies: % 131.54/18.55 | | | | | | | | | | | | (1355) all_8_2 = e2 % 131.54/18.55 | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | REDUCE: (347), (1355) imply: % 131.54/18.55 | | | | | | | | | | | | (1356) ~ (all_52_1 = e2) % 131.54/18.55 | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | REDUCE: (352), (1355) imply: % 131.54/18.55 | | | | | | | | | | | | (1357) ~ (all_52_6 = e2) % 131.54/18.55 | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | REDUCE: (356), (1355) imply: % 131.54/18.55 | | | | | | | | | | | | (1358) ~ (all_52_9 = e2) % 131.54/18.55 | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | REDUCE: (376), (1355) imply: % 131.54/18.55 | | | | | | | | | | | | (1359) ~ (e3 = e2) % 131.54/18.55 | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | REDUCE: (42), (1355) imply: % 131.54/18.55 | | | | | | | | | | | | (1360) op(e2, e2) = e2 % 131.54/18.55 | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | BETA: splitting (221) gives: % 131.54/18.55 | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | Case 1: % 131.54/18.55 | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | (1361) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 131.54/18.55 | | | | | | | | | | | | | & op(e2, e1) = e2) % 131.54/18.55 | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | BETA: splitting (1361) gives: % 131.54/18.55 | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | Case 1: % 131.54/18.55 | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | (1362) all_57_4 = e2 & op(e3, e1) = e2 % 131.54/18.55 | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | ALPHA: (1362) implies: % 131.54/18.55 | | | | | | | | | | | | | | (1363) op(e3, e1) = e2 % 131.54/18.55 | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | BETA: splitting (235) gives: % 131.54/18.55 | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | Case 1: % 131.54/18.55 | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | (1364) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 131.54/18.55 | | | | | | | | | | | | | | | & op(e2, e3) = e2) % 131.54/18.55 | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | REF_CLOSE: (45), (167), (378), (1356), (1364), % 131.54/18.55 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.54/18.55 | | | | | | | | | | | | | | | #535. % 131.54/18.55 | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | Case 2: % 131.54/18.55 | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | (1365) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 131.54/18.55 | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 131.54/18.55 | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | BETA: splitting (1365) gives: % 131.54/18.55 | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | Case 1: % 131.54/18.55 | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | (1366) all_57_6 = e2 & op(e1, e3) = e2 % 131.54/18.55 | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | ALPHA: (1366) implies: % 131.54/18.55 | | | | | | | | | | | | | | | | (1367) op(e1, e3) = e2 % 131.54/18.55 | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (45), (91), (121), (123), (149), % 131.54/18.55 | | | | | | | | | | | | | | | | (157), (163), (164), (165), (167), (169), (190), % 131.54/18.55 | | | | | | | | | | | | | | | | (206), (246), (332), (344), (361), (364), (374), % 131.54/18.55 | | | | | | | | | | | | | | | | (1343), (1345), (1347), (1360), (1363), (1367), % 131.54/18.55 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.54/18.55 | | | | | | | | | | | | | | | | #522. % 131.54/18.55 | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | Case 2: % 131.54/18.55 | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | (1368) all_57_12 = e2 & op(e0, e3) = e2 % 131.54/18.55 | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | ALPHA: (1368) implies: % 131.54/18.55 | | | | | | | | | | | | | | | | (1369) all_57_12 = e2 % 131.54/18.55 | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 131.54/18.55 | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | Case 1: % 131.54/18.55 | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | (1370) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 131.54/18.55 | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 131.54/18.55 | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | BETA: splitting (1370) gives: % 131.54/18.55 | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | Case 1: % 131.54/18.55 | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | (1371) all_57_6 = e2 & op(e1, e3) = e2 % 131.54/18.55 | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | ALPHA: (1371) implies: % 131.54/18.55 | | | | | | | | | | | | | | | | | | (1372) all_57_6 = e2 % 131.54/18.55 | | | | | | | | | | | | | | | | | | (1373) op(e1, e3) = e2 % 131.54/18.55 | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 131.54/18.55 | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | Case 1: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | (1374) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 131.54/18.55 | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | BETA: splitting (1374) gives: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | Case 1: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | (1375) all_57_0 = e0 & op(e3, e3) = e0 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | ALPHA: (1375) implies: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | (1376) op(e3, e3) = e0 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (374), (1376), (function-axioms) are % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #534. % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | Case 2: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | (1377) all_57_2 = e0 & op(e2, e3) = e0 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | ALPHA: (1377) implies: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | (1378) all_57_2 = e0 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | Case 1: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | (1379) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1379) gives: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | (1380) all_57_0 = e1 & op(e3, e3) = e1 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1380) implies: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | (1381) op(e3, e3) = e1 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | (1382) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1382) gives: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | (1383) all_57_0 = e3 & op(e3, e3) = e3 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1383) implies: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | (1384) op(e3, e3) = e3 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1381), (1384), (function-axioms) are % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #775. % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | (1385) all_57_2 = e3 & op(e2, e3) = e3 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1385) implies: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | (1386) all_57_2 = e3 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (231), (1369), (1372), (1381), % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | (1386), (function-axioms) are inconsistent by % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #519. % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | (1387) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1387) gives: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | (1388) all_57_6 = e3 & op(e1, e3) = e3 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1388) implies: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | (1389) all_57_6 = e3 % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1372), (1389) are inconsistent by sub-proof % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | #592. % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.54/18.55 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | | (1390) all_57_12 = e3 & op(e0, e3) = e3 % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1390) implies: % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | | (1391) all_57_12 = e3 % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1369), (1391) are inconsistent by sub-proof % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | | #518. % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | End of split % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | (1392) all_57_2 = e1 & op(e2, e3) = e1 % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1392) implies: % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | (1393) all_57_2 = e1 % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1378), (1393) are inconsistent by sub-proof % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | #646. % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | End of split % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | Case 2: % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | (1394) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1394) gives: % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | (1395) all_57_6 = e1 & op(e1, e3) = e1 % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1395) implies: % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | (1396) op(e1, e3) = e1 % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (1373), (1396), (function-axioms) are % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #517. % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | (1397) all_57_12 = e1 & op(e0, e3) = e1 % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1369), (1397) are inconsistent by sub-proof % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | #516. % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | End of split % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | End of split % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | End of split % 131.54/18.56 | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | Case 2: % 131.54/18.56 | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | (1398) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 131.54/18.56 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 131.54/18.56 | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | BETA: splitting (1398) gives: % 131.54/18.56 | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | Case 1: % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | (1399) all_57_6 = e0 & op(e1, e3) = e0 % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1372), (1399) are inconsistent by sub-proof % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | #520. % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | Case 2: % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | (1400) all_57_12 = e0 & op(e0, e3) = e0 % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1369), (1400) are inconsistent by sub-proof % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | #578. % 131.54/18.56 | | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | | End of split % 131.54/18.56 | | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | End of split % 131.54/18.56 | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | Case 2: % 131.54/18.56 | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | (1401) all_57_7 = e2 & op(e1, e2) = e2 % 131.54/18.56 | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (1357), (1401), (function-axioms) are % 131.54/18.56 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515. % 131.54/18.56 | | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | End of split % 131.54/18.56 | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | Case 2: % 131.54/18.56 | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | (1402) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 131.54/18.56 | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 131.54/18.56 | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (372), (1344), (1402), % 131.54/18.56 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.54/18.56 | | | | | | | | | | | | | | | | | #513. % 131.54/18.56 | | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | End of split % 131.54/18.56 | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | End of split % 131.54/18.56 | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | End of split % 131.54/18.56 | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | Case 2: % 131.54/18.56 | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | (1403) all_57_5 = e2 & op(e2, e1) = e2 % 131.54/18.56 | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | ALPHA: (1403) implies: % 131.54/18.56 | | | | | | | | | | | | | | (1404) op(e2, e1) = e2 % 131.54/18.56 | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | REF_CLOSE: (165), (1358), (1404), (function-axioms) are % 131.54/18.56 | | | | | | | | | | | | | | inconsistent by sub-proof #770. % 131.54/18.56 | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | End of split % 131.54/18.56 | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | Case 2: % 131.54/18.56 | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | (1405) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 131.54/18.56 | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 131.54/18.56 | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | REF_CLOSE: (39), (157), (372), (1341), (1405), % 131.54/18.56 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.54/18.56 | | | | | | | | | | | | | #511. % 131.54/18.56 | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | End of split % 131.54/18.56 | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | Case 2: % 131.54/18.56 | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | (1406) all_54_5 = e1 | all_54_5 = e0 % 131.54/18.56 | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | REF_CLOSE: (267), (373), (1349), (1406) are inconsistent by % 131.54/18.56 | | | | | | | | | | | | sub-proof #624. % 131.54/18.56 | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | End of split % 131.54/18.56 | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | End of split % 131.54/18.56 | | | | | | | | | | % 131.54/18.56 | | | | | | | | | Case 2: % 131.54/18.56 | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | (1407) all_30_2 = e0 % 131.54/18.56 | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | COMBINE_EQS: (309), (1407) imply: % 131.54/18.56 | | | | | | | | | | (1408) all_8_2 = e0 % 131.54/18.56 | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | SIMP: (1408) implies: % 131.54/18.56 | | | | | | | | | | (1409) all_8_2 = e0 % 131.54/18.56 | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | REDUCE: (350), (1409) imply: % 131.54/18.56 | | | | | | | | | | (1410) ~ (all_52_4 = e0) % 131.54/18.56 | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | REDUCE: (354), (1409) imply: % 131.54/18.56 | | | | | | | | | | (1411) ~ (all_52_7 = e0) % 131.54/18.56 | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | REDUCE: (376), (1409) imply: % 131.54/18.56 | | | | | | | | | | (1412) ~ (e3 = e0) % 131.54/18.56 | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | REDUCE: (373), (1409) imply: % 131.54/18.56 | | | | | | | | | | (1413) ~ (e1 = e0) % 131.54/18.56 | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | REDUCE: (42), (1409) imply: % 131.54/18.56 | | | | | | | | | | (1414) op(e2, e2) = e0 % 131.54/18.56 | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | BETA: splitting (79) gives: % 131.54/18.56 | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | Case 1: % 131.54/18.56 | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | (1415) ~ (all_32_2 = e1) % 131.54/18.56 | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | REDUCE: (312), (1415) imply: % 131.54/18.56 | | | | | | | | | | | (1416) ~ (all_10_2 = e1) % 131.54/18.56 | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | BETA: splitting (204) gives: % 131.54/18.56 | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | Case 1: % 131.54/18.56 | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | (1417) all_54_0 = e3 % 131.54/18.56 | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | COMBINE_EQS: (278), (1417) imply: % 131.54/18.56 | | | | | | | | | | | | (1418) all_10_2 = e3 % 131.54/18.56 | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | SIMP: (1418) implies: % 131.54/18.56 | | | | | | | | | | | | (1419) all_10_2 = e3 % 131.54/18.56 | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | REDUCE: (346), (1419) imply: % 131.54/18.56 | | | | | | | | | | | | (1420) ~ (all_52_12 = e3) % 131.54/18.56 | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | REDUCE: (45), (1419) imply: % 131.54/18.56 | | | | | | | | | | | | (1421) op(e3, e3) = e3 % 131.54/18.56 | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | BETA: splitting (206) gives: % 131.54/18.56 | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | Case 1: % 131.54/18.56 | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | (1422) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.54/18.56 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.54/18.56 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.54/18.56 | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.54/18.56 | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.54/18.56 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.54/18.56 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.54/18.56 | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.54/18.56 | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.54/18.56 | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.54/18.56 | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.54/18.56 | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.54/18.56 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.54/18.56 | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 131.54/18.56 | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.54/18.56 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.54/18.56 | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.54/18.56 | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.54/18.56 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.54/18.56 | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.54/18.56 | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.54/18.56 | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.54/18.56 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.54/18.56 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.54/18.56 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.54/18.56 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.54/18.56 | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.54/18.56 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.54/18.56 | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | BETA: splitting (1422) gives: % 131.54/18.56 | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | Case 1: % 131.54/18.56 | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | (1423) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.54/18.56 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.54/18.56 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.54/18.56 | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.54/18.56 | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.54/18.56 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.54/18.56 | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.54/18.56 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.54/18.56 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.54/18.56 | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.54/18.56 | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.54/18.56 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 131.54/18.56 | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (1421), (1423), (function-axioms) are % 131.54/18.56 | | | | | | | | | | | | | | inconsistent by sub-proof #623. % 131.54/18.56 | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | Case 2: % 131.54/18.56 | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | (1424) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.54/18.56 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.54/18.56 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.54/18.56 | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.54/18.56 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.54/18.56 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.54/18.56 | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.54/18.56 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.54/18.56 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.54/18.56 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.54/18.56 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.54/18.56 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.54/18.56 | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (1414), (1420), (1424), % 131.54/18.56 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.54/18.56 | | | | | | | | | | | | | | #622. % 131.54/18.56 | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | End of split % 131.54/18.56 | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | Case 2: % 131.54/18.56 | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | (1425) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.54/18.56 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.54/18.56 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.54/18.56 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.54/18.56 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.54/18.56 | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.54/18.56 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.54/18.56 | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.54/18.56 | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.54/18.56 | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.54/18.56 | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.54/18.56 | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.54/18.56 | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.54/18.56 | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 131.54/18.56 | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 131.54/18.56 | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.54/18.56 | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 131.54/18.56 | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.54/18.56 | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 131.54/18.56 | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.54/18.56 | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 131.54/18.56 | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 131.54/18.56 | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.54/18.56 | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.54/18.56 | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 131.54/18.56 | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 131.54/18.56 | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.54/18.56 | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 131.54/18.56 | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 131.54/18.56 | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 131.54/18.56 | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 131.54/18.56 | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.54/18.56 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 131.54/18.56 | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.54/18.56 | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.54/18.56 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 131.54/18.56 | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 131.54/18.56 | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 131.54/18.56 | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.54/18.56 | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.54/18.56 | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.54/18.56 | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.54/18.56 | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 131.54/18.56 | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 131.54/18.56 | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 131.54/18.56 | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 131.54/18.56 | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 131.54/18.56 | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 131.54/18.56 | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 131.54/18.56 | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.54/18.56 | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.54/18.56 | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.54/18.56 | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.54/18.56 | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.54/18.56 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.54/18.56 | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.54/18.56 | | | | | | | | | | | | | & $i(all_56_29)))) % 131.54/18.56 | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | BETA: splitting (1425) gives: % 131.54/18.56 | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | Case 1: % 131.54/18.56 | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | (1426) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.54/18.56 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.54/18.56 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.54/18.56 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.54/18.56 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.54/18.56 | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.54/18.56 | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.54/18.56 | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.54/18.56 | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.54/18.56 | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.54/18.56 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.54/18.56 | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.54/18.56 | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (1347), (1414), (1426), % 131.54/18.56 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.54/18.56 | | | | | | | | | | | | | | #621. % 131.54/18.56 | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | Case 2: % 131.54/18.56 | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | (1427) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.54/18.56 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.54/18.56 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 131.54/18.56 | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 131.54/18.56 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.54/18.56 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.54/18.56 | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.54/18.56 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.54/18.56 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.54/18.56 | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.54/18.56 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.54/18.56 | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.54/18.56 | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.54/18.56 | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.54/18.56 | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.54/18.56 | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.54/18.56 | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.54/18.56 | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.54/18.56 | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.54/18.56 | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.54/18.56 | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.54/18.56 | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.54/18.56 | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.54/18.56 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.54/18.56 | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.54/18.56 | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.54/18.56 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.54/18.56 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.54/18.56 | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.54/18.56 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.54/18.56 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.54/18.56 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.54/18.56 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.54/18.56 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.54/18.56 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.54/18.56 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.54/18.56 | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.54/18.56 | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | BETA: splitting (1427) gives: % 131.54/18.56 | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | Case 1: % 131.54/18.56 | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | (1428) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.54/18.56 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 131.54/18.56 | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 131.54/18.56 | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.54/18.56 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 131.54/18.56 | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.54/18.56 | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 131.54/18.56 | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | ALPHA: (1428) implies: % 131.54/18.56 | | | | | | | | | | | | | | | (1429) op(e2, e0) = e2 % 131.54/18.56 | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | REF_CLOSE: (164), (1343), (1429), (function-axioms) are % 131.54/18.56 | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 131.54/18.56 | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | Case 2: % 131.54/18.56 | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | (1430) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.54/18.56 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.54/18.56 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.54/18.56 | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.54/18.56 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.54/18.56 | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.54/18.56 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.54/18.56 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.54/18.56 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.54/18.56 | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.54/18.56 | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.54/18.56 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.54/18.56 | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.54/18.56 | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.54/18.56 | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.54/18.56 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.54/18.56 | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.54/18.56 | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.54/18.56 | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.54/18.56 | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.54/18.56 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.54/18.56 | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.54/18.56 | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.54/18.56 | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.54/18.56 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.54/18.56 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.54/18.56 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.54/18.56 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.54/18.56 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.54/18.56 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.54/18.56 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.54/18.56 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.54/18.56 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.54/18.56 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.54/18.56 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.54/18.56 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.54/18.56 | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.54/18.56 | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | BETA: splitting (1430) gives: % 131.54/18.56 | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | Case 1: % 131.54/18.56 | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | (1431) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.54/18.56 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 131.54/18.56 | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.54/18.56 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.54/18.56 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 131.54/18.56 | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.54/18.56 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 131.54/18.56 | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | ALPHA: (1431) implies: % 131.54/18.56 | | | | | | | | | | | | | | | | (1432) op(e1, e1) = e2 % 131.54/18.56 | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1432), (function-axioms) are % 131.54/18.56 | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 131.54/18.56 | | | | | | | | | | | | | | | | % 131.54/18.56 | | | | | | | | | | | | | | | Case 2: % 131.54/18.56 | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | | (1433) op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.54/18.57 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.54/18.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 131.54/18.57 | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.54/18.57 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 131.54/18.57 | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.54/18.57 | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 131.54/18.57 | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.54/18.57 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.54/18.57 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.54/18.57 | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 131.54/18.57 | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.54/18.57 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.54/18.57 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 131.54/18.57 | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 131.54/18.57 | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 131.54/18.57 | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 131.54/18.57 | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_29))) % 131.54/18.57 | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | | ALPHA: (1433) implies: % 131.54/18.57 | | | | | | | | | | | | | | | | (1434) op(e0, e0) = all_56_31 % 131.54/18.57 | | | | | | | | | | | | | | | | (1435) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.54/18.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.54/18.57 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.54/18.57 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.54/18.57 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 131.54/18.57 | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 131.54/18.57 | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 131.54/18.57 | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 131.54/18.57 | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 131.54/18.57 | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 131.54/18.57 | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 131.54/18.57 | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 131.54/18.57 | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.54/18.57 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 131.54/18.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.54/18.57 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 131.54/18.57 | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 131.54/18.57 | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 131.54/18.57 | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.54/18.57 | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, % 131.54/18.57 | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (1345), (1434) % 131.54/18.57 | | | | | | | | | | | | | | | | gives: % 131.54/18.57 | | | | | | | | | | | | | | | | (1436) all_56_31 = e2 % 131.54/18.57 | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | | BETA: splitting (1435) gives: % 131.54/18.57 | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | | Case 1: % 131.54/18.57 | | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | | | (1437) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.54/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.54/18.57 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.54/18.57 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.54/18.57 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 131.54/18.57 | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 131.54/18.57 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 131.54/18.57 | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 131.54/18.57 | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 131.54/18.57 | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 131.54/18.57 | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 131.54/18.57 | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 131.54/18.57 | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 131.54/18.57 | | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1411), (1421), (1437), (function-axioms) % 131.54/18.57 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #544. % 131.54/18.57 | | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | | Case 2: % 131.54/18.57 | | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | | | (1438) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 131.54/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.54/18.57 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 131.54/18.57 | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.54/18.57 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.54/18.57 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 131.54/18.57 | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 131.54/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.54/18.57 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 131.54/18.57 | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 131.54/18.57 | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 131.54/18.57 | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 131.54/18.57 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.54/18.57 | | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (91), (157), (190), (246), (332), % 131.54/18.57 | | | | | | | | | | | | | | | | | (364), (1341), (1345), (1436), (1438), % 131.54/18.57 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.54/18.57 | | | | | | | | | | | | | | | | | #524. % 131.54/18.57 | | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | | End of split % 131.54/18.57 | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | End of split % 131.54/18.57 | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | End of split % 131.54/18.57 | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | End of split % 131.54/18.57 | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | End of split % 131.54/18.57 | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | Case 2: % 131.54/18.57 | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | (1439) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 131.54/18.57 | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | REF_CLOSE: (278), (374), (378), (1416), (1439) are % 131.54/18.57 | | | | | | | | | | | | inconsistent by sub-proof #777. % 131.54/18.57 | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | End of split % 131.54/18.57 | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | Case 2: % 131.54/18.57 | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | (1440) all_32_2 = e1 % 131.54/18.57 | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | COMBINE_EQS: (312), (1440) imply: % 131.54/18.57 | | | | | | | | | | | (1441) all_10_2 = e1 % 131.54/18.57 | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | SIMP: (1441) implies: % 131.54/18.57 | | | | | | | | | | | (1442) all_10_2 = e1 % 131.54/18.57 | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | COMBINE_EQS: (280), (1442) imply: % 131.54/18.57 | | | | | | | | | | | (1443) all_50_2 = e1 % 131.54/18.57 | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | REDUCE: (336), (1442) imply: % 131.54/18.57 | | | | | | | | | | | (1444) ~ (all_52_1 = e1) % 131.54/18.57 | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | REDUCE: (338), (1442) imply: % 131.54/18.57 | | | | | | | | | | | (1445) ~ (all_52_2 = e1) % 131.54/18.57 | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | REDUCE: (342), (1442) imply: % 131.54/18.57 | | | | | | | | | | | (1446) ~ (all_52_4 = e1) % 131.54/18.57 | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | REDUCE: (378), (1442) imply: % 131.54/18.57 | | | | | | | | | | | (1447) ~ (e2 = e1) % 131.54/18.57 | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | REDUCE: (45), (1442) imply: % 131.54/18.57 | | | | | | | | | | | (1448) op(e3, e3) = e1 % 131.54/18.57 | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | BETA: splitting (91) gives: % 131.54/18.57 | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | Case 1: % 131.54/18.57 | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | (1449) ~ (all_40_2 = e0) % 131.54/18.57 | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | REDUCE: (332), (1449) imply: % 131.54/18.57 | | | | | | | | | | | | (1450) ~ (all_6_2 = e0) % 131.54/18.57 | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | BETA: splitting (194) gives: % 131.54/18.57 | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | Case 1: % 131.54/18.57 | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | (1451) all_54_10 = e3 % 131.54/18.57 | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | REF_CLOSE: (334), (1347), (1451) are inconsistent by % 131.54/18.57 | | | | | | | | | | | | | sub-proof #742. % 131.54/18.57 | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | Case 2: % 131.54/18.57 | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | (1452) ~ (all_54_10 = e3) % 131.54/18.57 | | | | | | | | | | | | | (1453) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 131.54/18.57 | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | BETA: splitting (1453) gives: % 131.54/18.57 | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | Case 1: % 131.54/18.57 | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | (1454) all_54_10 = e2 % 131.54/18.57 | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | REF_CLOSE: (334), (372), (1454) are inconsistent by sub-proof % 131.54/18.57 | | | | | | | | | | | | | | #741. % 131.54/18.57 | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | Case 2: % 131.54/18.57 | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | (1455) ~ (all_54_10 = e2) % 131.54/18.57 | | | | | | | | | | | | | | (1456) all_54_10 = e1 | all_54_10 = e0 % 131.54/18.57 | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | BETA: splitting (1456) gives: % 131.54/18.57 | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | Case 1: % 131.54/18.57 | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | (1457) all_54_10 = e1 % 131.54/18.57 | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | COMBINE_EQS: (334), (1457) imply: % 131.54/18.57 | | | | | | | | | | | | | | | (1458) all_6_2 = e1 % 131.54/18.57 | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | SIMP: (1458) implies: % 131.54/18.57 | | | | | | | | | | | | | | | (1459) all_6_2 = e1 % 131.54/18.57 | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | REDUCE: (1347), (1459) imply: % 131.54/18.57 | | | | | | | | | | | | | | | (1460) ~ (e3 = e1) % 131.54/18.57 | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | REDUCE: (39), (1459) imply: % 131.54/18.57 | | | | | | | | | | | | | | | (1461) op(e1, e1) = e1 % 131.54/18.57 | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 131.54/18.57 | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | Case 1: % 131.54/18.57 | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | | (1462) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.54/18.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.54/18.57 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.54/18.57 | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.54/18.57 | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.54/18.57 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.54/18.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.54/18.57 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.54/18.57 | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.54/18.57 | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.54/18.57 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.54/18.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.54/18.57 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.54/18.57 | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.54/18.57 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.54/18.57 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.54/18.57 | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.54/18.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.54/18.57 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.54/18.57 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.54/18.57 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.54/18.57 | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.54/18.57 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.54/18.57 | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | | BETA: splitting (1462) gives: % 131.54/18.57 | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | | Case 1: % 131.54/18.57 | | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | | | (1463) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.54/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.54/18.57 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.54/18.57 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.54/18.57 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.54/18.57 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.54/18.57 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.54/18.57 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.54/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.54/18.57 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.54/18.57 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.54/18.57 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.54/18.57 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.54/18.57 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 131.54/18.57 | | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1448), (1461), (1463), (function-axioms) are % 131.54/18.57 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #509. % 131.54/18.57 | | | | | | | | | | | | | | | | | % 131.54/18.57 | | | | | | | | | | | | | | | | Case 2: % 131.54/18.57 | | | | | | | | | | | | | | | | | % 131.67/18.57 | | | | | | | | | | | | | | | | | (1464) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.67/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.67/18.57 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.67/18.57 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.57 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.57 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.67/18.57 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.67/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.67/18.57 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.57 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.57 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.67/18.57 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.67/18.57 | | | | | | | | | | | | | | | | | % 131.67/18.57 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (1414), (1448), (1464), % 131.67/18.57 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.57 | | | | | | | | | | | | | | | | | #598. % 131.67/18.57 | | | | | | | | | | | | | | | | | % 131.67/18.57 | | | | | | | | | | | | | | | | End of split % 131.67/18.57 | | | | | | | | | | | | | | | | % 131.67/18.57 | | | | | | | | | | | | | | | Case 2: % 131.67/18.57 | | | | | | | | | | | | | | | | % 131.67/18.57 | | | | | | | | | | | | | | | | (1465) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.67/18.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.67/18.57 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.57 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.57 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.67/18.57 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.57 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.67/18.57 | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.67/18.57 | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.67/18.57 | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.67/18.57 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.67/18.57 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.67/18.57 | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.67/18.57 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 131.67/18.57 | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 131.67/18.57 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.67/18.57 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 131.67/18.57 | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.67/18.57 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 131.67/18.57 | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.67/18.57 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 131.67/18.57 | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 131.67/18.57 | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.67/18.57 | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.67/18.57 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 131.67/18.57 | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 131.67/18.57 | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.67/18.57 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 131.67/18.57 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 131.67/18.57 | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 131.67/18.57 | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 131.67/18.57 | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.57 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 131.67/18.57 | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.67/18.57 | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.57 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 131.67/18.57 | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 131.67/18.57 | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 131.67/18.57 | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.67/18.57 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.67/18.57 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.67/18.57 | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.67/18.57 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 131.67/18.57 | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 131.67/18.57 | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 131.67/18.57 | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 131.67/18.57 | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 131.67/18.57 | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 131.67/18.57 | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 131.67/18.57 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.67/18.57 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.67/18.57 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.67/18.57 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.67/18.57 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.67/18.57 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.67/18.57 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.67/18.57 | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.67/18.57 | | | | | | | | | | | | | | | | % 131.67/18.57 | | | | | | | | | | | | | | | | BETA: splitting (1465) gives: % 131.67/18.57 | | | | | | | | | | | | | | | | % 131.67/18.57 | | | | | | | | | | | | | | | | Case 1: % 131.67/18.57 | | | | | | | | | | | | | | | | | % 131.67/18.57 | | | | | | | | | | | | | | | | | (1466) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.67/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.67/18.57 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.57 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.57 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.67/18.57 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.67/18.57 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.67/18.57 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.67/18.57 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.67/18.57 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.67/18.57 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.67/18.57 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.67/18.57 | | | | | | | | | | | | | | | | | % 131.67/18.57 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (39), (1414), (1461), (1466), % 131.67/18.57 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.57 | | | | | | | | | | | | | | | | | #508. % 131.67/18.57 | | | | | | | | | | | | | | | | | % 131.67/18.57 | | | | | | | | | | | | | | | | Case 2: % 131.67/18.57 | | | | | | | | | | | | | | | | | % 131.67/18.57 | | | | | | | | | | | | | | | | | (1467) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.67/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.67/18.57 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 131.67/18.57 | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.57 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.57 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.67/18.57 | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.67/18.57 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.67/18.57 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.67/18.57 | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.67/18.57 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.67/18.57 | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.67/18.57 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.67/18.57 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.67/18.57 | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.67/18.57 | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.67/18.57 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.67/18.57 | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.67/18.57 | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.67/18.57 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.67/18.57 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.67/18.57 | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.67/18.57 | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.67/18.57 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.67/18.57 | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.67/18.57 | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.67/18.57 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.67/18.57 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.67/18.57 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.57 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.67/18.57 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.67/18.57 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.67/18.57 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.67/18.57 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.67/18.57 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.67/18.57 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.67/18.57 | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.67/18.57 | | | | | | | | | | | | | | | | | % 131.67/18.57 | | | | | | | | | | | | | | | | | BETA: splitting (1467) gives: % 131.67/18.57 | | | | | | | | | | | | | | | | | % 131.67/18.57 | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.57 | | | | | | | | | | | | | | | | | | % 131.67/18.57 | | | | | | | | | | | | | | | | | | (1468) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.67/18.57 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 131.67/18.57 | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 131.67/18.57 | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.67/18.57 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 131.67/18.57 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.67/18.57 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 131.67/18.57 | | | | | | | | | | | | | | | | | | % 131.67/18.57 | | | | | | | | | | | | | | | | | | ALPHA: (1468) implies: % 131.67/18.57 | | | | | | | | | | | | | | | | | | (1469) op(e2, e0) = e2 % 131.67/18.57 | | | | | | | | | | | | | | | | | | % 131.67/18.57 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1343), (1469), (function-axioms) are % 131.67/18.57 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 131.67/18.57 | | | | | | | | | | | | | | | | | | % 131.67/18.57 | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.57 | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | (1470) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.67/18.58 | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.67/18.58 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.67/18.58 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.67/18.58 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.67/18.58 | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.67/18.58 | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.67/18.58 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.67/18.58 | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.67/18.58 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.67/18.58 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.67/18.58 | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.67/18.58 | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.67/18.58 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.67/18.58 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.67/18.58 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.58 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.67/18.58 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.67/18.58 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.67/18.58 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.67/18.58 | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.67/18.58 | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | BETA: splitting (1470) gives: % 131.67/18.58 | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (1471) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 131.67/18.58 | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | ALPHA: (1471) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (1472) op(e1, e1) = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1472), (function-axioms) are % 131.67/18.58 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (1473) op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.67/18.58 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.67/18.58 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.67/18.58 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.58 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | ALPHA: (1473) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (1474) op(e0, e0) = all_56_31 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (1475) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | BETA: splitting (1475) gives: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1476) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (158), (1345), (1411), (1474), (1476), % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | #507. % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1477) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1477) gives: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (1478) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1478) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (1479) op(e1, e1) = e0 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1461), (1479), (function-axioms) are % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #721. % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (1480) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1480) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (1481) all_56_31 = e1 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1474), (1481) imply: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (1482) op(e0, e0) = e1 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1345), (1482), (function-axioms) are % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636. % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | End of split % 131.67/18.58 | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | End of split % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | End of split % 131.67/18.58 | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | End of split % 131.67/18.58 | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | (1483) all_54_10 = e0 % 131.67/18.58 | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | REF_CLOSE: (334), (1450), (1483) are inconsistent by % 131.67/18.58 | | | | | | | | | | | | | | | sub-proof #506. % 131.67/18.58 | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | End of split % 131.67/18.58 | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | End of split % 131.67/18.58 | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | End of split % 131.67/18.58 | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | (1484) all_40_2 = e0 % 131.67/18.58 | | | | | | | | | | | | (1485) ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & % 131.67/18.58 | | | | | | | | | | | | $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) % 131.67/18.58 | | | | | | | | | | | | = all_40_1 & $i(all_40_1)) % 131.67/18.58 | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | COMBINE_EQS: (332), (1484) imply: % 131.67/18.58 | | | | | | | | | | | | (1486) all_6_2 = e0 % 131.67/18.58 | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | SIMP: (1486) implies: % 131.67/18.58 | | | | | | | | | | | | (1487) all_6_2 = e0 % 131.67/18.58 | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | REDUCE: (348), (1487) imply: % 131.67/18.58 | | | | | | | | | | | | (1488) ~ (all_52_2 = e0) % 131.67/18.58 | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | REDUCE: (359), (1487) imply: % 131.67/18.58 | | | | | | | | | | | | (1489) ~ (all_52_6 = e0) % 131.67/18.58 | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | REDUCE: (362), (1487) imply: % 131.67/18.58 | | | | | | | | | | | | (1490) ~ (all_52_9 = e0) % 131.67/18.58 | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | REDUCE: (364), (1487) imply: % 131.67/18.58 | | | | | | | | | | | | (1491) ~ (all_52_11 = e0) % 131.67/18.58 | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | REDUCE: (372), (1487) imply: % 131.67/18.58 | | | | | | | | | | | | (1492) ~ (e2 = e0) % 131.67/18.58 | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | REDUCE: (39), (1487) imply: % 131.67/18.58 | | | | | | | | | | | | (1493) op(e1, e1) = e0 % 131.67/18.58 | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | BETA: splitting (106) gives: % 131.67/18.58 | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | (1494) ~ (all_50_2 = e1) % 131.67/18.58 | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | REDUCE: (1443), (1494) imply: % 131.67/18.58 | | | | | | | | | | | | | (1495) $false % 131.67/18.58 | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | CLOSE: (1495) is inconsistent. % 131.67/18.58 | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | (1496) ( ~ (all_50_0 = e2) & op(e1, e3) = all_50_0 & % 131.67/18.58 | | | | | | | | | | | | | $i(all_50_0)) | ( ~ (all_50_1 = e0) & op(e1, e1) % 131.67/18.58 | | | | | | | | | | | | | = all_50_1 & $i(all_50_1)) % 131.67/18.58 | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | BETA: splitting (231) gives: % 131.67/18.58 | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | (1497) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 131.67/18.58 | | | | | | | | | | | | | | & op(e2, e3) = e0) % 131.67/18.58 | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | BETA: splitting (1497) gives: % 131.67/18.58 | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | (1498) all_57_0 = e0 & op(e3, e3) = e0 % 131.67/18.58 | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | ALPHA: (1498) implies: % 131.67/18.58 | | | | | | | | | | | | | | | (1499) op(e3, e3) = e0 % 131.67/18.58 | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | REF_CLOSE: (4), (1448), (1499), (function-axioms) are % 131.67/18.58 | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 131.67/18.58 | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | (1500) all_57_2 = e0 & op(e2, e3) = e0 % 131.67/18.58 | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | ALPHA: (1500) implies: % 131.67/18.58 | | | | | | | | | | | | | | | (1501) all_57_2 = e0 % 131.67/18.58 | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (162), (164), % 131.67/18.58 | | | | | | | | | | | | | | | (170), (224), (225), (226), (227), (1343), (1410), % 131.67/18.58 | | | | | | | | | | | | | | | (1411), (1414), (1489), (1501), (function-axioms) % 131.67/18.58 | | | | | | | | | | | | | | | are inconsistent by sub-proof #498. % 131.67/18.58 | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | End of split % 131.67/18.58 | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | (1502) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 131.67/18.58 | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 131.67/18.58 | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | BETA: splitting (1502) gives: % 131.67/18.58 | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | (1503) all_57_6 = e0 & op(e1, e3) = e0 % 131.67/18.58 | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | ALPHA: (1503) implies: % 131.67/18.58 | | | | | | | | | | | | | | | (1504) all_57_6 = e0 % 131.67/18.58 | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 131.67/18.58 | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | (1505) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | & op(e2, e3) = e2) % 131.67/18.58 | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | BETA: splitting (1505) gives: % 131.67/18.58 | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | (1506) all_57_0 = e2 & op(e3, e3) = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | ALPHA: (1506) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | (1507) op(e3, e3) = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1448), (1507), (function-axioms) are % 131.67/18.58 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743. % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | (1508) all_57_2 = e2 & op(e2, e3) = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | ALPHA: (1508) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | (1509) all_57_2 = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | BETA: splitting (1485) gives: % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | (1510) ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_40_0) % 131.67/18.58 | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | ALPHA: (1510) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | | (1511) ~ (all_40_0 = e3) % 131.67/18.58 | | | | | | | | | | | | | | | | | | (1512) op(e0, e1) = all_40_0 % 131.67/18.58 | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 131.67/18.58 | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (1513) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (1448), (1509), (1513), % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.58 | | | | | | | | | | | | | | | | | | | #589. % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (1514) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | BETA: splitting (1514) gives: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1515) all_57_6 = e3 & op(e1, e3) = e3 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | ALPHA: (1515) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1516) all_57_6 = e3 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1504), (1516) are inconsistent by sub-proof % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | #588. % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1517) all_57_12 = e3 & op(e0, e3) = e3 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | ALPHA: (1517) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1518) all_57_12 = e3 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (1519) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1519) gives: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1520) all_57_6 = e2 & op(e1, e3) = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1520) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1521) all_57_6 = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1504), (1521) imply: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1522) e2 = e0 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1522) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1523) e2 = e0 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1509), (1523) imply: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1524) all_57_2 = e0 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (162), (164), % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (170), (224), (225), (226), (227), (1343), (1410), % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1411), (1414), (1489), (1524), (function-axioms) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #498. % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1525) all_57_7 = e2 & op(e1, e2) = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1525) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1526) all_57_7 = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (163), (167), % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (169), (170), (214), (216), (218), (222), (224), % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (228), (230), (231), (232), (233), (236), (237), % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (238), (361), (1345), (1410), (1414), (1444), % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1445), (1446), (1448), (1493), (1504), (1509), % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1511), (1512), (1518), (1526), (function-axioms) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #485. % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (1527) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (372), (1344), (1527), % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | #513. % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | End of split % 131.67/18.58 | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | (1528) ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_40_1) % 131.67/18.58 | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1345), (1528), (function-axioms) are inconsistent % 131.67/18.58 | | | | | | | | | | | | | | | | | | by sub-proof #528. % 131.67/18.58 | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | End of split % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | End of split % 131.67/18.58 | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | (1529) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 131.67/18.58 | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 131.67/18.58 | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | BETA: splitting (1529) gives: % 131.67/18.58 | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | (1530) all_57_6 = e2 & op(e1, e3) = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | ALPHA: (1530) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | (1531) all_57_6 = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1504), (1531) are inconsistent by sub-proof % 131.67/18.58 | | | | | | | | | | | | | | | | | #586. % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | (1532) all_57_12 = e2 & op(e0, e3) = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | ALPHA: (1532) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | (1533) all_57_12 = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | BETA: splitting (1485) gives: % 131.67/18.58 | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | (1534) ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & % 131.67/18.58 | | | | | | | | | | | | | | | | | | $i(all_40_0) % 131.67/18.58 | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | ALPHA: (1534) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | | (1535) ~ (all_40_0 = e3) % 131.67/18.58 | | | | | | | | | | | | | | | | | | (1536) op(e0, e1) = all_40_0 % 131.67/18.58 | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 131.67/18.58 | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | (1537) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | BETA: splitting (1537) gives: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1538) all_57_0 = e3 & op(e3, e3) = e3 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | ALPHA: (1538) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1539) op(e3, e3) = e3 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1448), (1539), (function-axioms) are % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #775. % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1540) all_57_2 = e3 & op(e2, e3) = e3 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | ALPHA: (1540) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | (1541) all_57_2 = e3 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | (1542) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1542) gives: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1543) all_57_6 = e2 & op(e1, e3) = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1543) implies: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1544) all_57_6 = e2 % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (231), (1448), (1533), (1541), % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | (1544), (function-axioms) are inconsistent by % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | sub-proof #519. % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.58 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | (1545) all_57_7 = e2 & op(e1, e2) = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1545) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | (1546) all_57_7 = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | (1547) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1547) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1548) all_57_12 = e3 & op(e0, e3) = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1548) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1549) all_57_12 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1533), (1549) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1550) e3 = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1550) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1551) e3 = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1541), (1551) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1552) all_57_2 = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (163), (167), % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (169), (170), (214), (216), (218), (222), (224), % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (228), (230), (231), (232), (233), (236), (237), % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (238), (361), (1345), (1410), (1414), (1444), % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1445), (1446), (1448), (1493), (1504), (1535), % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1536), (1546), (1549), (1552), (function-axioms) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #485. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1553) all_57_13 = e3 & op(e0, e2) = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1553) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1554) all_57_13 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (208), (209), (1345), % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1533), (1554), (function-axioms) are inconsistent % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #482. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | (1555) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1555) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1556) all_57_14 = e3 & op(e0, e1) = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1556) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1557) op(e0, e1) = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1535), (1536), (1557), (function-axioms) are % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #529. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1558) all_57_15 = e3 & op(e0, e0) = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1558) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1559) op(e0, e0) = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1345), (1559), (function-axioms) are % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1560) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (372), (1344), (1560), % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | #513. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1561) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 131.67/18.59 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (1561) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | (1562) all_57_6 = e3 & op(e1, e3) = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (1562) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | (1563) all_57_6 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1504), (1563) are inconsistent by sub-proof % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | #588. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | (1564) all_57_12 = e3 & op(e0, e3) = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (1564) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | (1565) all_57_12 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1533), (1565) are inconsistent by sub-proof % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | #518. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | (1566) ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & % 131.67/18.59 | | | | | | | | | | | | | | | | | | $i(all_40_1) % 131.67/18.59 | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1345), (1566), (function-axioms) are inconsistent % 131.67/18.59 | | | | | | | | | | | | | | | | | | by sub-proof #528. % 131.67/18.59 | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | (1567) all_57_12 = e0 & op(e0, e3) = e0 % 131.67/18.59 | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | ALPHA: (1567) implies: % 131.67/18.59 | | | | | | | | | | | | | | | (1568) all_57_12 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | (1569) op(e0, e3) = e0 % 131.67/18.59 | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 131.67/18.59 | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | (1570) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 131.67/18.59 | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (1410), (1448), (1570), % 131.67/18.59 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.59 | | | | | | | | | | | | | | | | #692. % 131.67/18.59 | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | (1571) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 131.67/18.59 | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | BETA: splitting (1571) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | (1572) all_57_4 = e0 & op(e3, e1) = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | ALPHA: (1572) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | (1573) op(e3, e1) = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (169), (361), (1493), (1573), % 131.67/18.59 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.59 | | | | | | | | | | | | | | | | | #619. % 131.67/18.59 | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | (1574) all_57_9 = e0 & op(e3, e0) = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | ALPHA: (1574) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | (1575) op(e3, e0) = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | BETA: splitting (1485) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | (1576) ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & % 131.67/18.59 | | | | | | | | | | | | | | | | | | $i(all_40_0) % 131.67/18.59 | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | ALPHA: (1576) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | (1577) ~ (all_40_0 = e3) % 131.67/18.59 | | | | | | | | | | | | | | | | | | (1578) op(e0, e1) = all_40_0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | BETA: splitting (1496) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1579) ~ (all_50_0 = e2) & op(e1, e3) = all_50_0 & % 131.67/18.59 | | | | | | | | | | | | | | | | | | | $i(all_50_0) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | ALPHA: (1579) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1580) ~ (all_50_0 = e2) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1581) op(e1, e3) = all_50_0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11, % 131.67/18.59 | | | | | | | | | | | | | | | | | | | all_40_0, e1, e0, simplifying with (157), (1578) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1582) all_52_11 = all_40_0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0, % 131.67/18.59 | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (1569) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1583) all_52_3 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 131.67/18.59 | | | | | | | | | | | | | | | | | | | all_50_0, e3, e1, simplifying with (163), (1581) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1584) all_52_2 = all_50_0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 131.67/18.59 | | | | | | | | | | | | | | | | | | | e0, e0, e3, simplifying with (168), (1575) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1585) all_52_12 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (1582) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1586) all_54_14 = all_40_0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (1584) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1587) all_54_8 = all_50_0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | REDUCE: (149), (1584) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1588) ~ (all_52_1 = all_50_0) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | REDUCE: (140), (1583) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1589) ~ (all_52_7 = e0) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | REDUCE: (125), (1582) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1590) ~ (all_52_7 = all_40_0) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | REDUCE: (121), (1582) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1591) ~ (all_52_8 = all_40_0) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | REDUCE: (118), (1582) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1592) ~ (all_52_9 = all_40_0) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | REDUCE: (1341), (1582) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1593) ~ (all_40_0 = e2) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | REDUCE: (1491), (1582) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | (1594) ~ (all_40_0 = e0) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | (1595) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1595) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1596) all_57_0 = e2 & op(e3, e3) = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1596) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1597) op(e3, e3) = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1448), (1597), (function-axioms) are % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1598) all_57_2 = e2 & op(e2, e3) = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1598) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1599) op(e2, e3) = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | (1600) all_54_14 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1586), (1600) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | (1601) all_40_0 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1601) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | (1602) all_40_0 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1577), (1602) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | (1603) $false % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1603) is inconsistent. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | (1604) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1604) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | (1605) all_54_14 = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1586), (1605) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | (1606) all_40_0 = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1606) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | (1607) all_40_0 = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1593), (1607) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | (1608) $false % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1608) is inconsistent. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | (1609) all_54_14 = e1 | all_54_14 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1609) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1610) all_54_14 = e1 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1586), (1610) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1611) all_40_0 = e1 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1611) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1612) all_40_0 = e1 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1590), (1612) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1613) ~ (all_52_7 = e1) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1591), (1612) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1614) ~ (all_52_8 = e1) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1592), (1612) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1615) ~ (all_52_9 = e1) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1616) all_54_13 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (1616) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1617) all_52_7 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1617) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1618) all_52_7 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (1618) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1619) ~ (all_52_4 = e3) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (1620) all_54_8 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1587), (1620) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (1621) all_50_0 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1621) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (1622) all_50_0 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1588), (1622) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (1623) ~ (all_52_1 = e3) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1624) all_54_4 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (1623), (1624) are inconsistent by % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #481. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1625) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1626) all_54_1 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (1619), (1626) are inconsistent by % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #740. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1627) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1625) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1628) all_54_4 = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (1628) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1629) all_52_1 = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (1629) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1630) ~ (all_52_9 = e2) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1630) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1631) ~ (all_52_9 = e2) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1627) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1632) all_54_1 = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (1632) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1633) all_52_4 = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1633) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1634) all_52_4 = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (1634) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1635) ~ (all_52_8 = e2) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1635) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1636) ~ (all_52_8 = e2) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1637) all_54_2 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (1637) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1638) all_52_8 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1638) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1639) all_52_8 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (1639) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1640) ~ (all_52_9 = e3) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1640) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1641) ~ (all_52_9 = e3) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1642) all_54_6 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (1642) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1643) all_52_9 = e3 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1641), (1643) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1644) $false % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1644) is inconsistent. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1645) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (1490), (1615), (1631), (1645) are % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #478. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1646) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (194), (270), (334), (361), (372), (1347), % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1493), (1614), (1636), (1646), (function-axioms) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #476. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1647) all_54_1 = e1 | all_54_1 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1647) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1648) all_54_1 = e1 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (1446), (1648) are inconsistent by % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #731. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1649) all_54_1 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (1410), (1649) are inconsistent by % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #702. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1650) ~ (all_54_4 = e2) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (268), (1650) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1651) ~ (all_52_1 = e2) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (1599), (1651), (function-axioms) are % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #779. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (1652) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (1445), (1488), (1580), (1587), (1652) are % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #473. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | (1653) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1653) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (1654) all_54_13 = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (1340), (1654) are inconsistent by % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #472. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (1655) all_54_13 = e1 | all_54_13 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (1411), (1613), (1655) are inconsistent by % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #470. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1656) all_54_14 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1586), (1656) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1657) all_40_0 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1657) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1658) all_40_0 = e0 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1594), (1658) imply: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | (1659) $false % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1659) is inconsistent. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | (1660) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1660) gives: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1661) all_57_6 = e2 & op(e1, e3) = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1661) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1662) op(e1, e3) = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1580), (1581), (1662), (function-axioms) are % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #735. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1663) all_57_12 = e2 & op(e0, e3) = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1663) implies: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | (1664) all_57_12 = e2 % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1568), (1664) are inconsistent by sub-proof % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | #682. % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.59 | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.59 | | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | | (1665) ~ (all_50_1 = e0) & op(e1, e1) = all_50_1 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_50_1) % 131.67/18.60 | | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1493), (1665), (function-axioms) are inconsistent % 131.67/18.60 | | | | | | | | | | | | | | | | | | | by sub-proof #719. % 131.67/18.60 | | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | End of split % 131.67/18.60 | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.60 | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | (1666) ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_40_1) % 131.67/18.60 | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1345), (1666), (function-axioms) are inconsistent % 131.67/18.60 | | | | | | | | | | | | | | | | | | by sub-proof #528. % 131.67/18.60 | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | End of split % 131.67/18.60 | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | End of split % 131.67/18.60 | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | End of split % 131.67/18.60 | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | End of split % 131.67/18.60 | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | End of split % 131.67/18.60 | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | End of split % 131.67/18.60 | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | End of split % 131.67/18.60 | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | End of split % 131.67/18.60 | | | | | | | | | | % 131.67/18.60 | | | | | | | | | End of split % 131.67/18.60 | | | | | | | | | % 131.67/18.60 | | | | | | | | Case 2: % 131.67/18.60 | | | | | | | | | % 131.67/18.60 | | | | | | | | | (1667) all_28_2 = e3 % 131.67/18.60 | | | | | | | | | % 131.67/18.60 | | | | | | | | | COMBINE_EQS: (316), (1667) imply: % 131.67/18.60 | | | | | | | | | (1668) all_6_2 = e3 % 131.67/18.60 | | | | | | | | | % 131.67/18.60 | | | | | | | | | SIMP: (1668) implies: % 131.67/18.60 | | | | | | | | | (1669) all_6_2 = e3 % 131.67/18.60 | | | | | | | | | % 131.67/18.60 | | | | | | | | | REDUCE: (359), (1669) imply: % 131.67/18.60 | | | | | | | | | (1670) ~ (all_52_6 = e3) % 131.67/18.60 | | | | | | | | | % 131.67/18.60 | | | | | | | | | REDUCE: (361), (1669) imply: % 131.67/18.60 | | | | | | | | | (1671) ~ (all_52_8 = e3) % 131.67/18.60 | | | | | | | | | % 131.67/18.60 | | | | | | | | | REDUCE: (362), (1669) imply: % 131.67/18.60 | | | | | | | | | (1672) ~ (all_52_9 = e3) % 131.67/18.60 | | | | | | | | | % 131.67/18.60 | | | | | | | | | REDUCE: (364), (1669) imply: % 131.67/18.60 | | | | | | | | | (1673) ~ (all_52_11 = e3) % 131.67/18.60 | | | | | | | | | % 131.67/18.60 | | | | | | | | | REDUCE: (39), (1669) imply: % 131.67/18.60 | | | | | | | | | (1674) op(e1, e1) = e3 % 131.67/18.60 | | | | | | | | | % 131.67/18.60 | | | | | | | | | BETA: splitting (76) gives: % 131.67/18.60 | | | | | | | | | % 131.67/18.60 | | | | | | | | | Case 1: % 131.67/18.60 | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | (1675) ~ (all_30_2 = e0) % 131.67/18.60 | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | REDUCE: (309), (1675) imply: % 131.67/18.60 | | | | | | | | | | (1676) ~ (all_8_2 = e0) % 131.67/18.60 | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | BETA: splitting (199) gives: % 131.67/18.60 | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | Case 1: % 131.67/18.60 | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | (1677) all_54_5 = e3 % 131.67/18.60 | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | COMBINE_EQS: (267), (1677) imply: % 131.67/18.60 | | | | | | | | | | | (1678) all_8_2 = e3 % 131.67/18.60 | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | REDUCE: (376), (1678) imply: % 131.67/18.60 | | | | | | | | | | | (1679) $false % 131.67/18.60 | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | CLOSE: (1679) is inconsistent. % 131.67/18.60 | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | Case 2: % 131.67/18.60 | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | (1680) ~ (all_54_5 = e3) % 131.67/18.60 | | | | | | | | | | | (1681) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 131.67/18.60 | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | BETA: splitting (1681) gives: % 131.67/18.60 | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | Case 1: % 131.67/18.60 | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | (1682) all_54_5 = e2 % 131.67/18.60 | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | COMBINE_EQS: (267), (1682) imply: % 131.67/18.60 | | | | | | | | | | | | (1683) all_8_2 = e2 % 131.67/18.60 | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | REDUCE: (347), (1683) imply: % 131.67/18.60 | | | | | | | | | | | | (1684) ~ (all_52_1 = e2) % 131.67/18.60 | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | REDUCE: (356), (1683) imply: % 131.67/18.60 | | | | | | | | | | | | (1685) ~ (all_52_9 = e2) % 131.67/18.60 | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | REDUCE: (376), (1683) imply: % 131.67/18.60 | | | | | | | | | | | | (1686) ~ (e3 = e2) % 131.67/18.60 | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | BETA: splitting (225) gives: % 131.67/18.60 | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | Case 1: % 131.67/18.60 | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | (1687) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 131.67/18.60 | | | | | | | | | | | | | & op(e2, e2) = e2) % 131.67/18.60 | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | BETA: splitting (1687) gives: % 131.67/18.60 | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | Case 1: % 131.67/18.60 | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | (1688) all_57_2 = e2 & op(e2, e3) = e2 % 131.67/18.60 | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | ALPHA: (1688) implies: % 131.67/18.60 | | | | | | | | | | | | | | (1689) op(e2, e3) = e2 % 131.67/18.60 | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | REF_CLOSE: (167), (1684), (1689), (function-axioms) are % 131.67/18.60 | | | | | | | | | | | | | | inconsistent by sub-proof #779. % 131.67/18.60 | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | Case 2: % 131.67/18.60 | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | (1690) all_57_3 = e2 & op(e2, e2) = e2 % 131.67/18.60 | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | ALPHA: (1690) implies: % 131.67/18.60 | | | | | | | | | | | | | | (1691) all_57_3 = e2 % 131.67/18.60 | | | | | | | | | | | | | | (1692) op(e2, e2) = e2 % 131.67/18.60 | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | BETA: splitting (235) gives: % 131.67/18.60 | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | Case 1: % 131.67/18.60 | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | (1693) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 131.67/18.60 | | | | | | | | | | | | | | | & op(e2, e3) = e2) % 131.67/18.60 | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | REF_CLOSE: (45), (167), (378), (1684), (1693), % 131.67/18.60 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.60 | | | | | | | | | | | | | | | #535. % 131.67/18.60 | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | Case 2: % 131.67/18.60 | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | (1694) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 131.67/18.60 | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 131.67/18.60 | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | BETA: splitting (1694) gives: % 131.67/18.60 | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | Case 1: % 131.67/18.60 | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | (1695) all_57_6 = e2 & op(e1, e3) = e2 % 131.67/18.60 | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | ALPHA: (1695) implies: % 131.67/18.60 | | | | | | | | | | | | | | | | (1696) op(e1, e3) = e2 % 131.67/18.60 | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 131.67/18.60 | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | Case 1: % 131.67/18.60 | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | (1697) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.67/18.60 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.67/18.60 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.67/18.60 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.67/18.60 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.67/18.60 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.67/18.60 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.67/18.60 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.67/18.60 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.60 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.67/18.60 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.67/18.60 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.67/18.60 | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | BETA: splitting (1697) gives: % 131.67/18.60 | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.60 | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | (1698) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.67/18.60 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.67/18.60 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.67/18.60 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 131.67/18.60 | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (169), (378), (1671), (1698), % 131.67/18.60 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.60 | | | | | | | | | | | | | | | | | | #469. % 131.67/18.60 | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.60 | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | (1699) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.60 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.67/18.60 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.67/18.60 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.67/18.60 | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (167), (374), (1684), (1699), % 131.67/18.60 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.60 | | | | | | | | | | | | | | | | | | #533. % 131.67/18.60 | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | End of split % 131.67/18.60 | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | Case 2: % 131.67/18.60 | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | (1700) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.67/18.60 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.67/18.60 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.67/18.60 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.67/18.60 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.67/18.60 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.67/18.60 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 131.67/18.60 | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 131.67/18.60 | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.67/18.60 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 131.67/18.60 | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 131.67/18.60 | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 131.67/18.60 | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 131.67/18.60 | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 131.67/18.60 | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 131.67/18.60 | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 131.67/18.60 | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.67/18.60 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 131.67/18.60 | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 131.67/18.60 | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 131.67/18.60 | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.67/18.60 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.67/18.60 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 131.67/18.60 | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 131.67/18.60 | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 131.67/18.60 | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 131.67/18.60 | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.67/18.60 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.67/18.60 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.67/18.60 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.67/18.60 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.67/18.60 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.67/18.60 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.67/18.60 | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.67/18.60 | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | BETA: splitting (1700) gives: % 131.67/18.60 | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.60 | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | (1701) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.67/18.60 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.67/18.60 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.67/18.60 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.67/18.60 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.67/18.60 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.67/18.60 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.67/18.60 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.67/18.60 | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (165), (1685), (1696), (1701), % 131.67/18.60 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.60 | | | | | | | | | | | | | | | | | | #468. % 131.67/18.60 | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.60 | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | (1702) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.60 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.67/18.60 | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.67/18.60 | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.67/18.60 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.67/18.60 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.67/18.60 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.67/18.60 | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.67/18.60 | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.67/18.60 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.67/18.60 | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.67/18.60 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.67/18.60 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.67/18.60 | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.67/18.60 | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.67/18.60 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.67/18.60 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.67/18.60 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.60 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.67/18.60 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.67/18.60 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.67/18.60 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.67/18.60 | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.67/18.60 | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | BETA: splitting (1702) gives: % 131.67/18.60 | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.60 | | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | | (1703) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 131.67/18.60 | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 131.67/18.60 | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.67/18.60 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 131.67/18.60 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 131.67/18.60 | | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | | ALPHA: (1703) implies: % 131.67/18.60 | | | | | | | | | | | | | | | | | | | (1704) op(e2, e0) = e2 % 131.67/18.60 | | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1343), (1704), (function-axioms) are % 131.67/18.60 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 131.67/18.60 | | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.60 | | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | | (1705) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.67/18.60 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.67/18.60 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.67/18.60 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.67/18.60 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.67/18.60 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.67/18.60 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.67/18.60 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.67/18.60 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.67/18.60 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.67/18.60 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.67/18.60 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.67/18.60 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.67/18.60 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.67/18.60 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.67/18.60 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.60 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.67/18.60 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.67/18.60 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.67/18.60 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.67/18.60 | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.67/18.60 | | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | | BETA: splitting (1705) gives: % 131.67/18.60 | | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.60 | | | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | | | (1706) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.67/18.60 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 131.67/18.60 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.67/18.60 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 131.67/18.60 | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.67/18.60 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 131.67/18.60 | | | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | | | ALPHA: (1706) implies: % 131.67/18.60 | | | | | | | | | | | | | | | | | | | | (1707) op(e1, e1) = e2 % 131.67/18.60 | | | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1707), (function-axioms) are % 131.67/18.60 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 131.67/18.60 | | | | | | | | | | | | | | | | | | | | % 131.67/18.60 | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.60 | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (1708) op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | ALPHA: (1708) implies: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (1709) op(e0, e0) = all_56_31 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (1710) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | (1711) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1711) gives: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1712) all_57_4 = e2 & op(e3, e1) = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1712) implies: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1713) op(e3, e1) = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (1345), (1709) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | gives: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1714) all_56_31 = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2, % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (1713) gives: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1715) all_52_8 = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1710) gives: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | (1716) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1692), (1714), (1716), (function-axioms) are % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #530. % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | (1717) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (1674), (1714), (1717), % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | #467. % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1718) all_57_5 = e2 & op(e2, e1) = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1718) implies: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1719) op(e2, e1) = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (1685), (1719), (function-axioms) are % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770. % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | (1720) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1720) gives: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1721) all_57_8 = e2 & op(e1, e1) = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1721) implies: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1722) op(e1, e1) = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1722), (function-axioms) are % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1723) all_57_14 = e2 & op(e0, e1) = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1723) implies: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1724) all_57_14 = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | (1725) op(e0, e1) = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | (1726) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1726) gives: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | (1727) all_57_0 = e2 & op(e3, e3) = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1727) implies: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | (1728) op(e3, e3) = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (378), (1728), (function-axioms) are % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #536. % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | (1729) all_57_1 = e2 & op(e3, e2) = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1729) implies: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | (1730) all_57_1 = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228), % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | (230), (1670), (1691), (1730), (function-axioms) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #463. % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | (1731) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1731) gives: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | (1732) all_57_4 = e2 & op(e3, e1) = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1732) implies: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | (1733) all_57_4 = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | (1734) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1734) gives: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1735) all_57_4 = e1 & op(e3, e1) = e1 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1733), (1735) are inconsistent by sub-proof % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | #462. % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1736) all_57_5 = e1 & op(e2, e1) = e1 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1736) implies: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1737) all_57_5 = e1 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1738) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1738) gives: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1739) all_57_4 = e0 & op(e3, e1) = e0 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1733), (1739) are inconsistent by sub-proof % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #647. % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1740) all_57_5 = e0 & op(e2, e1) = e0 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1737), (1740) are inconsistent by sub-proof % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #461. % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1741) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1741) gives: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1742) all_57_8 = e0 & op(e1, e1) = e0 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1742) implies: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1743) op(e1, e1) = e0 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1674), (1743), (function-axioms) are % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1744) all_57_14 = e0 & op(e0, e1) = e0 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1744) implies: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1745) op(e0, e1) = e0 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1725), (1745), (function-axioms) are % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660. % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | (1746) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1746) gives: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1747) all_57_8 = e1 & op(e1, e1) = e1 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1747) implies: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1748) op(e1, e1) = e1 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (1674), (1748), (function-axioms) are % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662. % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1749) all_57_14 = e1 & op(e0, e1) = e1 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1749) implies: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1750) all_57_14 = e1 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1724), (1750) imply: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1751) e2 = e1 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (1751) imply: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | (1752) $false % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1752) is inconsistent. % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | (1753) all_57_9 = e2 & op(e3, e0) = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1342), (1753), (function-axioms) are % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | Case 2: % 131.67/18.61 | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | (1754) all_57_12 = e2 & op(e0, e3) = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | ALPHA: (1754) implies: % 131.67/18.61 | | | | | | | | | | | | | | | | (1755) all_57_12 = e2 % 131.67/18.61 | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (208), (209), % 131.67/18.61 | | | | | | | | | | | | | | | | (211), (1345), (1673), (1755), (function-axioms) % 131.67/18.61 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #458. % 131.67/18.61 | | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | Case 2: % 131.67/18.61 | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | (1756) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 131.67/18.61 | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 131.67/18.61 | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | | REF_CLOSE: (164), (165), (1343), (1685), (1756), % 131.67/18.61 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.61 | | | | | | | | | | | | | #625. % 131.67/18.61 | | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | Case 2: % 131.67/18.61 | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | (1757) all_54_5 = e1 | all_54_5 = e0 % 131.67/18.61 | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | REF_CLOSE: (267), (373), (1676), (1757) are inconsistent by % 131.67/18.61 | | | | | | | | | | | | sub-proof #624. % 131.67/18.61 | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | End of split % 131.67/18.61 | | | | | | | | | | % 131.67/18.61 | | | | | | | | | Case 2: % 131.67/18.61 | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | (1758) all_30_2 = e0 % 131.67/18.61 | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | COMBINE_EQS: (309), (1758) imply: % 131.67/18.61 | | | | | | | | | | (1759) all_8_2 = e0 % 131.67/18.61 | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | SIMP: (1759) implies: % 131.67/18.61 | | | | | | | | | | (1760) all_8_2 = e0 % 131.67/18.61 | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | REDUCE: (350), (1760) imply: % 131.67/18.61 | | | | | | | | | | (1761) ~ (all_52_4 = e0) % 131.67/18.61 | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | REDUCE: (352), (1760) imply: % 131.67/18.61 | | | | | | | | | | (1762) ~ (all_52_6 = e0) % 131.67/18.61 | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | REDUCE: (354), (1760) imply: % 131.67/18.61 | | | | | | | | | | (1763) ~ (all_52_7 = e0) % 131.67/18.61 | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | REDUCE: (356), (1760) imply: % 131.67/18.61 | | | | | | | | | | (1764) ~ (all_52_9 = e0) % 131.67/18.61 | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | REDUCE: (376), (1760) imply: % 131.67/18.61 | | | | | | | | | | (1765) ~ (e3 = e0) % 131.67/18.61 | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | REDUCE: (373), (1760) imply: % 131.67/18.61 | | | | | | | | | | (1766) ~ (e1 = e0) % 131.67/18.61 | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | REDUCE: (42), (1760) imply: % 131.67/18.61 | | | | | | | | | | (1767) op(e2, e2) = e0 % 131.67/18.61 | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | BETA: splitting (206) gives: % 131.67/18.61 | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | Case 1: % 131.67/18.61 | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | (1768) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.67/18.61 | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.67/18.61 | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.67/18.61 | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.67/18.61 | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.67/18.61 | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.67/18.61 | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.67/18.61 | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.67/18.61 | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.67/18.61 | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.67/18.61 | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.67/18.61 | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.67/18.61 | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.67/18.61 | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 131.67/18.61 | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.67/18.61 | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.67/18.61 | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.67/18.61 | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.61 | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.61 | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.67/18.61 | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.67/18.61 | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.67/18.61 | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.67/18.61 | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.61 | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.61 | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.67/18.61 | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.61 | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.67/18.61 | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | BETA: splitting (1768) gives: % 131.67/18.61 | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | Case 1: % 131.67/18.61 | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | (1769) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.67/18.61 | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.67/18.61 | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.67/18.61 | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.67/18.61 | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.67/18.61 | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.67/18.61 | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.67/18.61 | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.67/18.61 | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.67/18.61 | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.67/18.61 | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.67/18.61 | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.67/18.61 | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.67/18.61 | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 131.67/18.61 | | | | | | | | | | | | % 131.67/18.61 | | | | | | | | | | | | REF_CLOSE: (45), (169), (378), (1671), (1769), % 131.67/18.62 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.62 | | | | | | | | | | | | #469. % 131.67/18.62 | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | Case 2: % 131.67/18.62 | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | (1770) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.67/18.62 | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.67/18.62 | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.67/18.62 | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.62 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.62 | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.67/18.62 | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.67/18.62 | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.67/18.62 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.67/18.62 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.62 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.62 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.67/18.62 | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.62 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.67/18.62 | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | REF_CLOSE: (7), (45), (374), (1767), (1770), % 131.67/18.62 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.62 | | | | | | | | | | | | #457. % 131.67/18.62 | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | End of split % 131.67/18.62 | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | Case 2: % 131.67/18.62 | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | (1771) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.67/18.62 | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.67/18.62 | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.62 | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.62 | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.67/18.62 | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.62 | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.67/18.62 | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.67/18.62 | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.67/18.62 | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.67/18.62 | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.67/18.62 | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.67/18.62 | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.67/18.62 | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 131.67/18.62 | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 131.67/18.62 | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.67/18.62 | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 131.67/18.62 | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.67/18.62 | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 131.67/18.62 | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.67/18.62 | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 131.67/18.62 | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 131.67/18.62 | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.67/18.62 | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.67/18.62 | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 131.67/18.62 | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 131.67/18.62 | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.67/18.62 | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 131.67/18.62 | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 131.67/18.62 | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 131.67/18.62 | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 131.67/18.62 | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.62 | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 131.67/18.62 | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.67/18.62 | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.62 | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 131.67/18.62 | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 131.67/18.62 | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 131.67/18.62 | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.67/18.62 | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.67/18.62 | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.67/18.62 | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.67/18.62 | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 131.67/18.62 | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 131.67/18.62 | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 131.67/18.62 | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 131.67/18.62 | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 131.67/18.62 | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 131.67/18.62 | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 131.67/18.62 | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.67/18.62 | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.67/18.62 | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.67/18.62 | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.67/18.62 | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.67/18.62 | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.67/18.62 | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.67/18.62 | | | | | | | | | | | & $i(all_56_29)))) % 131.67/18.62 | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | BETA: splitting (1771) gives: % 131.67/18.62 | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | Case 1: % 131.67/18.62 | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | (1772) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.67/18.62 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.67/18.62 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.62 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.62 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.67/18.62 | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.62 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.67/18.62 | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.67/18.62 | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.67/18.62 | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.67/18.62 | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.67/18.62 | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.67/18.62 | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.67/18.62 | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.67/18.62 | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | BETA: splitting (1772) gives: % 131.67/18.62 | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | Case 1: % 131.67/18.62 | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | (1773) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.67/18.62 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 131.67/18.62 | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.62 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.62 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 131.67/18.62 | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.62 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 131.67/18.62 | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | ALPHA: (1773) implies: % 131.67/18.62 | | | | | | | | | | | | | (1774) op(e1, e3) = e1 % 131.67/18.62 | | | | | | | | | | | | | (1775) op(e3, e0) = all_56_25 % 131.67/18.62 | | | | | | | | | | | | | (1776) op(e3, e3) = all_56_1 % 131.67/18.62 | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | BETA: splitting (223) gives: % 131.67/18.62 | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | Case 1: % 131.67/18.62 | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | (1777) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 % 131.67/18.62 | | | | | | | | | | | | | | & op(e2, e2) = e0) % 131.67/18.62 | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | BETA: splitting (1777) gives: % 131.67/18.62 | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | Case 1: % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | (1778) all_57_2 = e0 & op(e2, e3) = e0 % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | ALPHA: (1778) implies: % 131.67/18.62 | | | | | | | | | | | | | | | (1779) all_57_2 = e0 % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | Case 1: % 131.67/18.62 | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | (1780) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 131.67/18.62 | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 131.67/18.62 | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | BETA: splitting (1780) gives: % 131.67/18.62 | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | Case 1: % 131.67/18.62 | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | (1781) all_57_1 = e0 & op(e3, e2) = e0 % 131.67/18.62 | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (1761), (1781), (function-axioms) are % 131.67/18.62 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #693. % 131.67/18.62 | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | Case 2: % 131.67/18.62 | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | (1782) all_57_3 = e0 & op(e2, e2) = e0 % 131.67/18.62 | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | ALPHA: (1782) implies: % 131.67/18.62 | | | | | | | | | | | | | | | | | (1783) all_57_3 = e0 % 131.67/18.62 | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 131.67/18.62 | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.62 | | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | | (1784) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 131.67/18.62 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 131.67/18.62 | | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1779), (1783), (1784) are inconsistent by % 131.67/18.62 | | | | | | | | | | | | | | | | | | sub-proof #678. % 131.67/18.62 | | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.62 | | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | | (1785) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 131.67/18.62 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 131.67/18.62 | | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | | BETA: splitting (1785) gives: % 131.67/18.62 | | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | | Case 1: % 131.67/18.62 | | | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | | | (1786) all_57_5 = e2 & op(e2, e1) = e2 % 131.67/18.62 | | | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | | | ALPHA: (1786) implies: % 131.67/18.62 | | | | | | | | | | | | | | | | | | | (1787) all_57_5 = e2 % 131.67/18.62 | | | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (165), (224), (226), (1672), % 131.67/18.62 | | | | | | | | | | | | | | | | | | | (1767), (1779), (1787), (function-axioms) are % 131.67/18.62 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #456. % 131.67/18.62 | | | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | | Case 2: % 131.67/18.62 | | | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | | | (1788) all_57_10 = e2 & op(e2, e0) = e2 % 131.67/18.62 | | | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | | | ALPHA: (1788) implies: % 131.67/18.62 | | | | | | | | | | | | | | | | | | | (1789) op(e2, e0) = e2 % 131.67/18.62 | | | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1343), (1789), (function-axioms) are % 131.67/18.62 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 131.67/18.62 | | | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | | End of split % 131.67/18.62 | | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | | End of split % 131.67/18.62 | | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | End of split % 131.67/18.62 | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | Case 2: % 131.67/18.62 | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | (1790) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 131.67/18.62 | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 131.67/18.62 | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (1762), (1763), (1790), % 131.67/18.62 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.62 | | | | | | | | | | | | | | | | #504. % 131.67/18.62 | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | End of split % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | Case 2: % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | (1791) all_57_3 = e0 & op(e2, e2) = e0 % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1, % 131.67/18.62 | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (1774) gives: % 131.67/18.62 | | | | | | | | | | | | | | | (1792) all_52_2 = e1 % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 131.67/18.62 | | | | | | | | | | | | | | | all_56_25, e0, e3, simplifying with (168), (1775) % 131.67/18.62 | | | | | | | | | | | | | | | gives: % 131.67/18.62 | | | | | | | | | | | | | | | (1793) all_56_25 = all_52_12 % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 131.67/18.62 | | | | | | | | | | | | | | | all_56_1, e3, e3, simplifying with (45), (1776) % 131.67/18.62 | | | | | | | | | | | | | | | gives: % 131.67/18.62 | | | | | | | | | | | | | | | (1794) all_56_1 = all_10_2 % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | REDUCE: (338), (1792) imply: % 131.67/18.62 | | | | | | | | | | | | | | | (1795) ~ (all_10_2 = e1) % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | SIMP: (1795) implies: % 131.67/18.62 | | | | | | | | | | | | | | | (1796) ~ (all_10_2 = e1) % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (39), (45), (158), (164), (165), (167), % 131.67/18.62 | | | | | | | | | | | | | | | (168), (204), (206), (226), (278), (336), (346), % 131.67/18.62 | | | | | | | | | | | | | | | (371), (372), (374), (378), (1672), (1674), % 131.67/18.62 | | | | | | | | | | | | | | | (1763), (1767), (1796), (function-axioms) are % 131.67/18.62 | | | | | | | | | | | | | | | inconsistent by sub-proof #541. % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | End of split % 131.67/18.62 | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | Case 2: % 131.67/18.62 | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | (1797) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = % 131.67/18.62 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) % 131.67/18.62 | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | BETA: splitting (1797) gives: % 131.67/18.62 | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | Case 1: % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | (1798) all_57_5 = e0 & op(e2, e1) = e0 % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | REF_CLOSE: (165), (1764), (1798), (function-axioms) are % 131.67/18.62 | | | | | | | | | | | | | | | inconsistent by sub-proof #455. % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | Case 2: % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | (1799) all_57_10 = e0 & op(e2, e0) = e0 % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | ALPHA: (1799) implies: % 131.67/18.62 | | | | | | | | | | | | | | | (1800) all_57_10 = e0 % 131.67/18.62 | | | | | | | | | | | | | | | (1801) op(e2, e0) = e0 % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | Case 1: % 131.67/18.62 | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | (1802) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 131.67/18.62 | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 131.67/18.62 | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (224), (225), % 131.67/18.62 | | | | | | | | | | | | | | | | (226), (1761), (1800), (1801), (1802), % 131.67/18.62 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.62 | | | | | | | | | | | | | | | | #445. % 131.67/18.62 | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | Case 2: % 131.67/18.62 | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | (1803) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 131.67/18.62 | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 131.67/18.62 | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (1762), (1763), (1803), % 131.67/18.62 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.62 | | | | | | | | | | | | | | | | #504. % 131.67/18.62 | | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | | End of split % 131.67/18.62 | | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | | End of split % 131.67/18.62 | | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | End of split % 131.67/18.62 | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | Case 2: % 131.67/18.62 | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | (1804) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 131.67/18.62 | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 131.67/18.62 | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 131.67/18.62 | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.67/18.62 | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 131.67/18.62 | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.67/18.62 | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 131.67/18.62 | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | ALPHA: (1804) implies: % 131.67/18.62 | | | | | | | | | | | | | (1805) op(e2, e2) = e1 % 131.67/18.62 | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | REF_CLOSE: (4), (1767), (1805), (function-axioms) are % 131.67/18.62 | | | | | | | | | | | | | inconsistent by sub-proof #675. % 131.67/18.62 | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | End of split % 131.67/18.62 | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | Case 2: % 131.67/18.62 | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | (1806) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.67/18.62 | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.67/18.62 | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 131.67/18.62 | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.62 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.62 | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.67/18.62 | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.67/18.62 | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.67/18.62 | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.67/18.62 | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.67/18.62 | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.67/18.62 | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.67/18.62 | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.67/18.62 | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.67/18.62 | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.67/18.62 | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.67/18.62 | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.67/18.62 | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.67/18.62 | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.67/18.62 | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.67/18.62 | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.67/18.62 | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.67/18.62 | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.67/18.62 | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.67/18.62 | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.67/18.62 | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.67/18.62 | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.67/18.62 | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.67/18.62 | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.67/18.62 | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.67/18.62 | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.67/18.62 | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.67/18.62 | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.67/18.62 | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.62 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.62 | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.67/18.62 | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.67/18.62 | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.67/18.62 | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.67/18.62 | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.67/18.62 | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.67/18.62 | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.67/18.62 | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.67/18.62 | | | | | | | | | | | | & $i(all_56_29)))) % 131.67/18.62 | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | BETA: splitting (1806) gives: % 131.67/18.62 | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | Case 1: % 131.67/18.62 | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | (1807) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.67/18.62 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 131.67/18.62 | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 131.67/18.62 | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.67/18.62 | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 131.67/18.62 | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.67/18.62 | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 131.67/18.62 | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | ALPHA: (1807) implies: % 131.67/18.62 | | | | | | | | | | | | | (1808) op(e2, e0) = e2 % 131.67/18.62 | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | REF_CLOSE: (164), (1343), (1808), (function-axioms) are % 131.67/18.62 | | | | | | | | | | | | | inconsistent by sub-proof #768. % 131.67/18.62 | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | Case 2: % 131.67/18.62 | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | (1809) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.67/18.62 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.67/18.62 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.67/18.62 | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.67/18.62 | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.67/18.62 | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.67/18.62 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.67/18.62 | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.67/18.62 | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.67/18.62 | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.67/18.62 | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.67/18.62 | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.67/18.62 | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.67/18.62 | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.67/18.62 | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.67/18.62 | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.67/18.62 | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.67/18.62 | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.67/18.62 | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.67/18.62 | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.67/18.62 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.67/18.62 | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.67/18.62 | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.67/18.62 | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.67/18.62 | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.67/18.62 | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.67/18.62 | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.62 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.62 | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.67/18.62 | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.67/18.62 | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.67/18.62 | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.67/18.62 | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.67/18.62 | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.67/18.62 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.67/18.62 | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.67/18.62 | | | | | | | | | | | | | & $i(all_56_29)))) % 131.67/18.62 | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | BETA: splitting (1809) gives: % 131.67/18.62 | | | | | | | | | | | | | % 131.67/18.62 | | | | | | | | | | | | | Case 1: % 131.67/18.62 | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | (1810) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.67/18.63 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 131.67/18.63 | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.67/18.63 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.67/18.63 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 131.67/18.63 | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 131.67/18.63 | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | ALPHA: (1810) implies: % 131.67/18.63 | | | | | | | | | | | | | | (1811) op(e1, e1) = e2 % 131.67/18.63 | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1811), (function-axioms) are % 131.67/18.63 | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 131.67/18.63 | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | Case 2: % 131.67/18.63 | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | (1812) op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.67/18.63 | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.67/18.63 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 131.67/18.63 | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.67/18.63 | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 131.67/18.63 | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.67/18.63 | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 131.67/18.63 | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 131.67/18.63 | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.67/18.63 | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.67/18.63 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.67/18.63 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.67/18.63 | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 131.67/18.63 | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.67/18.63 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.67/18.63 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.67/18.63 | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.63 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 131.67/18.63 | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 131.67/18.63 | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 131.67/18.63 | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 131.67/18.63 | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 131.67/18.63 | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 131.67/18.63 | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_29))) % 131.67/18.63 | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | ALPHA: (1812) implies: % 131.67/18.63 | | | | | | | | | | | | | | (1813) op(e0, e0) = all_56_31 % 131.67/18.63 | | | | | | | | | | | | | | (1814) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.67/18.63 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.67/18.63 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.63 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.63 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 131.67/18.63 | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 131.67/18.63 | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 131.67/18.63 | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 131.67/18.63 | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 131.67/18.63 | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 131.67/18.63 | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 131.67/18.63 | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.67/18.63 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.67/18.63 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 131.67/18.63 | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.67/18.63 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 131.67/18.63 | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 131.67/18.63 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.67/18.63 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 131.67/18.63 | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 131.67/18.63 | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 131.67/18.63 | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 131.67/18.63 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.67/18.63 | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, % 131.67/18.63 | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (1345), (1813) % 131.67/18.63 | | | | | | | | | | | | | | gives: % 131.67/18.63 | | | | | | | | | | | | | | (1815) all_56_31 = e2 % 131.67/18.63 | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | BETA: splitting (1814) gives: % 131.67/18.63 | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | Case 1: % 131.67/18.63 | | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | | (1816) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.67/18.63 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.67/18.63 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.63 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.63 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 131.67/18.63 | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 131.67/18.63 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 131.67/18.63 | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 131.67/18.63 | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 131.67/18.63 | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 131.67/18.63 | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 131.67/18.63 | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 131.67/18.63 | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 131.67/18.63 | | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | | BETA: splitting (1816) gives: % 131.67/18.63 | | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | | Case 1: % 131.67/18.63 | | | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | | | (1817) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.67/18.63 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 131.67/18.63 | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.67/18.63 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.67/18.63 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 131.67/18.63 | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 131.67/18.63 | | | | | | | | | | | | | | | | $i(all_56_25) % 131.67/18.63 | | | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | | | ALPHA: (1817) implies: % 131.67/18.63 | | | | | | | | | | | | | | | | (1818) all_56_31 = e3 % 131.67/18.63 | | | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1815), (1818) are inconsistent by sub-proof % 131.67/18.63 | | | | | | | | | | | | | | | | #532. % 131.67/18.63 | | | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | | Case 2: % 131.67/18.63 | | | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | | | (1819) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 131.67/18.63 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 131.67/18.63 | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.67/18.63 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.67/18.63 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.67/18.63 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 131.67/18.63 | | | | | | | | | | | | | | | | $i(all_56_27) % 131.67/18.63 | | | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | | | ALPHA: (1819) implies: % 131.67/18.63 | | | | | | | | | | | | | | | | (1820) op(e0, e2) = e0 % 131.67/18.63 | | | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1763), (1820), (function-axioms) are % 131.67/18.63 | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 131.67/18.63 | | | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | | End of split % 131.67/18.63 | | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | Case 2: % 131.67/18.63 | | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | | (1821) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 131.67/18.63 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.67/18.63 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 131.67/18.63 | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.67/18.63 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.67/18.63 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 131.67/18.63 | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 131.67/18.63 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.67/18.63 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 131.67/18.63 | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 131.67/18.63 | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 131.67/18.63 | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 131.67/18.63 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.67/18.63 | | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (1674), (1815), (1821), % 131.67/18.63 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.67/18.63 | | | | | | | | | | | | | | | #467. % 131.67/18.63 | | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | | End of split % 131.67/18.63 | | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | | End of split % 131.67/18.63 | | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | End of split % 131.67/18.63 | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | End of split % 131.67/18.63 | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | End of split % 131.67/18.63 | | | | | | | | | | % 131.67/18.63 | | | | | | | | | End of split % 131.67/18.63 | | | | | | | | | % 131.67/18.63 | | | | | | | | End of split % 131.67/18.63 | | | | | | | | % 131.67/18.63 | | | | | | | End of split % 131.67/18.63 | | | | | | | % 131.67/18.63 | | | | | | Case 2: % 131.67/18.63 | | | | | | | % 131.67/18.63 | | | | | | | (1822) all_16_2 = e2 % 131.67/18.63 | | | | | | | (1823) ( ~ (all_16_0 = e1) & op(e2, e3) = all_16_0 & % 131.67/18.63 | | | | | | | $i(all_16_0)) | ( ~ (all_16_1 = e0) & op(e2, e2) = % 131.67/18.63 | | | | | | | all_16_1 & $i(all_16_1)) % 131.67/18.63 | | | | | | | % 131.67/18.63 | | | | | | | COMBINE_EQS: (327), (1822) imply: % 131.67/18.63 | | | | | | | (1824) all_10_2 = e2 % 131.67/18.63 | | | | | | | % 131.67/18.63 | | | | | | | REDUCE: (336), (1824) imply: % 131.67/18.63 | | | | | | | (1825) ~ (all_52_1 = e2) % 131.67/18.63 | | | | | | | % 131.67/18.63 | | | | | | | REDUCE: (338), (1824) imply: % 131.67/18.63 | | | | | | | (1826) ~ (all_52_2 = e2) % 131.67/18.63 | | | | | | | % 131.67/18.63 | | | | | | | REDUCE: (340), (1824) imply: % 131.67/18.63 | | | | | | | (1827) ~ (all_52_3 = e2) % 131.67/18.63 | | | | | | | % 131.67/18.63 | | | | | | | REDUCE: (342), (1824) imply: % 131.67/18.63 | | | | | | | (1828) ~ (all_52_4 = e2) % 131.67/18.63 | | | | | | | % 131.67/18.63 | | | | | | | REDUCE: (344), (1824) imply: % 131.67/18.63 | | | | | | | (1829) ~ (all_52_8 = e2) % 131.67/18.63 | | | | | | | % 131.67/18.63 | | | | | | | REDUCE: (346), (1824) imply: % 131.67/18.63 | | | | | | | (1830) ~ (all_52_12 = e2) % 131.67/18.63 | | | | | | | % 131.67/18.63 | | | | | | | BETA: splitting (236) gives: % 131.67/18.63 | | | | | | | % 131.67/18.63 | | | | | | | Case 1: % 131.67/18.63 | | | | | | | | % 131.67/18.63 | | | | | | | | (1831) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & % 131.67/18.63 | | | | | | | | op(e3, e2) = e2) % 131.67/18.63 | | | | | | | | % 131.67/18.63 | | | | | | | | BETA: splitting (1831) gives: % 131.67/18.63 | | | | | | | | % 131.67/18.63 | | | | | | | | Case 1: % 131.67/18.63 | | | | | | | | | % 131.67/18.63 | | | | | | | | | (1832) all_57_0 = e2 & op(e3, e3) = e2 % 131.67/18.63 | | | | | | | | | % 131.67/18.63 | | | | | | | | | ALPHA: (1832) implies: % 131.67/18.63 | | | | | | | | | (1833) all_57_0 = e2 % 131.67/18.63 | | | | | | | | | (1834) op(e3, e3) = e2 % 131.67/18.63 | | | | | | | | | % 131.67/18.63 | | | | | | | | | BETA: splitting (61) gives: % 131.67/18.63 | | | | | | | | | % 131.67/18.63 | | | | | | | | | Case 1: % 131.67/18.63 | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | (1835) ~ (all_20_2 = e2) % 131.67/18.63 | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | REDUCE: (318), (1835) imply: % 131.67/18.63 | | | | | | | | | | (1836) ~ (all_4_2 = e2) % 131.67/18.63 | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | BETA: splitting (73) gives: % 131.67/18.63 | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | Case 1: % 131.67/18.63 | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | (1837) ~ (all_28_2 = e3) % 131.67/18.63 | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | REDUCE: (316), (1837) imply: % 131.67/18.63 | | | | | | | | | | | (1838) ~ (all_6_2 = e3) % 131.67/18.63 | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | BETA: splitting (76) gives: % 131.67/18.63 | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | Case 1: % 131.67/18.63 | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | (1839) ~ (all_30_2 = e0) % 131.67/18.63 | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | REDUCE: (309), (1839) imply: % 131.67/18.63 | | | | | | | | | | | | (1840) ~ (all_8_2 = e0) % 131.67/18.63 | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | BETA: splitting (199) gives: % 131.67/18.63 | | | | | | | | | | | | % 131.67/18.63 | | | | | | | | | | | | Case 1: % 131.67/18.63 | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | (1841) all_54_5 = e3 % 131.93/18.63 | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | COMBINE_EQS: (267), (1841) imply: % 131.93/18.63 | | | | | | | | | | | | | (1842) all_8_2 = e3 % 131.93/18.63 | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | REDUCE: (376), (1842) imply: % 131.93/18.63 | | | | | | | | | | | | | (1843) $false % 131.93/18.63 | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | CLOSE: (1843) is inconsistent. % 131.93/18.63 | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | Case 2: % 131.93/18.63 | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | (1844) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 131.93/18.63 | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | BETA: splitting (1844) gives: % 131.93/18.63 | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | Case 1: % 131.93/18.63 | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | (1845) all_54_5 = e2 % 131.93/18.63 | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | COMBINE_EQS: (267), (1845) imply: % 131.93/18.63 | | | | | | | | | | | | | | (1846) all_8_2 = e2 % 131.93/18.63 | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | REDUCE: (356), (1846) imply: % 131.93/18.63 | | | | | | | | | | | | | | (1847) ~ (all_52_9 = e2) % 131.93/18.63 | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | REDUCE: (358), (1846) imply: % 131.93/18.63 | | | | | | | | | | | | | | (1848) ~ (all_52_13 = e2) % 131.93/18.63 | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | REDUCE: (42), (1846) imply: % 131.93/18.63 | | | | | | | | | | | | | | (1849) op(e2, e2) = e2 % 131.93/18.63 | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | BETA: splitting (206) gives: % 131.93/18.63 | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | Case 1: % 131.93/18.63 | | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | | (1850) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.93/18.63 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.93/18.63 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.93/18.63 | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.93/18.63 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.93/18.63 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.93/18.63 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.93/18.63 | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 131.93/18.63 | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.93/18.63 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.93/18.63 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.93/18.63 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.93/18.63 | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.93/18.63 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.93/18.63 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.93/18.63 | | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | | BETA: splitting (1850) gives: % 131.93/18.63 | | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | | Case 1: % 131.93/18.63 | | | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | | | (1851) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 131.93/18.63 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.93/18.63 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 131.93/18.63 | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 131.93/18.63 | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.93/18.63 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 131.93/18.63 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.93/18.63 | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 131.93/18.63 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.93/18.63 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 131.93/18.63 | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 131.93/18.63 | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 131.93/18.63 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 131.93/18.63 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 131.93/18.63 | | | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (1849), (1851), (function-axioms) are % 131.93/18.63 | | | | | | | | | | | | | | | | inconsistent by sub-proof #444. % 131.93/18.63 | | | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | | Case 2: % 131.93/18.63 | | | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | | | (1852) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 131.93/18.63 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.93/18.63 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 131.93/18.63 | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 131.93/18.63 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.93/18.63 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.93/18.63 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.93/18.63 | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 131.93/18.63 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.93/18.63 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.93/18.63 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.93/18.63 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 131.93/18.63 | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.93/18.63 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 131.93/18.63 | | | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (1825), (1834), (1852), % 131.93/18.63 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.93/18.63 | | | | | | | | | | | | | | | | #443. % 131.93/18.63 | | | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | | End of split % 131.93/18.63 | | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | Case 2: % 131.93/18.63 | | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | | (1853) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.93/18.63 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.93/18.63 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.93/18.63 | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.93/18.63 | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.93/18.63 | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.93/18.63 | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.93/18.63 | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.93/18.63 | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 131.93/18.63 | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 131.93/18.63 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.93/18.63 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 131.93/18.63 | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.93/18.63 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 131.93/18.63 | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 131.93/18.63 | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 131.93/18.63 | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.93/18.63 | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 131.93/18.63 | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 131.93/18.63 | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 131.93/18.63 | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 131.93/18.63 | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 131.93/18.63 | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 131.93/18.63 | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.93/18.63 | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 131.93/18.63 | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 131.93/18.63 | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 131.93/18.63 | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.93/18.63 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.93/18.63 | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 131.93/18.63 | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 131.93/18.63 | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 131.93/18.63 | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 131.93/18.63 | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.93/18.63 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.93/18.63 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.93/18.63 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.93/18.63 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.93/18.63 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.93/18.63 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.93/18.63 | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.93/18.63 | | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | | BETA: splitting (1853) gives: % 131.93/18.63 | | | | | | | | | | | | | | | % 131.93/18.63 | | | | | | | | | | | | | | | Case 1: % 131.93/18.63 | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | (1854) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 131.93/18.64 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.93/18.64 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.93/18.64 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.93/18.64 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 131.93/18.64 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 131.93/18.64 | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 131.93/18.64 | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 131.93/18.64 | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 131.93/18.64 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 131.93/18.64 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 131.93/18.64 | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.93/18.64 | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | REF_CLOSE: (39), (165), (1838), (1847), (1854), % 131.93/18.64 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.93/18.64 | | | | | | | | | | | | | | | | #769. % 131.93/18.64 | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | Case 2: % 131.93/18.64 | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | (1855) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.93/18.64 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.93/18.64 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 131.93/18.64 | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 131.93/18.64 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.93/18.64 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 131.93/18.64 | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.93/18.64 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.93/18.64 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.93/18.64 | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.93/18.64 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.93/18.64 | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.93/18.64 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.93/18.64 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.93/18.64 | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.93/18.64 | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.93/18.64 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.93/18.64 | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.93/18.64 | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.93/18.64 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.93/18.64 | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.93/18.64 | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.93/18.64 | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.93/18.64 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.93/18.64 | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.93/18.64 | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.93/18.64 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.93/18.64 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.93/18.64 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.93/18.64 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.93/18.64 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.93/18.64 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.93/18.64 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.93/18.64 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.93/18.64 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.93/18.64 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.93/18.64 | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.93/18.64 | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | BETA: splitting (1855) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | (1856) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 131.93/18.64 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 131.93/18.64 | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 131.93/18.64 | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.93/18.64 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 131.93/18.64 | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 131.93/18.64 | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 131.93/18.64 | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | ALPHA: (1856) implies: % 131.93/18.64 | | | | | | | | | | | | | | | | | (1857) op(e2, e0) = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1848), (1857), (function-axioms) are % 131.93/18.64 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 131.93/18.64 | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | Case 2: % 131.93/18.64 | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | (1858) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.93/18.64 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 131.93/18.64 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 131.93/18.64 | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 131.93/18.64 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 131.93/18.64 | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 131.93/18.64 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 131.93/18.64 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.93/18.64 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 131.93/18.64 | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 131.93/18.64 | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.93/18.64 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 131.93/18.64 | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 131.93/18.64 | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 131.93/18.64 | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 131.93/18.64 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 131.93/18.64 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 131.93/18.64 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 131.93/18.64 | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 131.93/18.64 | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 131.93/18.64 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.93/18.64 | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 131.93/18.64 | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 131.93/18.64 | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.93/18.64 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.93/18.64 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.93/18.64 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.93/18.64 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.93/18.64 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 131.93/18.64 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 131.93/18.64 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 131.93/18.64 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 131.93/18.64 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 131.93/18.64 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 131.93/18.64 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 131.93/18.64 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 131.93/18.64 | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 131.93/18.64 | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | BETA: splitting (1858) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | (1859) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 131.93/18.64 | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.93/18.64 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.93/18.64 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 131.93/18.64 | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 131.93/18.64 | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | ALPHA: (1859) implies: % 131.93/18.64 | | | | | | | | | | | | | | | | | | (1860) op(e1, e1) = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1860), (function-axioms) are % 131.93/18.64 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 131.93/18.64 | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.64 | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | (1861) op(e0, e0) = all_56_31 & $i(all_56_31) & % 131.93/18.64 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 131.93/18.64 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 131.93/18.64 | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 131.93/18.64 | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.93/18.64 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 131.93/18.64 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 131.93/18.64 | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 131.93/18.64 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.93/18.64 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 131.93/18.64 | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 131.93/18.64 | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 131.93/18.64 | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 131.93/18.64 | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | ALPHA: (1861) implies: % 131.93/18.64 | | | | | | | | | | | | | | | | | | (1862) op(e0, e0) = all_56_31 % 131.93/18.64 | | | | | | | | | | | | | | | | | | (1863) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.93/18.64 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.93/18.64 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.93/18.64 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 131.93/18.64 | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 131.93/18.64 | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 131.93/18.64 | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 131.93/18.64 | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 131.93/18.64 | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 131.93/18.64 | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 131.93/18.64 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 131.93/18.64 | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 131.93/18.64 | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 131.93/18.64 | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 131.93/18.64 | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 131.93/18.64 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.93/18.64 | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | (1864) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (1829), (1847), (1864), % 131.93/18.64 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.93/18.64 | | | | | | | | | | | | | | | | | | | #441. % 131.93/18.64 | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | (1865) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | BETA: splitting (1865) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | (1866) all_57_8 = e2 & op(e1, e1) = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | ALPHA: (1866) implies: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | (1867) op(e1, e1) = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (1867), (function-axioms) are % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | (1868) all_57_14 = e2 & op(e0, e1) = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | ALPHA: (1868) implies: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | (1869) all_57_14 = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | (1870) op(e0, e1) = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | (1871) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (1830), (1848), (1871), % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | #440. % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | (1872) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1872) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | (1873) all_57_11 = e2 & op(e1, e0) = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1873) implies: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | (1874) all_57_11 = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | (1875) op(e1, e0) = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | (1876) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1876) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1877) all_57_2 = e2 & op(e2, e3) = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1877) implies: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1878) op(e2, e3) = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (1825), (1878), (function-axioms) are % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #779. % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1879) all_57_3 = e2 & op(e2, e2) = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1879) implies: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1880) all_57_3 = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (36), (1862) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1881) all_56_31 = all_4_2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11, % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, e0, simplifying with (157), (1870) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1882) all_52_11 = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e1, simplifying with (160), (1875) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1883) all_52_14 = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (1883) imply: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1884) ~ (all_6_2 = e2) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (1883) imply: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | (1885) ~ (all_4_2 = e2) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1863) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | (1886) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1886) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1887) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1887) implies: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1888) all_56_31 = e3 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1889) op(e0, e3) = e0 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1890) op(e3, e3) = all_56_1 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1881), (1888) imply: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1891) all_4_2 = e3 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1891) implies: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1892) all_4_2 = e3 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (1892) imply: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1893) all_44_2 = e3 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (1892) imply: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1894) ~ (all_52_7 = e3) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (1892) imply: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1895) ~ (all_52_13 = e3) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1892) imply: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (1896) op(e0, e0) = e3 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1897) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1897) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1898) all_57_9 = e3 & op(e3, e0) = e3 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1898) implies: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1899) all_57_9 = e3 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (208), (212), (1862), % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1863), (1874), (1875), (1896), (1899), % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #439. % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1900) all_57_10 = e3 & op(e2, e0) = e3 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1895), (1900), (function-axioms) are % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749. % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1901) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1901) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1902) all_57_11 = e3 & op(e1, e0) = e3 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1874), (1902) are inconsistent by sub-proof % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #723. % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1903) all_57_15 = e3 & op(e0, e0) = e3 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1903) implies: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1904) all_57_15 = e3 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1905) ~ (all_44_2 = e3) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1893), (1905) imply: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1906) $false % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1906) is inconsistent. % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1907) ( ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 & % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_44_0)) | ( ~ (all_44_1 = e2) & op(e3, e3) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_44_1 & $i(all_44_1)) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1908) ~ (all_46_2 = e0) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (295), (1908) imply: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1909) ~ (all_6_2 = e0) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1910) all_54_10 = e3 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (1838), (1910) are inconsistent by % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #742. % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1911) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1911) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1912) all_54_10 = e2 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (372), (1912) are inconsistent by sub-proof % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #741. % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1913) ~ (all_54_10 = e2) % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1914) all_54_10 = e1 | all_54_10 = e0 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1914) gives: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1915) all_54_10 = e1 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (1915) imply: % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1916) all_6_2 = e1 % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1916) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1917) all_6_2 = e1 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (1917) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1918) all_46_2 = e1 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (1917) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1919) ~ (all_52_2 = e1) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (1917) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1920) ~ (e2 = e1) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (1917) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1921) op(e1, e1) = e1 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0, % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (1889) gives: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1922) all_52_3 = e0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_1, % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (1834), (1890) gives: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1923) all_56_1 = e2 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (1922) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1924) ~ (all_52_2 = e0) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1827), (1922) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1925) ~ (e2 = e0) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1926) all_54_8 = e3 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (1926) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1927) all_52_2 = e3 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1927) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1928) all_52_2 = e3 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (1928) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1929) ~ (all_52_6 = e3) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1929) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1930) ~ (all_52_6 = e3) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1931) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1931) gives: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1932) all_57_1 = e3 & op(e3, e2) = e3 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1932) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1933) all_57_1 = e3 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1907) gives: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1934) ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 & % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_44_0) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1934) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1935) ~ (all_44_0 = e1) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1936) op(e3, e0) = all_44_0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1937) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1937) gives: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1938) all_57_0 = e1 & op(e3, e3) = e1 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1938) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1939) op(e3, e3) = e1 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (1939), (function-axioms) are % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1940) all_57_1 = e1 & op(e3, e2) = e1 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1940) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1941) all_57_1 = e1 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1933), (1941) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1942) e3 = e1 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (1942) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1943) $false % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1943) is inconsistent. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1944) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1944) gives: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1945) all_57_4 = e1 & op(e3, e1) = e1 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1945) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1946) all_57_4 = e1 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1947) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1947) gives: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1948) all_57_4 = e0 & op(e3, e1) = e0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1948) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1949) all_57_4 = e0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1946), (1949) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1950) e1 = e0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1950) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1951) e1 = e0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1918), (1951) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1952) all_46_2 = e0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (1870), (1896), (1952), (function-axioms) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #570. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1953) all_57_5 = e0 & op(e2, e1) = e0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1953) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1954) all_57_5 = e0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1955) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1955) gives: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1956) all_57_4 = e3 & op(e3, e1) = e3 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1946), (1956) are inconsistent by sub-proof % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #438. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1957) all_57_5 = e3 & op(e2, e1) = e3 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1957) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1958) all_57_5 = e3 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1954), (1958) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1959) e3 = e0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1959) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1960) e3 = e0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (1960) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1961) $false % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1961) is inconsistent. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1962) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1962) gives: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1963) all_57_8 = e3 & op(e1, e1) = e3 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1963) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1964) op(e1, e1) = e3 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (1921), (1964), (function-axioms) are % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1965) all_57_14 = e3 & op(e0, e1) = e3 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1965) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1966) all_57_14 = e3 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1869), (1966) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1967) e3 = e2 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1904), (1967) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1968) all_57_15 = e2 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (208), (209), % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (1869), (1894), (1968), (function-axioms) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #433. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1969) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1969) gives: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1970) all_57_8 = e0 & op(e1, e1) = e0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1970) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1971) op(e1, e1) = e0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1921), (1971), (function-axioms) are % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #721. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1972) all_57_14 = e0 & op(e0, e1) = e0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1972) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1973) op(e0, e1) = e0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1870), (1973), (function-axioms) are % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1974) all_57_9 = e1 & op(e3, e0) = e1 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1974) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1975) op(e3, e0) = e1 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1935), (1936), (1975), (function-axioms) are % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #432. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1976) ~ (all_44_1 = e2) & op(e3, e3) = all_44_1 & % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_44_1) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1834), (1976), (function-axioms) are inconsistent % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #431. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1977) all_57_3 = e3 & op(e2, e2) = e3 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1977) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1978) all_57_3 = e3 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1880), (1978) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1979) e3 = e2 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1979) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1980) e3 = e2 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1904), (1980) imply: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1981) all_57_15 = e2 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (208), (209), % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (1869), (1894), (1981), (function-axioms) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #433. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1982) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (1894), (1930), (1982), % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #555. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1983) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (1826), (1919), (1924), (1983) are % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #429. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1984) all_54_10 = e0 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (295), (334), (1870), (1896), (1984), % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #569. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1985) ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 & % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_46_1 & $i(all_46_1)) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1870), (1896), (1985), (function-axioms) are % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #757. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (1986) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1986) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (1987) ~ (all_56_11 = e2) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (1988) op(e2, e2) = all_56_11 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1849), (1987), (1988), (function-axioms) are % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #531. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | (1989) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (1870), (1875), (1989), % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | #428. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | (1990) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (1847), (1848), (1990), % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | #625. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | (1991) all_57_15 = e2 & op(e0, e0) = e2 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1991) implies: % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | (1992) op(e0, e0) = e2 % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (1836), (1862), (1992), (function-axioms) % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #427. % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | (1993) all_54_5 = e1 | all_54_5 = e0 % 131.93/18.65 | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | REF_CLOSE: (267), (373), (1840), (1993) are inconsistent by % 131.93/18.65 | | | | | | | | | | | | | | sub-proof #624. % 131.93/18.65 | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | End of split % 131.93/18.65 | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | Case 2: % 131.93/18.65 | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | (1994) all_30_2 = e0 % 131.93/18.65 | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | COMBINE_EQS: (309), (1994) imply: % 131.93/18.65 | | | | | | | | | | | | (1995) all_8_2 = e0 % 131.93/18.65 | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | COMBINE_EQS: (301), (1995) imply: % 131.93/18.65 | | | | | | | | | | | | (1996) all_42_2 = e0 % 131.93/18.65 | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | REDUCE: (347), (1995) imply: % 131.93/18.65 | | | | | | | | | | | | (1997) ~ (all_52_1 = e0) % 131.93/18.65 | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | REDUCE: (350), (1995) imply: % 131.93/18.65 | | | | | | | | | | | | (1998) ~ (all_52_4 = e0) % 131.93/18.65 | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | REDUCE: (352), (1995) imply: % 131.93/18.65 | | | | | | | | | | | | (1999) ~ (all_52_6 = e0) % 131.93/18.65 | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | REDUCE: (354), (1995) imply: % 131.93/18.65 | | | | | | | | | | | | (2000) ~ (all_52_7 = e0) % 131.93/18.65 | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | REDUCE: (373), (1995) imply: % 131.93/18.65 | | | | | | | | | | | | (2001) ~ (e1 = e0) % 131.93/18.65 | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | REDUCE: (42), (1995) imply: % 131.93/18.65 | | | | | | | | | | | | (2002) op(e2, e2) = e0 % 131.93/18.65 | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | BETA: splitting (1823) gives: % 131.93/18.65 | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | Case 1: % 131.93/18.65 | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | (2003) ~ (all_16_0 = e1) & op(e2, e3) = all_16_0 & % 131.93/18.65 | | | | | | | | | | | | | $i(all_16_0) % 131.93/18.65 | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | ALPHA: (2003) implies: % 131.93/18.65 | | | | | | | | | | | | | (2004) ~ (all_16_0 = e1) % 131.93/18.65 | | | | | | | | | | | | | (2005) op(e2, e3) = all_16_0 % 131.93/18.65 | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | BETA: splitting (227) gives: % 131.93/18.65 | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | Case 1: % 131.93/18.65 | | | | | | | | | | | | | | % 131.93/18.65 | | | | | | | | | | | | | | (2006) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 131.93/18.65 | | | | | | | | | | | | | | & op(e2, e2) = e0) % 131.93/18.65 | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | BETA: splitting (2006) gives: % 131.93/18.66 | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | Case 1: % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | (2007) all_57_1 = e0 & op(e3, e2) = e0 % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | REF_CLOSE: (170), (1998), (2007), (function-axioms) are % 131.93/18.66 | | | | | | | | | | | | | | | inconsistent by sub-proof #693. % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | Case 2: % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | (2008) all_57_3 = e0 & op(e2, e2) = e0 % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | ALPHA: (2008) implies: % 131.93/18.66 | | | | | | | | | | | | | | | (2009) all_57_3 = e0 % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, % 131.93/18.66 | | | | | | | | | | | | | | | all_16_0, e3, e2, simplifying with (167), (2005) % 131.93/18.66 | | | | | | | | | | | | | | | gives: % 131.93/18.66 | | | | | | | | | | | | | | | (2010) all_52_1 = all_16_0 % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | COMBINE_EQS: (268), (2010) imply: % 131.93/18.66 | | | | | | | | | | | | | | | (2011) all_54_4 = all_16_0 % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | REDUCE: (149), (2010) imply: % 131.93/18.66 | | | | | | | | | | | | | | | (2012) ~ (all_52_2 = all_16_0) % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | SIMP: (2012) implies: % 131.93/18.66 | | | | | | | | | | | | | | | (2013) ~ (all_52_2 = all_16_0) % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | REDUCE: (148), (2010) imply: % 131.93/18.66 | | | | | | | | | | | | | | | (2014) ~ (all_52_3 = all_16_0) % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | SIMP: (2014) implies: % 131.93/18.66 | | | | | | | | | | | | | | | (2015) ~ (all_52_3 = all_16_0) % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | REDUCE: (146), (2010) imply: % 131.93/18.66 | | | | | | | | | | | | | | | (2016) ~ (all_52_9 = all_16_0) % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | SIMP: (2016) implies: % 131.93/18.66 | | | | | | | | | | | | | | | (2017) ~ (all_52_9 = all_16_0) % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | REDUCE: (145), (2010) imply: % 131.93/18.66 | | | | | | | | | | | | | | | (2018) ~ (all_52_13 = all_16_0) % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | SIMP: (2018) implies: % 131.93/18.66 | | | | | | | | | | | | | | | (2019) ~ (all_52_13 = all_16_0) % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | REDUCE: (1825), (2010) imply: % 131.93/18.66 | | | | | | | | | | | | | | | (2020) ~ (all_16_0 = e2) % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | REDUCE: (1997), (2010) imply: % 131.93/18.66 | | | | | | | | | | | | | | | (2021) ~ (all_16_0 = e0) % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 131.93/18.66 | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | Case 1: % 131.93/18.66 | | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | | (2022) all_54_4 = e3 % 131.93/18.66 | | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | | COMBINE_EQS: (2011), (2022) imply: % 131.93/18.66 | | | | | | | | | | | | | | | | (2023) all_16_0 = e3 % 131.93/18.66 | | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | | REDUCE: (2013), (2023) imply: % 131.93/18.66 | | | | | | | | | | | | | | | | (2024) ~ (all_52_2 = e3) % 131.93/18.66 | | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | | REDUCE: (2015), (2023) imply: % 131.93/18.66 | | | | | | | | | | | | | | | | (2025) ~ (all_52_3 = e3) % 131.93/18.66 | | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | | REDUCE: (2017), (2023) imply: % 131.93/18.66 | | | | | | | | | | | | | | | | (2026) ~ (all_52_9 = e3) % 131.93/18.66 | | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | | REDUCE: (2019), (2023) imply: % 131.93/18.66 | | | | | | | | | | | | | | | | (2027) ~ (all_52_13 = e3) % 131.93/18.66 | | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 131.93/18.66 | | | | | | | | | | | | | | | | % 131.93/18.66 | | | | | | | | | | | | | | | | Case 1: % 131.93/18.66 | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | (2028) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 132.03/18.66 | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 132.03/18.66 | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | BETA: splitting (2028) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | (2029) all_57_2 = e3 & op(e2, e3) = e3 % 132.03/18.66 | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | ALPHA: (2029) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | (2030) all_57_2 = e3 % 132.03/18.66 | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | (2031) ~ (all_34_2 = e3) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | REDUCE: (307), (2031) imply: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | (2032) ~ (all_4_2 = e3) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | (2033) all_54_15 = e3 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (2032), (2033) are inconsistent by % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | sub-proof #601. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | (2034) ~ (all_54_15 = e3) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | (2035) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2035) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | (2036) all_54_15 = e2 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (1836), (2036) are inconsistent by % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | sub-proof #748. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | (2037) ~ (all_54_15 = e2) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | (2038) all_54_15 = e1 | all_54_15 = e0 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2038) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2039) all_54_15 = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (2039) are inconsistent by sub-proof % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | #747. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2040) all_54_15 = e0 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (2040) imply: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2041) all_4_2 = e0 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2041) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2042) all_4_2 = e0 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (2042) imply: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2043) ~ (all_52_3 = e0) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (2042) imply: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2044) ~ (all_52_12 = e0) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2032), (2042) imply: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2045) ~ (e3 = e0) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1836), (2042) imply: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2046) ~ (e2 = e0) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2042) imply: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | (2047) op(e0, e0) = e0 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | (2048) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (1834), (2030), (2048), % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | #426. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | (2049) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2049) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | (2050) all_57_6 = e0 & op(e1, e3) = e0 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2050) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | (2051) all_57_6 = e0 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | (2052) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2052) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (2053) all_57_0 = e1 & op(e3, e3) = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2053) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (2054) op(e3, e3) = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (168), (169), (170), % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (232), (372), (1838), (1998), (2002), % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (2044), (2047), (2054), (function-axioms) are % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #595. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (2055) all_57_2 = e1 & op(e2, e3) = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2004), (2005), (2055), (function-axioms) are % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #425. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | (2056) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2056) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (2057) all_57_6 = e1 & op(e1, e3) = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (163), (192), (248), (1827), (2025), % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (2043), (2057), (function-axioms) are inconsistent % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #422. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (2058) all_57_12 = e1 & op(e0, e3) = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2058) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (2059) all_57_12 = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2060) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2060) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2061) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2061) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2062) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2062) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2063) op(e3, e2) = e3 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2064) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (170), (1834), (1998), (2064), % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #421. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2065) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2065) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2066) all_57_4 = e0 & op(e3, e1) = e0 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2066) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2067) all_57_4 = e0 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2068) op(e3, e1) = e0 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2069) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (165), (169), (2026), (2068), (2069), % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #420. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2070) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2070) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2071) all_57_8 = e3 & op(e1, e1) = e3 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2071) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2072) op(e1, e1) = e3 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (1838), (2072), (function-axioms) are % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2073) all_57_14 = e3 & op(e0, e1) = e3 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2073) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2074) all_57_14 = e3 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2075) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2075) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2076) all_57_4 = e2 & op(e3, e1) = e2 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1829), (2076), (function-axioms) are % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2077) all_57_5 = e2 & op(e2, e1) = e2 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2077) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2078) all_57_5 = e2 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2079) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2079) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2080) all_57_4 = e1 & op(e3, e1) = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2067), (2080) are inconsistent by sub-proof % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #419. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2081) all_57_5 = e1 & op(e2, e1) = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2081) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2082) all_57_5 = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2078), (2082) are inconsistent by sub-proof % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #418. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2083) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2083) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2084) all_57_8 = e1 & op(e1, e1) = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2084) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2085) op(e1, e1) = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2086) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2086) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2087) all_57_12 = e2 & op(e0, e3) = e2 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2087) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2088) all_57_12 = e2 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (233), (1833), (2030), (2051), % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2088) are inconsistent by sub-proof #416. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2089) all_57_13 = e2 & op(e0, e2) = e2 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2089) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2090) all_57_13 = e2 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2091) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2002), (2004), (2005), (2091), % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #415. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2092) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2092) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2093) all_57_5 = e1 & op(e2, e1) = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2093) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2094) all_57_5 = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2078), (2094) are inconsistent by sub-proof % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #418. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2095) all_57_10 = e1 & op(e2, e0) = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2095) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2096) all_57_10 = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2097) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2097) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2098) all_57_9 = e2 & op(e3, e0) = e2 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1830), (2098), (function-axioms) are % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2099) all_57_10 = e2 & op(e2, e0) = e2 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2099) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2100) all_57_10 = e2 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2096), (2100) are inconsistent by sub-proof % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #414. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2101) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2101) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2102) all_57_11 = e2 & op(e1, e0) = e2 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2102) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2103) all_57_11 = e2 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2104) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2104) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2105) all_57_6 = e3 & op(e1, e3) = e3 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2024), (2105), (function-axioms) are % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #761. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2106) all_57_7 = e3 & op(e1, e2) = e3 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2106) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2107) all_57_7 = e3 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2108) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2108) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2109) all_57_1 = e1 & op(e3, e2) = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2109) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2110) op(e3, e2) = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2063), (2110), (function-axioms) are % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #413. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2111) all_57_3 = e1 & op(e2, e2) = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2111) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2112) op(e2, e2) = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2002), (2112), (function-axioms) are % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2113) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2113) gives: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2114) all_57_7 = e1 & op(e1, e2) = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2114) implies: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2115) all_57_7 = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2107), (2115) imply: % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2116) e3 = e1 % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2116) implies: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2117) e3 = e1 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2074), (2117) imply: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2118) all_57_14 = e1 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (221), (222), % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (1838), (2067), (2118), (function-axioms) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #558. % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2119) all_57_13 = e1 & op(e0, e2) = e1 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2119) implies: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2120) all_57_13 = e1 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2090), (2120) are inconsistent by sub-proof % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #567. % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2121) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2121) gives: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2122) all_57_8 = e3 & op(e1, e1) = e3 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2122) implies: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2123) op(e1, e1) = e3 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (2085), (2123), (function-axioms) are % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662. % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2124) all_57_11 = e3 & op(e1, e0) = e3 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2124) implies: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2125) all_57_11 = e3 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2103), (2125) imply: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2126) e3 = e2 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2126) implies: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2127) e3 = e2 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2074), (2127) imply: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2128) all_57_14 = e2 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209), (211), % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2090), (2128) are inconsistent by sub-proof #401. % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2129) all_57_15 = e2 & op(e0, e0) = e2 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2129) implies: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2130) all_57_15 = e2 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (208), (2059), (2074), (2090), % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2130) are inconsistent by sub-proof #398. % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2131) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2131) gives: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2132) all_57_14 = e2 & op(e0, e1) = e2 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2132) implies: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2133) all_57_14 = e2 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2074), (2133) are inconsistent by sub-proof % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #407. % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2134) all_57_15 = e2 & op(e0, e0) = e2 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2134) implies: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2135) op(e0, e0) = e2 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2047), (2135), (function-axioms) are % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #714. % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2136) all_57_14 = e1 & op(e0, e1) = e1 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2136) implies: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2137) all_57_14 = e1 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (221), (222), % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (1838), (2067), (2137), (function-axioms) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #558. % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2138) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2138) gives: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2139) all_57_8 = e2 & op(e1, e1) = e2 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2139) implies: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2140) op(e1, e1) = e2 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2140), (function-axioms) are % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2141) all_57_14 = e2 & op(e0, e1) = e2 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2074), (2141) are inconsistent by sub-proof % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #397. % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2142) all_57_9 = e0 & op(e3, e0) = e0 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (2044), (2142), (function-axioms) are % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #618. % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2143) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2143) implies: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2144) op(e3, e3) = e1 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (235), (237), % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2059), (2144), (function-axioms) are inconsistent % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #583. % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2145) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2145) gives: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2146) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2146) implies: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2147) op(e3, e3) = e0 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2147), (function-axioms) are % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2148) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2148) implies: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2149) op(e2, e2) = e3 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2002), (2149), (function-axioms) are % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2150) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2150) gives: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2151) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (1838), (2002), (2151), % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #621. % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2152) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (372), (2047), (2152), % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #596. % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | (2153) all_57_12 = e0 & op(e0, e3) = e0 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2153) implies: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | (2154) all_57_12 = e0 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | (2155) op(e0, e3) = e0 % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | (2156) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2156) gives: % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (2157) all_57_0 = e1 & op(e3, e3) = e1 % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2157) implies: % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (2158) op(e3, e3) = e1 % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2159) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2159) gives: % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2160) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2160) gives: % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2161) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2158), (function-axioms) are % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743. % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2162) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2162) implies: % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2163) op(e3, e1) = e3 % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (168), (169), (170), (232), (1998), % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2044), (2158), (2163), (function-axioms) are % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #599. % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2164) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2164) gives: % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2165) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2165) implies: % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2166) op(e0, e3) = all_56_7 % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2043), (2155), (2166), (function-axioms) % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #620. % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2167) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2167) implies: % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2168) op(e2, e2) = e3 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2002), (2168), (function-axioms) are % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2169) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2169) gives: % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2170) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (1838), (2002), (2170), % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #621. % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2171) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2171) gives: % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2172) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2172) implies: % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2173) op(e0, e3) = all_56_7 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2043), (2155), (2173), (function-axioms) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #620. % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2174) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (372), (2047), (2174), % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #709. % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (2175) all_57_2 = e1 & op(e2, e3) = e1 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2004), (2005), (2175), (function-axioms) are % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #425. % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | (2176) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2176) gives: % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (2177) all_57_6 = e1 & op(e1, e3) = e1 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (163), (192), (248), (1827), (2025), % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (2043), (2177), (function-axioms) are inconsistent % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #422. % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (2178) all_57_12 = e1 & op(e0, e3) = e1 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2178) implies: % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (2179) all_57_12 = e1 % 132.03/18.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2154), (2179) are inconsistent by sub-proof % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | #581. % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.71 | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | (2180) all_34_2 = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (2180) imply: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | (2181) all_4_2 = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | SIMP: (2181) implies: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | (2182) all_4_2 = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (2182) imply: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | (2183) all_44_2 = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | REDUCE: (367), (2182) imply: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | (2184) ~ (all_52_11 = e3) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | REDUCE: (368), (2182) imply: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | (2185) ~ (all_52_12 = e3) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | REDUCE: (370), (2182) imply: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | (2186) ~ (all_52_14 = e3) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2182) imply: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | (2187) op(e0, e0) = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | (2188) ~ (all_42_2 = e0) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | REDUCE: (1996), (2188) imply: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | (2189) $false % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | CLOSE: (2189) is inconsistent. % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | (2190) ( ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 & % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | $i(all_42_0)) | ( ~ (all_42_1 = e3) & op(e0, e0) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | = all_42_1 & $i(all_42_1)) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | (2191) ~ (all_44_2 = e3) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2183), (2191) imply: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | (2192) $false % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | CLOSE: (2192) is inconsistent. % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | (2193) ( ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 & % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | $i(all_44_0)) | ( ~ (all_44_1 = e2) & op(e3, e3) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | = all_44_1 & $i(all_44_1)) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | (2194) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2194) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | (2195) all_57_4 = e3 & op(e3, e1) = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2195) implies: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | (2196) all_57_4 = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | (2197) op(e3, e1) = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | (2198) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2198) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | (2199) all_57_6 = e3 & op(e1, e3) = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2024), (2199), (function-axioms) are % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #761. % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | (2200) all_57_7 = e3 & op(e1, e2) = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2200) implies: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | (2201) all_57_7 = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (2202) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (170), (1834), (1998), (2202), % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | #421. % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (2203) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2203) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2204) all_57_4 = e0 & op(e3, e1) = e0 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2204) implies: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2205) op(e3, e1) = e0 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (2197), (2205), (function-axioms) are % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #600. % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2206) all_57_9 = e0 & op(e3, e0) = e0 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2206) implies: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2207) all_57_9 = e0 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2208) op(e3, e0) = e0 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2209) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2209) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2210) all_57_0 = e1 & op(e3, e3) = e1 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2210) implies: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2211) op(e3, e3) = e1 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2211), (function-axioms) are % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743. % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2212) all_57_1 = e1 & op(e3, e2) = e1 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2212) implies: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2213) all_57_1 = e1 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2214) op(e3, e2) = e1 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2215) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2215) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2216) all_57_6 = e2 & op(e1, e3) = e2 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2216) implies: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2217) all_57_6 = e2 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2218) op(e1, e3) = e2 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2219) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (162), (170), (227), (1828), (1998), % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1999), (2000), (2219), (function-axioms) are % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #395. % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2220) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2220) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2221) all_57_7 = e2 & op(e1, e2) = e2 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2221) implies: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2222) all_57_7 = e2 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2201), (2222) imply: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2223) e3 = e2 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2030), (2223) imply: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2224) all_57_2 = e2 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (233), (237), (1834), (2217), % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2224), (function-axioms) are inconsistent by % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #393. % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2225) all_57_13 = e2 & op(e0, e2) = e2 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2225) implies: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2226) all_57_13 = e2 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2227) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2227) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2228) all_57_12 = e3 & op(e0, e3) = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (231), (233), (1834), % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2217), (2228), (function-axioms) are inconsistent % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #391. % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2229) all_57_13 = e3 & op(e0, e2) = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (228), (229), (2009), % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2201), (2229) are inconsistent by sub-proof #388. % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2230) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2230) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2231) all_57_14 = e3 & op(e0, e1) = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (2184), (2231), (function-axioms) are % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #652. % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2232) all_57_15 = e3 & op(e0, e0) = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2232) implies: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2233) all_57_15 = e3 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2234) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2234) gives: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2235) all_57_0 = e1 & op(e3, e3) = e1 % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2235) implies: % 132.03/18.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2236) op(e3, e3) = e1 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2236), (function-axioms) are % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743. % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2237) all_57_2 = e1 & op(e2, e3) = e1 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2004), (2005), (2237), (function-axioms) are % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #425. % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2238) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2238) gives: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2239) all_57_6 = e1 & op(e1, e3) = e1 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2239) implies: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2240) op(e1, e3) = e1 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (2218), (2240), (function-axioms) are % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #517. % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2241) all_57_12 = e1 & op(e0, e3) = e1 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2241) implies: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2242) all_57_12 = e1 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2243) all_57_15 = e0 & op(e0, e0) = e0 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2243) implies: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2244) op(e0, e0) = e0 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (164), (214), (2027), (2186), (2207), % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2244), (function-axioms) are inconsistent by % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #386. % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2245) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2245) implies: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2246) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2247) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2247) gives: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2248) all_57_4 = e2 & op(e3, e1) = e2 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2248) implies: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2249) op(e3, e1) = e2 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e3, e1, % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (2197), (2249) gives: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2250) e3 = e2 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2250) imply: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2251) $false % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2251) is inconsistent. % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2252) all_57_5 = e2 & op(e2, e1) = e2 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2252) implies: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2253) all_57_5 = e2 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2254) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2254) gives: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2255) all_57_0 = e0 & op(e3, e3) = e0 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2255) implies: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2256) op(e3, e3) = e0 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2256), (function-axioms) are % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2257) all_57_2 = e0 & op(e2, e3) = e0 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2257) implies: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2258) all_57_2 = e0 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (165), (224), (226), (2002), % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2026), (2253), (2258), (function-axioms) are % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #456. % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2259) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2259) gives: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2260) all_57_6 = e0 & op(e1, e3) = e0 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2260) implies: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2261) all_57_6 = e0 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2217), (2261) are inconsistent by sub-proof % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #586. % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2262) all_57_12 = e0 & op(e0, e3) = e0 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2262) implies: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2263) all_57_12 = e0 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2242), (2263) are inconsistent by sub-proof % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #581. % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2264) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2264) gives: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2265) all_57_8 = e2 & op(e1, e1) = e2 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2265) implies: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2266) op(e1, e1) = e2 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2266), (function-axioms) are % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2267) all_57_14 = e2 & op(e0, e1) = e2 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2267) implies: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2268) all_57_14 = e2 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (209), (2226), (2233), (2246), % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2268) are inconsistent by sub-proof #403. % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2269) all_57_7 = e2 & op(e1, e2) = e2 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2201), (2269) are inconsistent by sub-proof % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #385. % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2270) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2270) gives: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2271) all_57_8 = e2 & op(e1, e1) = e2 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2271) implies: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2272) op(e1, e1) = e2 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2272), (function-axioms) are % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2273) all_57_11 = e2 & op(e1, e0) = e2 % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.03/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2273) implies: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2274) op(e1, e0) = e2 % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2275) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2275) gives: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2276) all_57_9 = e1 & op(e3, e0) = e1 % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2276) implies: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2277) all_57_9 = e1 % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2278) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2278) gives: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2279) all_57_0 = e0 & op(e3, e3) = e0 % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2279) implies: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2280) op(e3, e3) = e0 % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2280), (function-axioms) are % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2281) all_57_1 = e0 & op(e3, e2) = e0 % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2281) implies: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2282) all_57_1 = e0 % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2213), (2282) imply: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2283) e1 = e0 % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (2283) imply: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2284) $false % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2284) is inconsistent. % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2203) gives: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2285) all_57_4 = e0 & op(e3, e1) = e0 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2196), (2285) are inconsistent by sub-proof % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #384. % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2207), (2277) are inconsistent by sub-proof % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #383. % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2286) all_57_10 = e1 & op(e2, e0) = e1 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2286) implies: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2287) op(e2, e0) = e1 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2190) gives: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2288) ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_42_0) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2288) implies: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2289) ~ (all_42_0 = e1) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2290) op(e0, e2) = all_42_0 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2291) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (162), (170), (227), (1828), (1998), % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1999), (2000), (2291), (function-axioms) are % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #395. % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2292) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2292) gives: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2293) all_57_7 = e2 & op(e1, e2) = e2 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2201), (2293) are inconsistent by sub-proof % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #385. % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2294) all_57_13 = e2 & op(e0, e2) = e2 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2294) implies: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2295) op(e0, e2) = e2 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2193) gives: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2296) ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_44_0) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2296) implies: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2297) ~ (all_44_0 = e1) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2298) op(e3, e0) = all_44_0 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2, % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (158), (2295) gives: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2299) all_52_7 = e2 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_42_0, e2, e0, simplifying with (158), (2290) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2300) all_52_7 = all_42_0 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e1, simplifying with (160), (2274) gives: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2301) all_52_14 = e2 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, e2, simplifying with (164), (2287) gives: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2302) all_52_13 = e1 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e0, e3, simplifying with (168), (2208) gives: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2303) all_52_12 = e0 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_44_0, e0, e3, simplifying with (168), (2298) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2304) all_52_12 = all_44_0 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e1, % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (2214) gives: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2305) all_52_4 = e1 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2299), (2300) imply: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2306) all_42_0 = e2 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2306) implies: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2307) all_42_0 = e2 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2303), (2304) imply: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2308) all_44_0 = e0 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2185), (2303) imply: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2309) ~ (e3 = e0) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2027), (2302) imply: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2310) ~ (e3 = e1) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (2301) imply: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2311) ~ (all_6_2 = e2) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2312) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2312) gives: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2313) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2313) gives: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2314) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2314) implies: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2315) op(e3, e2) = e3 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2214), (2315), (function-axioms) are % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #413. % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2316) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2316) implies: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2317) op(e3, e3) = e1 % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2317), (function-axioms) are % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743. % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2318) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (2002), (2185), (2318), % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #622. % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2319) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2319) gives: % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2320) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2002), (2208), (2320), (function-axioms) are % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #540. % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2321) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2321) gives: % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2322) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2322) implies: % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2323) ~ (all_56_15 = e2) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2324) op(e0, e2) = all_56_15 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2295), (2323), (2324), (function-axioms) are % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609. % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2325) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2325) gives: % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2326) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2326) implies: % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2327) op(e1, e1) = e2 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2327), (function-axioms) are % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2328) op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2328) implies: % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2329) op(e0, e0) = all_56_31 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2330) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2330) gives: % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2331) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.31/18.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (2000), (2208), (2331), (function-axioms) % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #538. % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2332) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2332) gives: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2333) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2333) implies: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2334) op(e1, e0) = e1 % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2274), (2334), (function-axioms) are % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #720. % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2335) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2335) implies: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2336) all_56_31 = e1 % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2329), (2336) imply: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2337) op(e0, e0) = e1 % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2187), (2337), (function-axioms) are % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606. % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2338) ~ (all_44_1 = e2) & op(e3, e3) = all_44_1 & % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_44_1) % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1834), (2338), (function-axioms) are inconsistent % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #431. % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2339) ~ (all_42_1 = e3) & op(e0, e0) = all_42_1 & % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_42_1) % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2187), (2339), (function-axioms) are inconsistent % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #602. % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2340) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (2187), (2274), (2340), % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #557. % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2341) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2341) gives: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2342) all_57_4 = e1 & op(e3, e1) = e1 % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2196), (2342) are inconsistent by sub-proof % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #382. % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2343) all_57_9 = e1 & op(e3, e0) = e1 % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2343) implies: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2344) all_57_9 = e1 % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2207), (2344) are inconsistent by sub-proof % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #383. % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | (2345) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (1838), (2186), (2345), % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | #653. % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | (2346) all_57_5 = e3 & op(e2, e1) = e3 % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2026), (2346), (function-axioms) are % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | (2347) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (1838), (2184), (2347), % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | #651. % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | (2348) all_57_3 = e3 & op(e2, e2) = e3 % 132.31/18.75 | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | ALPHA: (2348) implies: % 132.31/18.75 | | | | | | | | | | | | | | | | | | (2349) op(e2, e2) = e3 % 132.31/18.75 | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2002), (2349), (function-axioms) are % 132.31/18.75 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 132.31/18.75 | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | (2350) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 132.31/18.75 | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 132.31/18.75 | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | BETA: splitting (2350) gives: % 132.31/18.75 | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.75 | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | (2351) all_57_5 = e3 & op(e2, e1) = e3 % 132.31/18.75 | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2026), (2351), (function-axioms) are % 132.31/18.75 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 132.31/18.75 | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | (2352) all_57_10 = e3 & op(e2, e0) = e3 % 132.31/18.75 | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2027), (2352), (function-axioms) are % 132.31/18.75 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749. % 132.31/18.75 | | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | (2353) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 132.31/18.75 | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | | REF_CLOSE: (2004), (2011), (2020), (2021), (2353) are % 132.31/18.75 | | | | | | | | | | | | | | | | inconsistent by sub-proof #381. % 132.31/18.75 | | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | (2354) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 132.31/18.75 | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 132.31/18.75 | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (1999), (2000), (2354), % 132.31/18.75 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.31/18.75 | | | | | | | | | | | | | | #504. % 132.31/18.75 | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | (2355) ~ (all_16_1 = e0) & op(e2, e2) = all_16_1 & % 132.31/18.75 | | | | | | | | | | | | | $i(all_16_1) % 132.31/18.75 | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | REF_CLOSE: (2002), (2355), (function-axioms) are inconsistent % 132.31/18.75 | | | | | | | | | | | | | by sub-proof #380. % 132.31/18.75 | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | (2356) all_28_2 = e3 % 132.31/18.75 | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | COMBINE_EQS: (316), (2356) imply: % 132.31/18.75 | | | | | | | | | | | (2357) all_6_2 = e3 % 132.31/18.75 | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | COMBINE_EQS: (302), (2357) imply: % 132.31/18.75 | | | | | | | | | | | (2358) all_36_2 = e3 % 132.31/18.75 | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | REDUCE: (359), (2357) imply: % 132.31/18.75 | | | | | | | | | | | (2359) ~ (all_52_6 = e3) % 132.31/18.75 | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | REDUCE: (361), (2357) imply: % 132.31/18.75 | | | | | | | | | | | (2360) ~ (all_52_8 = e3) % 132.31/18.75 | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | REDUCE: (362), (2357) imply: % 132.31/18.75 | | | | | | | | | | | (2361) ~ (all_52_9 = e3) % 132.31/18.75 | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | REDUCE: (364), (2357) imply: % 132.31/18.75 | | | | | | | | | | | (2362) ~ (all_52_11 = e3) % 132.31/18.75 | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | REDUCE: (366), (2357) imply: % 132.31/18.75 | | | | | | | | | | | (2363) ~ (all_52_14 = e3) % 132.31/18.75 | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | BETA: splitting (85) gives: % 132.31/18.75 | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | Case 1: % 132.31/18.75 | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | (2364) ~ (all_36_2 = e3) % 132.31/18.75 | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | REDUCE: (2358), (2364) imply: % 132.31/18.75 | | | | | | | | | | | | (2365) $false % 132.31/18.75 | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | CLOSE: (2365) is inconsistent. % 132.31/18.75 | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | (2366) ( ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 & % 132.31/18.75 | | | | | | | | | | | | $i(all_36_0)) | ( ~ (all_36_1 = e2) & op(e3, e3) % 132.31/18.75 | | | | | | | | | | | | = all_36_1 & $i(all_36_1)) % 132.31/18.75 | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | BETA: splitting (2366) gives: % 132.31/18.75 | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | Case 1: % 132.31/18.75 | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | (2367) ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 & % 132.31/18.75 | | | | | | | | | | | | | $i(all_36_0) % 132.31/18.75 | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | ALPHA: (2367) implies: % 132.31/18.75 | | | | | | | | | | | | | (2368) ~ (all_36_0 = e0) % 132.31/18.75 | | | | | | | | | | | | | (2369) op(e3, e1) = all_36_0 % 132.31/18.75 | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | BETA: splitting (222) gives: % 132.31/18.75 | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | Case 1: % 132.31/18.75 | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | (2370) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 132.31/18.75 | | | | | | | | | | | | | | & op(e2, e1) = e3) % 132.31/18.75 | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | BETA: splitting (2370) gives: % 132.31/18.75 | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | Case 1: % 132.31/18.75 | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | (2371) all_57_4 = e3 & op(e3, e1) = e3 % 132.31/18.75 | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | REF_CLOSE: (169), (2360), (2369), (2371), (function-axioms) % 132.31/18.75 | | | | | | | | | | | | | | | are inconsistent by sub-proof #379. % 132.31/18.75 | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | (2372) all_57_5 = e3 & op(e2, e1) = e3 % 132.31/18.75 | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | REF_CLOSE: (165), (2361), (2372), (function-axioms) are % 132.31/18.75 | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 132.31/18.75 | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | End of split % 132.31/18.75 | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | Case 2: % 132.31/18.75 | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | (2373) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 132.31/18.75 | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 132.31/18.75 | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | BETA: splitting (2373) gives: % 132.31/18.75 | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | Case 1: % 132.31/18.75 | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | (2374) all_57_8 = e3 & op(e1, e1) = e3 % 132.31/18.75 | | | | | | | | | | | | | | | % 132.31/18.75 | | | | | | | | | | | | | | | ALPHA: (2374) implies: % 132.31/18.75 | | | | | | | | | | | | | | | (2375) all_57_8 = e3 % 132.31/18.75 | | | | | | | | | | | | | | | (2376) op(e1, e1) = e3 % 132.31/18.75 | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 132.31/18.76 | | | | | | | | | | | | | | | all_36_0, e1, e3, simplifying with (169), (2369) % 132.31/18.76 | | | | | | | | | | | | | | | gives: % 132.31/18.76 | | | | | | | | | | | | | | | (2377) all_52_8 = all_36_0 % 132.31/18.76 | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | COMBINE_EQS: (270), (2377) imply: % 132.31/18.76 | | | | | | | | | | | | | | | (2378) all_54_2 = all_36_0 % 132.31/18.76 | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | REDUCE: (134), (2377) imply: % 132.31/18.76 | | | | | | | | | | | | | | | (2379) ~ (all_52_4 = all_36_0) % 132.31/18.76 | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | REDUCE: (123), (2377) imply: % 132.31/18.76 | | | | | | | | | | | | | | | (2380) ~ (all_52_9 = all_36_0) % 132.31/18.76 | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | SIMP: (2380) implies: % 132.31/18.76 | | | | | | | | | | | | | | | (2381) ~ (all_52_9 = all_36_0) % 132.31/18.76 | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | REDUCE: (121), (2377) imply: % 132.31/18.76 | | | | | | | | | | | | | | | (2382) ~ (all_52_11 = all_36_0) % 132.31/18.76 | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | SIMP: (2382) implies: % 132.31/18.76 | | | | | | | | | | | | | | | (2383) ~ (all_52_11 = all_36_0) % 132.31/18.76 | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | REDUCE: (2360), (2377) imply: % 132.31/18.76 | | | | | | | | | | | | | | | (2384) ~ (all_36_0 = e3) % 132.31/18.76 | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | REDUCE: (1829), (2377) imply: % 132.31/18.76 | | | | | | | | | | | | | | | (2385) ~ (all_36_0 = e2) % 132.31/18.76 | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 132.31/18.76 | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | Case 1: % 132.31/18.76 | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | (2386) all_54_2 = e3 % 132.31/18.76 | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | COMBINE_EQS: (2378), (2386) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | (2387) all_36_0 = e3 % 132.31/18.76 | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | REDUCE: (2384), (2387) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | (2388) $false % 132.31/18.76 | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | CLOSE: (2388) is inconsistent. % 132.31/18.76 | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | Case 2: % 132.31/18.76 | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | (2389) ~ (all_54_2 = e3) % 132.31/18.76 | | | | | | | | | | | | | | | | (2390) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 132.31/18.76 | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | BETA: splitting (2390) gives: % 132.31/18.76 | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | Case 1: % 132.31/18.76 | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | (2391) all_54_2 = e2 % 132.31/18.76 | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2378), (2391) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | | (2392) all_36_0 = e2 % 132.31/18.76 | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | REDUCE: (2385), (2392) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | | (2393) $false % 132.31/18.76 | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | CLOSE: (2393) is inconsistent. % 132.31/18.76 | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | Case 2: % 132.31/18.76 | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | (2394) ~ (all_54_2 = e2) % 132.31/18.76 | | | | | | | | | | | | | | | | | (2395) all_54_2 = e1 | all_54_2 = e0 % 132.31/18.76 | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | BETA: splitting (2395) gives: % 132.31/18.76 | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.76 | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | (2396) all_54_2 = e1 % 132.31/18.76 | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2378), (2396) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | | | (2397) all_36_0 = e1 % 132.31/18.76 | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | REDUCE: (2379), (2397) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | | | (2398) ~ (all_52_4 = e1) % 132.31/18.76 | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | REDUCE: (2381), (2397) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | | | (2399) ~ (all_52_9 = e1) % 132.31/18.76 | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | REDUCE: (2383), (2397) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | | | (2400) ~ (all_52_11 = e1) % 132.31/18.76 | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | REDUCE: (2384), (2397) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | | | (2401) ~ (e3 = e1) % 132.31/18.76 | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | REDUCE: (2385), (2397) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | | | (2402) ~ (e2 = e1) % 132.31/18.76 | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | REDUCE: (2369), (2397) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | | | (2403) op(e3, e1) = e1 % 132.31/18.76 | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 132.31/18.76 | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | (2404) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 132.31/18.76 | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (1834), (2398), (2404), % 132.31/18.76 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.31/18.76 | | | | | | | | | | | | | | | | | | | #378. % 132.31/18.76 | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | (2405) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 132.31/18.76 | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | BETA: splitting (2405) gives: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | (2406) all_57_4 = e1 & op(e3, e1) = e1 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | ALPHA: (2406) implies: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | (2407) all_57_4 = e1 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | (2408) ~ (all_30_2 = e0) % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (2408) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | (2409) ~ (all_8_2 = e0) % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | (2410) all_54_5 = e3 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (376), (2410) are inconsistent by sub-proof % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | #554. % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | (2411) ~ (all_54_5 = e3) % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | (2412) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2412) gives: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | (2413) all_54_5 = e2 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (2413) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | (2414) all_8_2 = e2 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2414) implies: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | (2415) all_8_2 = e2 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (352), (2415) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | (2416) ~ (all_52_6 = e2) % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (2415) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | (2417) ~ (all_52_9 = e2) % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (2415) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | (2418) ~ (all_52_13 = e2) % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (376), (2415) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | (2419) ~ (e3 = e2) % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (2415) imply: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | (2420) op(e2, e2) = e2 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | (2421) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2421) gives: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | (2422) all_57_6 = e2 & op(e1, e3) = e2 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2422) implies: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | (2423) all_57_6 = e2 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | (2424) op(e1, e3) = e2 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (2425) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (1830), (2418), (2425), % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | #440. % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (2426) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2426) gives: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2427) all_57_11 = e2 & op(e1, e0) = e2 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2427) implies: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2428) all_57_11 = e2 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2429) op(e1, e0) = e2 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2430) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (1829), (2417), (2430), % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #441. % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2431) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2431) gives: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2432) all_57_8 = e2 & op(e1, e1) = e2 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2432) implies: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2433) all_57_8 = e2 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (215), (216), % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (2359), (2428), (2433), (function-axioms) % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #571. % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2434) all_57_14 = e2 & op(e0, e1) = e2 % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.31/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2434) implies: % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2435) all_57_14 = e2 % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2436) op(e0, e1) = e2 % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2437) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2437) gives: % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2438) all_57_9 = e1 & op(e3, e0) = e1 % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2438) implies: % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2439) all_57_9 = e1 % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2440) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2440) gives: % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2441) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2420), (2441), (function-axioms) are % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #444. % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2442) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (1825), (1834), (2442), % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #443. % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2443) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2443) gives: % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2444) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (165), (2417), (2424), (2444), % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #468. % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2445) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2445) gives: % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2446) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2446) implies: % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2447) op(e2, e0) = e2 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2418), (2447), (function-axioms) are % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2448) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2448) gives: % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2449) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2449) implies: % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2450) op(e1, e1) = e2 % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2450), (function-axioms) are % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2451) op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2451) implies: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2452) op(e0, e0) = all_56_31 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2453) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2454) all_57_15 = e0 & op(e0, e0) = e0 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2454) implies: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2455) op(e0, e0) = e0 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (2452), (2453), (2455), % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #710. % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2456) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2456) implies: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2457) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2458) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2458) gives: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2459) all_57_0 = e0 & op(e3, e3) = e0 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2459) implies: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2460) op(e3, e3) = e0 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2460), (function-axioms) are % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2461) all_57_1 = e0 & op(e3, e2) = e0 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2461) implies: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2462) all_57_1 = e0 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2463) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2463) gives: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2464) all_57_2 = e2 & op(e2, e3) = e2 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2464) implies: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2465) all_57_2 = e2 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (233), (237), (1834), (2423), % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2465), (function-axioms) are inconsistent by % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #393. % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2466) all_57_3 = e2 & op(e2, e2) = e2 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2466) implies: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2467) all_57_3 = e2 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2457) gives: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2468) all_57_9 = e0 & op(e3, e0) = e0 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2468) implies: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2469) all_57_9 = e0 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2439), (2469) are inconsistent by sub-proof % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #383. % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2470) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2470) gives: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2471) all_57_10 = e0 & op(e2, e0) = e0 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2471) implies: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2472) all_57_10 = e0 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2473) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2473) gives: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2474) all_57_9 = e3 & op(e3, e0) = e3 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2474) implies: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2475) all_57_9 = e3 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2453) gives: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2476) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2476) gives: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2477) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2477) implies: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2478) all_56_31 = e3 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2452), (2478) imply: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2479) op(e0, e0) = e3 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (208), (212), (2428), % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2429), (2452), (2453), (2475), (2479), % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #439. % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2480) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2480) implies: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2481) all_56_31 = e2 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2452), (2481) imply: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2482) op(e0, e0) = e2 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (208), (212), (2428), % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2475), (2482), (function-axioms) are inconsistent % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #635. % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2483) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (2429), (2436), (2483), % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #428. % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2484) all_57_10 = e3 & op(e2, e0) = e3 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2472), (2484) are inconsistent by sub-proof % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #377. % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2485) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2485) gives: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2486) all_57_11 = e3 & op(e1, e0) = e3 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2363), (2486), (function-axioms) are % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750. % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2487) all_57_15 = e3 & op(e0, e0) = e3 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2487) implies: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2488) op(e0, e0) = e3 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2489) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2489) gives: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2490) all_57_1 = e3 & op(e3, e2) = e3 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2462), (2490) are inconsistent by sub-proof % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #376. % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2491) all_57_3 = e3 & op(e2, e2) = e3 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2491) implies: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2492) all_57_3 = e3 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225), % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (237), (1834), (2423), (2492), % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #360. % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2493) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2493) gives: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2494) all_57_7 = e3 & op(e1, e2) = e3 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2494) implies: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2495) op(e1, e2) = e3 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2359), (2495), (function-axioms) are % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654. % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2496) all_57_13 = e3 & op(e0, e2) = e3 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2496) implies: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2497) all_57_13 = e3 % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2498) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2498) gives: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2499) all_57_12 = e1 & op(e0, e3) = e1 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2499) implies: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2500) all_57_12 = e1 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2501) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2501) gives: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2502) all_57_2 = e3 & op(e2, e3) = e3 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2502) implies: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2503) all_57_2 = e3 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (164), (165), (167), (225), (231), % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1825), (1834), (2417), (2418), (2423), (2467), % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2500), (2503), (function-axioms) are inconsistent % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #358. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2504) all_57_3 = e3 & op(e2, e2) = e3 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2504) implies: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2505) all_57_3 = e3 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225), % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (237), (1834), (2423), (2505), % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #360. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2506) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2506) gives: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2507) all_57_5 = e3 & op(e2, e1) = e3 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2361), (2507), (function-axioms) are % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2508) all_57_10 = e3 & op(e2, e0) = e3 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2472), (2508) are inconsistent by sub-proof % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #377. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2509) all_57_13 = e1 & op(e0, e2) = e1 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2497), (2509) are inconsistent by sub-proof % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #389. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2510) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2510) gives: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2511) all_57_14 = e1 & op(e0, e1) = e1 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2511) implies: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2512) all_57_14 = e1 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2435), (2512) are inconsistent by sub-proof % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #560. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2513) all_57_15 = e1 & op(e0, e0) = e1 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2513) implies: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2514) op(e0, e0) = e1 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2488), (2514), (function-axioms) are % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2515) all_57_11 = e0 & op(e1, e0) = e0 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2515) implies: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2516) all_57_11 = e0 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2428), (2516) imply: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2517) e2 = e0 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2517) implies: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2518) e2 = e0 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (164), (165), (167), (225), (1825), (2417), % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2418), (2467), (2518), (function-axioms) are % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #359. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2519) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (165), (2417), (2428), (2439), (2457), % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2519), (function-axioms) are inconsistent by % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #357. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2520) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2520) gives: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2521) all_57_4 = e0 & op(e3, e1) = e0 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2407), (2521) are inconsistent by sub-proof % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #672. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2522) all_57_9 = e0 & op(e3, e0) = e0 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2439), (2522) are inconsistent by sub-proof % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #687. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2523) all_57_10 = e1 & op(e2, e0) = e1 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2523) implies: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2524) all_57_10 = e1 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2525) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2525) gives: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2526) all_57_2 = e2 & op(e2, e3) = e2 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2526) implies: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2527) all_57_2 = e2 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (233), (237), (1834), (2423), % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2527), (function-axioms) are inconsistent by % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #393. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2528) all_57_3 = e2 & op(e2, e2) = e2 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2528) implies: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2529) all_57_3 = e2 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2530) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2530) gives: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2531) all_57_2 = e3 & op(e2, e3) = e3 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2531) implies: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2532) all_57_2 = e3 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2533) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (1834), (2532), (2533), % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #356. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2534) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2534) gives: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2535) all_57_6 = e1 & op(e1, e3) = e1 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2535) implies: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2536) op(e1, e3) = e1 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (2424), (2536), (function-axioms) are % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #517. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2537) all_57_12 = e1 & op(e0, e3) = e1 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2537) implies: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2538) all_57_12 = e1 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (164), (165), (167), (225), (231), % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1825), (1834), (2417), (2418), (2423), (2529), % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2532), (2538), (function-axioms) are inconsistent % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #358. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2539) all_57_3 = e3 & op(e2, e2) = e3 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2539) implies: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2540) all_57_3 = e3 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225), % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (237), (1834), (2423), (2540), % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #360. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2541) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2541) gives: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2542) all_57_5 = e3 & op(e2, e1) = e3 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2361), (2542), (function-axioms) are % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2543) all_57_10 = e3 & op(e2, e0) = e3 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2524), (2543) are inconsistent by sub-proof % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #355. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2544) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (2417), (2418), (2544), % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #625. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2545) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (371), (2429), (2545), % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #353. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2546) all_57_15 = e2 & op(e0, e0) = e2 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2546) implies: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2547) op(e0, e0) = e2 % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2548) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2548) gives: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2549) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2420), (2549), (function-axioms) are % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #444. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2550) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (1825), (1834), (2550), % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #443. % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2551) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2551) gives: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2552) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (165), (2417), (2424), (2552), % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #468. % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2553) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2553) gives: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2554) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2554) implies: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2555) op(e2, e0) = e2 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2418), (2555), (function-axioms) are % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2556) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (39), (372), (1836), (2547), (2556), % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #352. % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | (2557) all_57_7 = e2 & op(e1, e2) = e2 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2416), (2557), (function-axioms) are % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515. % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | (2558) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2558) gives: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | (2559) all_57_8 = e2 & op(e1, e1) = e2 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2559) implies: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | (2560) op(e1, e1) = e2 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2560), (function-axioms) are % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | (2561) all_57_11 = e2 & op(e1, e0) = e2 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2561) implies: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | (2562) all_57_11 = e2 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | (2563) op(e1, e0) = e2 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (2564) all_54_6 = e3 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2564) imply: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (2565) all_52_9 = e3 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2361), (2565) imply: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (2566) $false % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2566) is inconsistent. % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (2567) ~ (all_54_6 = e3) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (2568) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2568) gives: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2569) all_54_6 = e2 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2569) imply: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2570) all_52_9 = e2 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2417), (2570) imply: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2571) $false % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2571) is inconsistent. % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2572) ~ (all_54_6 = e2) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2573) all_54_6 = e1 | all_54_6 = e0 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2574) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (1829), (2417), (2574), % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #441. % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2575) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2575) gives: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2576) all_57_8 = e2 & op(e1, e1) = e2 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2576) implies: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2577) all_57_8 = e2 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (215), (216), % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (2359), (2562), (2577), (function-axioms) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #571. % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2578) all_57_14 = e2 & op(e0, e1) = e2 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2578) implies: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2579) all_57_14 = e2 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2580) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2580) gives: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2581) all_57_9 = e1 & op(e3, e0) = e1 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2581) implies: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2582) all_57_9 = e1 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2583) op(e3, e0) = e1 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2584) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2584) gives: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2585) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2420), (2585), (function-axioms) are % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #444. % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2586) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (1825), (1834), (2586), % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #443. % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2587) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2587) gives: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2588) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2588) gives: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2589) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2589) implies: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2590) ~ (all_56_1 = e3) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2591) op(e3, e0) = all_56_25 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2592) op(e3, e3) = all_56_1 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2593) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2593) gives: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2594) all_57_0 = e3 & op(e3, e3) = e3 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2594) implies: % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2595) op(e3, e3) = e3 % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2590), (2592), (2595), (function-axioms) are % 132.37/18.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #766. % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2596) all_57_1 = e3 & op(e3, e2) = e3 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2596) implies: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2597) all_57_1 = e3 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2598) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2598) gives: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2599) all_57_0 = e0 & op(e3, e3) = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2599) implies: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2600) op(e3, e3) = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2600), (function-axioms) are % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2601) all_57_1 = e0 & op(e3, e2) = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2597), (2601) are inconsistent by sub-proof % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #649. % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2602) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2602) gives: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2603) all_57_4 = e0 & op(e3, e1) = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2407), (2603) are inconsistent by sub-proof % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #672. % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2604) all_57_9 = e0 & op(e3, e0) = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2604) implies: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2605) op(e3, e0) = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25, e0, e3, simplifying with (2583), (2591) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2606) all_56_25 = e1 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25, e0, e3, simplifying with (2591), (2605) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2607) all_56_25 = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2606), (2607) imply: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2608) e1 = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2608) implies: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2609) e1 = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (2609) imply: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2610) $false % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2610) is inconsistent. % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2611) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2611) gives: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2612) all_57_4 = e3 & op(e3, e1) = e3 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2360), (2369), (2612), (function-axioms) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #379. % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2613) all_57_9 = e3 & op(e3, e0) = e3 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2613) implies: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2614) all_57_9 = e3 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2582), (2614) are inconsistent by sub-proof % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #690. % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2615) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2615) implies: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2616) op(e2, e1) = e2 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2417), (2616), (function-axioms) are % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770. % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2617) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2617) gives: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2618) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2618) implies: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2619) op(e2, e0) = e2 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2418), (2619), (function-axioms) are % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2620) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2620) gives: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2621) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2621) implies: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2622) op(e1, e1) = e2 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2622), (function-axioms) are % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2623) op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2623) implies: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2624) op(e0, e0) = all_56_31 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2625) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2573) gives: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2626) all_54_6 = e1 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2626) imply: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2627) all_52_9 = e1 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2399), (2627) imply: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2628) $false % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2628) is inconsistent. % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2629) all_54_6 = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2629) imply: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2630) all_52_9 = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (2630) imply: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2631) ~ (all_52_11 = e0) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2631) implies: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2632) ~ (all_52_11 = e0) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2361), (2630) imply: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2633) ~ (e3 = e0) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2417), (2630) imply: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2634) ~ (e2 = e0) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2399), (2630) imply: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2635) ~ (e1 = e0) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2636) all_54_14 = e3 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (2362), (2636) are inconsistent by % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #760. % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2637) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2638) all_57_15 = e0 & op(e0, e0) = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2638) implies: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2639) op(e0, e0) = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (2624), (2625), (2639), % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #710. % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2640) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2640) implies: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2641) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2642) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2643) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2643) gives: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2644) all_57_0 = e0 & op(e3, e3) = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2644) implies: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2645) op(e3, e3) = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2645), (function-axioms) are % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2646) all_57_1 = e0 & op(e3, e2) = e0 % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2646) implies: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2647) all_57_1 = e0 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2648) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2648) gives: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2649) all_57_2 = e2 & op(e2, e3) = e2 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2649) implies: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2650) op(e2, e3) = e2 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (1825), (2650), (function-axioms) are % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #779. % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2651) all_57_3 = e2 & op(e2, e2) = e2 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2651) implies: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2652) all_57_3 = e2 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2653) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2653) gives: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2654) all_57_1 = e3 & op(e3, e2) = e3 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2647), (2654) are inconsistent by sub-proof % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #376. % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2655) all_57_3 = e3 & op(e2, e2) = e3 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2655) implies: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2656) all_57_3 = e3 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2652), (2656) imply: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2657) e3 = e2 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2657) implies: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2658) e3 = e2 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2375), (2658) imply: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2659) all_57_8 = e2 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (215), (216), % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (2359), (2562), (2659), (function-axioms) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #571. % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2660) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2660) gives: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2661) all_57_7 = e3 & op(e1, e2) = e3 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2661) implies: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2662) op(e1, e2) = e3 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2359), (2662), (function-axioms) are % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654. % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2663) all_57_13 = e3 & op(e0, e2) = e3 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2663) implies: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2664) all_57_13 = e3 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2665) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2665) gives: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2666) all_57_12 = e1 & op(e0, e3) = e1 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2666) implies: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2667) all_57_12 = e1 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2641) gives: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2668) all_57_12 = e0 & op(e0, e3) = e0 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2668) implies: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2669) all_57_12 = e0 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2667), (2669) are inconsistent by sub-proof % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #581. % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2670) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2670) gives: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2671) all_57_13 = e0 & op(e0, e2) = e0 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2671) implies: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2672) all_57_13 = e0 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2664), (2672) are inconsistent by sub-proof % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #484. % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2673) all_57_14 = e0 & op(e0, e1) = e0 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2673) implies: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2674) op(e0, e1) = e0 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (246), (2400), (2632), (2637), (2674), % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #351. % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2675) all_57_13 = e1 & op(e0, e2) = e1 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2664), (2675) are inconsistent by sub-proof % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #389. % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2676) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (371), (2579), (2676), % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #350. % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2677) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (165), (2417), (2562), (2582), (2642), % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2677), (function-axioms) are inconsistent by % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #357. % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2678) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2678) gives: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2679) all_57_4 = e0 & op(e3, e1) = e0 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2407), (2679) are inconsistent by sub-proof % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #672. % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2680) all_57_9 = e0 & op(e3, e0) = e0 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2582), (2680) are inconsistent by sub-proof % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #687. % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2681) all_57_10 = e1 & op(e2, e0) = e1 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2681) implies: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2682) all_57_10 = e1 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2683) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2683) gives: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2684) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2420), (2684), (function-axioms) are % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #444. % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2685) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2685) gives: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2686) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2686) implies: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2687) op(e3, e3) = e0 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2687), (function-axioms) are % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2688) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2688) implies: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2689) ~ (all_56_17 = e1) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2690) op(e3, e1) = all_56_17 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2403), (2689), (2690), (function-axioms) are % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349. % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2691) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.37/18.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2691) gives: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2692) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2403), (2417), (2692), (function-axioms) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #348. % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2693) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2693) gives: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2694) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2694) implies: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2695) op(e2, e0) = e2 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2418), (2695), (function-axioms) are % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2696) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2696) gives: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2697) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2697) implies: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2698) op(e1, e1) = e2 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2698), (function-axioms) are % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2699) op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2699) implies: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2700) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2573) gives: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2701) all_54_6 = e1 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2701) imply: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2702) all_52_9 = e1 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2399), (2702) imply: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2703) $false % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2703) is inconsistent. % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2704) all_54_6 = e0 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2704) imply: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2705) all_52_9 = e0 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (2705) imply: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2706) ~ (all_52_11 = e0) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2706) implies: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2707) ~ (all_52_11 = e0) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2361), (2705) imply: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2708) ~ (e3 = e0) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2417), (2705) imply: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2709) ~ (e2 = e0) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2399), (2705) imply: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2710) ~ (e1 = e0) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2711) all_54_14 = e3 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (2362), (2711) are inconsistent by % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #760. % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2712) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2713) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2713) gives: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2714) all_57_2 = e3 & op(e2, e3) = e3 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2714) implies: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2715) op(e2, e3) = e3 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2700) gives: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2716) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2403), (2715), (2716), (function-axioms) are % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #346. % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2717) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2717) gives: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2718) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2718) implies: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2719) op(e1, e0) = e1 % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2563), (2719), (function-axioms) are % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #720. % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2720) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2720) implies: % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2721) op(e0, e1) = e0 % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (246), (2400), (2707), (2712), (2721), % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #351. % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2722) all_57_3 = e3 & op(e2, e2) = e3 % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2722) implies: % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2723) all_57_3 = e3 % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2724) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2724) gives: % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2725) all_57_1 = e2 & op(e3, e2) = e2 % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (1828), (2725), (function-axioms) are % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #396. % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2726) all_57_3 = e2 & op(e2, e2) = e2 % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2726) implies: % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2727) all_57_3 = e2 % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2723), (2727) imply: % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2728) e3 = e2 % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2375), (2728) imply: % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2729) all_57_8 = e2 % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (215), (216), % 132.37/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (2359), (2562), (2729), (function-axioms) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #571. % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2730) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2730) gives: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2731) all_57_7 = e2 & op(e1, e2) = e2 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2416), (2731), (function-axioms) are % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515. % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2732) all_57_13 = e2 & op(e0, e2) = e2 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2732) implies: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2733) all_57_13 = e2 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209), (211), % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2579), (2733) are inconsistent by sub-proof #401. % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2734) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2734) gives: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2735) all_57_5 = e3 & op(e2, e1) = e3 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2361), (2735), (function-axioms) are % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2736) all_57_10 = e3 & op(e2, e0) = e3 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2682), (2736) are inconsistent by sub-proof % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #355. % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2737) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (371), (2563), (2737), % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #353. % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | (2738) all_54_5 = e1 | all_54_5 = e0 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (373), (2409), (2738) are inconsistent by % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #624. % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | (2739) all_30_2 = e0 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (2739) imply: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | (2740) all_8_2 = e0 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | SIMP: (2740) implies: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | (2741) all_8_2 = e0 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (2741) imply: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | (2742) ~ (all_52_4 = e0) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (2741) imply: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | (2743) ~ (all_52_7 = e0) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | REDUCE: (356), (2741) imply: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | (2744) ~ (all_52_9 = e0) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (2741) imply: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | (2745) ~ (e1 = e0) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (2741) imply: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | (2746) op(e2, e2) = e0 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | (2747) all_54_6 = e3 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2747) imply: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | (2748) all_52_9 = e3 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2361), (2748) imply: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | (2749) $false % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2749) is inconsistent. % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | (2750) ~ (all_54_6 = e3) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | (2751) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | (2752) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (170), (1834), (2742), (2752), % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | #421. % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | (2753) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2753) gives: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | (2754) all_57_4 = e0 & op(e3, e1) = e0 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2407), (2754) are inconsistent by sub-proof % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | #672. % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | (2755) all_57_9 = e0 & op(e3, e0) = e0 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2755) implies: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | (2756) all_57_9 = e0 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | (2757) op(e3, e0) = e0 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2751) gives: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | (2758) all_54_6 = e2 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2758) imply: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | (2759) all_52_9 = e2 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (2759) imply: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | (2760) ~ (all_52_11 = e2) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2760) implies: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | (2761) ~ (all_52_11 = e2) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (2759) imply: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | (2762) ~ (all_52_13 = e2) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2762) implies: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | (2763) ~ (all_52_13 = e2) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (2764) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (1830), (2763), (2764), % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | #440. % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (2765) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2765) gives: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2766) all_57_11 = e2 & op(e1, e0) = e2 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2766) implies: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2767) op(e1, e0) = e2 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2768) all_54_1 = e3 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (2768) imply: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2769) all_52_4 = e3 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2769) implies: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2770) all_52_4 = e3 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (2770) imply: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2771) ~ (all_52_12 = e3) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2771) implies: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2772) ~ (all_52_12 = e3) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2773) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2773) gives: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2774) all_57_9 = e1 & op(e3, e0) = e1 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2774) implies: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2775) all_57_9 = e1 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2756), (2775) are inconsistent by sub-proof % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #383. % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2776) all_57_10 = e1 & op(e2, e0) = e1 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2776) implies: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2777) all_57_10 = e1 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2778) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2778) gives: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2779) all_57_9 = e3 & op(e3, e0) = e3 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2779) implies: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2780) op(e3, e0) = e3 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (2772), (2780), (function-axioms) are % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #733. % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2781) all_57_10 = e3 & op(e2, e0) = e3 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2777), (2781) are inconsistent by sub-proof % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #355. % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2782) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2782) gives: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2783) all_57_11 = e3 & op(e1, e0) = e3 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2363), (2783), (function-axioms) are % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750. % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2784) all_57_15 = e3 & op(e0, e0) = e3 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2784) implies: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2785) op(e0, e0) = e3 % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2786) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2786) gives: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2787) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2787) gives: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2788) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2788) implies: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2789) ~ (all_56_3 = e3) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2790) op(e2, e3) = all_56_3 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2791) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2791) gives: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2792) all_57_2 = e3 & op(e2, e3) = e3 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2792) implies: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2793) op(e2, e3) = e3 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2789), (2790), (2793), (function-axioms) are % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #347. % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2794) all_57_3 = e3 & op(e2, e2) = e3 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2794) implies: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2795) op(e2, e2) = e3 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2746), (2795), (function-axioms) are % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2796) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2796) gives: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2797) all_57_5 = e3 & op(e2, e1) = e3 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2361), (2797), (function-axioms) are % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2798) all_57_10 = e3 & op(e2, e0) = e3 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2777), (2798) are inconsistent by sub-proof % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #355. % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2799) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2799) implies: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2800) op(e3, e3) = e1 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (236), (238), (2407), % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2756), (2800), (function-axioms) are inconsistent % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #668. % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2801) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (2746), (2772), (2801), % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #622. % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2802) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2802) gives: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2803) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2746), (2757), (2803), (function-axioms) are % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #540. % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2804) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2804) gives: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2805) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2805) implies: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2806) op(e2, e0) = e2 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2763), (2806), (function-axioms) are % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2807) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (39), (158), (372), (2376), (2743), % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2757), (2785), (2807), (function-axioms) are % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #537. % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2808) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (371), (2767), (2808), % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #353. % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2809) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (1828), (2398), (2742), (2809) are % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #701. % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2810) all_57_15 = e2 & op(e0, e0) = e2 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2810) implies: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2811) op(e0, e0) = e2 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2812) all_54_14 = e3 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (2362), (2812) are inconsistent by % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #760. % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2813) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2813) gives: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2814) all_54_14 = e2 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (2761), (2814) are inconsistent by % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #527. % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2815) all_54_14 = e1 | all_54_14 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2815) gives: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2816) all_54_14 = e1 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (2400), (2816) are inconsistent by % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #756. % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2817) all_54_14 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (2817) imply: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2818) all_52_11 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2818) implies: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2819) all_52_11 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (2819) imply: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2820) ~ (all_4_2 = e0) % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2820) implies: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2821) ~ (all_4_2 = e0) % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2822) all_54_15 = e3 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (2822) imply: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2823) all_4_2 = e3 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2823) implies: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2824) all_4_2 = e3 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2824) imply: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2825) op(e0, e0) = e3 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2811), (2825), (function-axioms) are % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634. % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2826) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (1836), (2821), (2826) are % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #746. % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | (2827) all_54_6 = e1 | all_54_6 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (2399), (2744), (2827) are inconsistent by % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #479. % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | (2828) all_57_9 = e1 & op(e3, e0) = e1 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | ALPHA: (2828) implies: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | (2829) all_57_9 = e1 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | (2830) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2830) gives: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | (2831) all_57_0 = e0 & op(e3, e3) = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2831) implies: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | (2832) op(e3, e3) = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2832), (function-axioms) are % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | (2833) all_57_1 = e0 & op(e3, e2) = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2833) implies: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | (2834) all_57_1 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (169), (238), (1834), (2360), % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | (2369), (2829), (2834), (function-axioms) are % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #344. % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | (2835) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2835) gives: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | (2836) all_57_4 = e0 & op(e3, e1) = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2836) implies: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | (2837) op(e3, e1) = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2403), (2837), (function-axioms) are % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #343. % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | (2838) all_57_9 = e0 & op(e3, e0) = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2829), (2838) are inconsistent by sub-proof % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | #687. % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | (2839) all_54_2 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2378), (2839) imply: % 132.56/18.86 | | | | | | | | | | | | | | | | | | (2840) all_36_0 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | REDUCE: (2368), (2840) imply: % 132.56/18.86 | | | | | | | | | | | | | | | | | | (2841) $false % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | CLOSE: (2841) is inconsistent. % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | (2842) all_57_14 = e3 & op(e0, e1) = e3 % 132.56/18.86 | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | REF_CLOSE: (157), (2362), (2842), (function-axioms) are % 132.56/18.86 | | | | | | | | | | | | | | | inconsistent by sub-proof #652. % 132.56/18.86 | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | (2843) ~ (all_36_1 = e2) & op(e3, e3) = all_36_1 & % 132.56/18.86 | | | | | | | | | | | | | $i(all_36_1) % 132.56/18.86 | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | REF_CLOSE: (1834), (2843), (function-axioms) are inconsistent % 132.56/18.86 | | | | | | | | | | | | | by sub-proof #342. % 132.56/18.86 | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | End of split % 132.56/18.86 | | | | | | | | | | % 132.56/18.86 | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | (2844) all_20_2 = e2 % 132.56/18.86 | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | COMBINE_EQS: (318), (2844) imply: % 132.56/18.86 | | | | | | | | | | (2845) all_4_2 = e2 % 132.56/18.86 | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | SIMP: (2845) implies: % 132.56/18.86 | | | | | | | | | | (2846) all_4_2 = e2 % 132.56/18.86 | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | COMBINE_EQS: (331), (2846) imply: % 132.56/18.86 | | | | | | | | | | (2847) all_26_2 = e2 % 132.56/18.86 | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | REDUCE: (367), (2846) imply: % 132.56/18.86 | | | | | | | | | | (2848) ~ (all_52_11 = e2) % 132.56/18.86 | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | REDUCE: (370), (2846) imply: % 132.56/18.86 | | | | | | | | | | (2849) ~ (all_52_14 = e2) % 132.56/18.86 | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | REDUCE: (36), (2846) imply: % 132.56/18.86 | | | | | | | | | | (2850) op(e0, e0) = e2 % 132.56/18.86 | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | BETA: splitting (221) gives: % 132.56/18.86 | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | Case 1: % 132.56/18.86 | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | (2851) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 132.56/18.86 | | | | | | | | | | | & op(e2, e1) = e2) % 132.56/18.86 | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | BETA: splitting (2851) gives: % 132.56/18.86 | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | Case 1: % 132.56/18.86 | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | (2852) all_57_4 = e2 & op(e3, e1) = e2 % 132.56/18.86 | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | REF_CLOSE: (169), (1829), (2852), (function-axioms) are % 132.56/18.86 | | | | | | | | | | | | inconsistent by sub-proof #442. % 132.56/18.86 | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | (2853) all_57_5 = e2 & op(e2, e1) = e2 % 132.56/18.86 | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | ALPHA: (2853) implies: % 132.56/18.86 | | | | | | | | | | | | (2854) op(e2, e1) = e2 % 132.56/18.86 | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | BETA: splitting (217) gives: % 132.56/18.86 | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | Case 1: % 132.56/18.86 | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | (2855) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 132.56/18.86 | | | | | | | | | | | | | & op(e1, e2) = e2) % 132.56/18.86 | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | BETA: splitting (2855) gives: % 132.56/18.86 | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | Case 1: % 132.56/18.86 | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | (2856) all_57_6 = e2 & op(e1, e3) = e2 % 132.56/18.86 | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | REF_CLOSE: (163), (1826), (2856), (function-axioms) are % 132.56/18.86 | | | | | | | | | | | | | | inconsistent by sub-proof #341. % 132.56/18.86 | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | (2857) all_57_7 = e2 & op(e1, e2) = e2 % 132.56/18.86 | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | ALPHA: (2857) implies: % 132.56/18.86 | | | | | | | | | | | | | | (2858) op(e1, e2) = e2 % 132.56/18.86 | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e2, % 132.56/18.86 | | | | | | | | | | | | | | e2, e1, simplifying with (162), (2858) gives: % 132.56/18.86 | | | | | | | | | | | | | | (2859) all_52_6 = e2 % 132.56/18.86 | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2, % 132.56/18.86 | | | | | | | | | | | | | | e1, e2, simplifying with (165), (2854) gives: % 132.56/18.86 | | | | | | | | | | | | | | (2860) all_52_9 = e2 % 132.56/18.86 | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | REDUCE: (117), (2860) imply: % 132.56/18.86 | | | | | | | | | | | | | | (2861) ~ (all_52_13 = e2) % 132.56/18.86 | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | SIMP: (2861) implies: % 132.56/18.86 | | | | | | | | | | | | | | (2862) ~ (all_52_13 = e2) % 132.56/18.86 | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | REDUCE: (356), (2860) imply: % 132.56/18.86 | | | | | | | | | | | | | | (2863) ~ (all_8_2 = e2) % 132.56/18.86 | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | SIMP: (2863) implies: % 132.56/18.86 | | | | | | | | | | | | | | (2864) ~ (all_8_2 = e2) % 132.56/18.86 | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | REDUCE: (362), (2860) imply: % 132.56/18.86 | | | | | | | | | | | | | | (2865) ~ (all_6_2 = e2) % 132.56/18.86 | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | BETA: splitting (199) gives: % 132.56/18.86 | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | Case 1: % 132.56/18.86 | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | (2866) all_54_5 = e3 % 132.56/18.86 | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | REF_CLOSE: (267), (376), (2866) are inconsistent by sub-proof % 132.56/18.86 | | | | | | | | | | | | | | | #554. % 132.56/18.86 | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | (2867) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | BETA: splitting (2867) gives: % 132.56/18.86 | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | Case 1: % 132.56/18.86 | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | (2868) all_54_5 = e2 % 132.56/18.86 | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | REF_CLOSE: (267), (2864), (2868) are inconsistent by % 132.56/18.86 | | | | | | | | | | | | | | | | sub-proof #340. % 132.56/18.86 | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | (2869) ~ (all_54_5 = e2) % 132.56/18.86 | | | | | | | | | | | | | | | | (2870) all_54_5 = e1 | all_54_5 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | BETA: splitting (2870) gives: % 132.56/18.86 | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | Case 1: % 132.56/18.86 | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | (2871) all_54_5 = e1 % 132.56/18.86 | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (373), (2871) are inconsistent by sub-proof % 132.56/18.86 | | | | | | | | | | | | | | | | | #339. % 132.56/18.86 | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | Case 2: % 132.56/18.86 | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | (2872) all_54_5 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (2872) imply: % 132.56/18.86 | | | | | | | | | | | | | | | | | (2873) all_8_2 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | SIMP: (2873) implies: % 132.56/18.86 | | | | | | | | | | | | | | | | | (2874) all_8_2 = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | REDUCE: (347), (2874) imply: % 132.56/18.86 | | | | | | | | | | | | | | | | | (2875) ~ (all_52_1 = e0) % 132.56/18.86 | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | REDUCE: (354), (2874) imply: % 132.56/18.86 | | | | | | | | | | | | | | | | | (2876) ~ (all_52_7 = e0) % 132.56/18.86 | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | REDUCE: (358), (2874) imply: % 132.56/18.86 | | | | | | | | | | | | | | | | | (2877) ~ (all_52_13 = e0) % 132.56/18.86 | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | REDUCE: (2864), (2874) imply: % 132.56/18.86 | | | | | | | | | | | | | | | | | (2878) ~ (e2 = e0) % 132.56/18.86 | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | REDUCE: (42), (2874) imply: % 132.56/18.86 | | | | | | | | | | | | | | | | | (2879) op(e2, e2) = e0 % 132.56/18.86 | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | BETA: splitting (1823) gives: % 132.56/18.86 | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | (2880) ~ (all_16_0 = e1) & op(e2, e3) = all_16_0 & % 132.56/18.86 | | | | | | | | | | | | | | | | | | $i(all_16_0) % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | ALPHA: (2880) implies: % 132.56/18.86 | | | | | | | | | | | | | | | | | | (2881) ~ (all_16_0 = e1) % 132.56/18.86 | | | | | | | | | | | | | | | | | | (2882) op(e2, e3) = all_16_0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, % 132.56/18.86 | | | | | | | | | | | | | | | | | | all_16_0, e3, e2, simplifying with (167), (2882) % 132.56/18.86 | | | | | | | | | | | | | | | | | | gives: % 132.56/18.86 | | | | | | | | | | | | | | | | | | (2883) all_52_1 = all_16_0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (2883) imply: % 132.56/18.86 | | | | | | | | | | | | | | | | | | (2884) all_54_4 = all_16_0 % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | REDUCE: (149), (2883) imply: % 132.56/18.86 | | | | | | | | | | | | | | | | | | (2885) ~ (all_52_2 = all_16_0) % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | SIMP: (2885) implies: % 132.56/18.86 | | | | | | | | | | | | | | | | | | (2886) ~ (all_52_2 = all_16_0) % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | REDUCE: (145), (2883) imply: % 132.56/18.86 | | | | | | | | | | | | | | | | | | (2887) ~ (all_52_13 = all_16_0) % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | SIMP: (2887) implies: % 132.56/18.86 | | | | | | | | | | | | | | | | | | (2888) ~ (all_52_13 = all_16_0) % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | REDUCE: (1825), (2883) imply: % 132.56/18.86 | | | | | | | | | | | | | | | | | | (2889) ~ (all_16_0 = e2) % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | REDUCE: (2875), (2883) imply: % 132.56/18.86 | | | | | | | | | | | | | | | | | | (2890) ~ (all_16_0 = e0) % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 132.56/18.86 | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.86 | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | (2891) all_54_4 = e3 % 132.56/18.86 | | | | | | | | | | | | | | | | | | | % 132.56/18.86 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2884), (2891) imply: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | (2892) all_16_0 = e3 % 132.56/18.87 | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | REDUCE: (2886), (2892) imply: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | (2893) ~ (all_52_2 = e3) % 132.56/18.87 | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | REDUCE: (2888), (2892) imply: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | (2894) ~ (all_52_13 = e3) % 132.56/18.87 | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | REDUCE: (2882), (2892) imply: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | (2895) op(e2, e3) = e3 % 132.56/18.87 | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | (2896) all_54_7 = e3 % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (2894), (2896) are inconsistent by % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | sub-proof #338. % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | (2897) ~ (all_54_7 = e3) % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | (2898) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2898) gives: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | (2899) all_54_7 = e2 % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (2862), (2899) are inconsistent by % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | sub-proof #337. % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | (2900) ~ (all_54_7 = e2) % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | (2901) all_54_7 = e1 | all_54_7 = e0 % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2901) gives: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | (2902) all_54_7 = e1 % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (2902) imply: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | (2903) all_52_13 = e1 % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2903) implies: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | (2904) all_52_13 = e1 % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (2904) imply: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | (2905) ~ (all_52_14 = e1) % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2905) implies: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | (2906) ~ (all_52_14 = e1) % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2862), (2904) imply: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | (2907) ~ (e2 = e1) % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (2904) imply: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | (2908) op(e2, e0) = e1 % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | (2909) ~ (all_26_2 = e2) % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2847), (2909) imply: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | (2910) $false % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2910) is inconsistent. % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | (2911) ( ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_0)) | ( ~ (all_26_1 = e3) & op(e2, e2) % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | = all_26_1 & $i(all_26_1)) % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2911) gives: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | (2912) ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_0) % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2912) implies: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | (2913) ~ (all_26_0 = e1) % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | (2914) op(e2, e0) = all_26_0 % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2908), (2913), (2914), (function-axioms) are % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #336. % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | (2915) ~ (all_26_1 = e3) & op(e2, e2) = all_26_1 & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_1) % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2915) implies: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | (2916) ~ (all_26_1 = e3) % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | (2917) op(e2, e2) = all_26_1 % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | (2918) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2918) gives: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (2919) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1834), (2895), (2919), (function-axioms) are % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #335. % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (2920) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2920) gives: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2921) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2921) implies: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2922) op(e3, e3) = e0 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1834), (2922), (function-axioms) are % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2923) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2923) implies: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2924) op(e2, e2) = e3 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2916), (2917), (2924), (function-axioms) are % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #334. % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (2925) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2925) gives: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (2926) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2926) gives: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2927) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2927) implies: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2928) ~ (all_56_25 = e0) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2929) ~ (all_56_17 = e1) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2930) op(e1, e1) = e3 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2931) op(e1, e3) = e1 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2932) op(e3, e0) = all_56_25 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2933) op(e3, e1) = all_56_17 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2934) op(e3, e3) = all_56_1 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e3, % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (39), (2930) gives: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2935) all_6_2 = e3 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1, % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (2931) gives: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2936) all_52_2 = e1 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25, e0, e3, simplifying with (168), (2932) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2937) all_56_25 = all_52_12 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_1, % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (1834), (2934) gives: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2938) all_56_1 = e2 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (2935) imply: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2939) all_36_2 = e3 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2928), (2937) imply: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2940) ~ (all_52_12 = e0) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2893), (2936) imply: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2941) ~ (e3 = e1) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (2935) imply: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2942) ~ (all_52_14 = e3) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2943) ~ (all_36_2 = e3) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2939), (2943) imply: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2944) $false % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2944) is inconsistent. % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2945) ( ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_36_0)) | ( ~ (all_36_1 = e2) & op(e3, e3) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_36_1 & $i(all_36_1)) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (160), (164), (168), % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214), (232), (234), (1834), (2850), (2894), % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2929), (2933), (2940), (2942), (2945), % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #328. % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2946) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2946) implies: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2947) op(e2, e2) = e1 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2879), (2947), (function-axioms) are % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (2948) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2948) gives: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2949) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2949) implies: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2950) op(e2, e0) = e2 % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2862), (2950), (function-axioms) are % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2951) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2951) gives: % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2952) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2952) implies: % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2953) op(e1, e1) = e2 % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (2953), (function-axioms) are % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2954) op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2954) implies: % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2955) op(e0, e0) = all_56_31 % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2956) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2956) gives: % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2957) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (158), (2850), (2876), (2955), (2957), % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #507. % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2958) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2958) gives: % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2959) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2959) implies: % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2960) op(e1, e0) = e1 % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2906), (2960), (function-axioms) are % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #327. % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2961) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2961) implies: % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2962) all_56_31 = e1 % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2955), (2962) imply: % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2963) op(e0, e0) = e1 % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2850), (2963), (function-axioms) are % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636. % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | (2964) all_54_7 = e0 % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (2877), (2964) are inconsistent by % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | sub-proof #326. % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.89 | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | (2965) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 132.56/18.89 | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2881), (2884), (2889), (2890), (2965) are % 132.56/18.89 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #381. % 132.56/18.89 | | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.89 | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | (2966) ~ (all_16_1 = e0) & op(e2, e2) = all_16_1 & % 132.56/18.89 | | | | | | | | | | | | | | | | | | $i(all_16_1) % 132.56/18.89 | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2879), (2966), (function-axioms) are inconsistent % 132.56/18.89 | | | | | | | | | | | | | | | | | | by sub-proof #380. % 132.56/18.89 | | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | Case 2: % 132.56/18.89 | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | (2967) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 132.56/18.89 | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 132.56/18.89 | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | REF_CLOSE: (39), (160), (372), (2849), (2967), % 132.56/18.89 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.89 | | | | | | | | | | | | | #513. % 132.56/18.89 | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | Case 2: % 132.56/18.89 | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | (2968) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 132.56/18.89 | | | | | | | | | | | e2 & op(e0, e1) = e2) % 132.56/18.89 | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | REF_CLOSE: (39), (157), (372), (2848), (2968), % 132.56/18.89 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.89 | | | | | | | | | | | #511. % 132.56/18.89 | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | % 132.56/18.89 | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | % 132.56/18.89 | | | | | | | | Case 2: % 132.56/18.89 | | | | | | | | | % 132.56/18.89 | | | | | | | | | (2969) all_57_1 = e2 & op(e3, e2) = e2 % 132.56/18.89 | | | | | | | | | % 132.56/18.89 | | | | | | | | | REF_CLOSE: (170), (1828), (2969), (function-axioms) are % 132.56/18.89 | | | | | | | | | inconsistent by sub-proof #396. % 132.56/18.89 | | | | | | | | | % 132.56/18.89 | | | | | | | | End of split % 132.56/18.89 | | | | | | | | % 132.56/18.89 | | | | | | | Case 2: % 132.56/18.89 | | | | | | | | % 132.56/18.89 | | | | | | | | (2970) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & % 132.56/18.89 | | | | | | | | op(e3, e0) = e2) % 132.56/18.89 | | | | | | | | % 132.56/18.89 | | | | | | | | BETA: splitting (2970) gives: % 132.56/18.89 | | | | | | | | % 132.56/18.89 | | | | | | | | Case 1: % 132.56/18.89 | | | | | | | | | % 132.56/18.89 | | | | | | | | | (2971) all_57_4 = e2 & op(e3, e1) = e2 % 132.56/18.89 | | | | | | | | | % 132.56/18.89 | | | | | | | | | REF_CLOSE: (169), (1829), (2971), (function-axioms) are % 132.56/18.89 | | | | | | | | | inconsistent by sub-proof #442. % 132.56/18.89 | | | | | | | | | % 132.56/18.89 | | | | | | | | Case 2: % 132.56/18.89 | | | | | | | | | % 132.56/18.89 | | | | | | | | | (2972) all_57_9 = e2 & op(e3, e0) = e2 % 132.56/18.89 | | | | | | | | | % 132.56/18.89 | | | | | | | | | REF_CLOSE: (168), (1830), (2972), (function-axioms) are % 132.56/18.89 | | | | | | | | | inconsistent by sub-proof #460. % 132.56/18.89 | | | | | | | | | % 132.56/18.89 | | | | | | | | End of split % 132.56/18.89 | | | | | | | | % 132.56/18.89 | | | | | | | End of split % 132.56/18.89 | | | | | | | % 132.56/18.89 | | | | | | End of split % 132.56/18.89 | | | | | | % 132.56/18.89 | | | | | Case 2: % 132.56/18.89 | | | | | | % 132.56/18.89 | | | | | | (2973) all_14_2 = e3 % 132.56/18.89 | | | | | | % 132.56/18.89 | | | | | | COMBINE_EQS: (329), (2973) imply: % 132.56/18.89 | | | | | | (2974) all_8_2 = e3 % 132.56/18.89 | | | | | | % 132.56/18.89 | | | | | | SIMP: (2974) implies: % 132.56/18.89 | | | | | | (2975) all_8_2 = e3 % 132.56/18.89 | | | | | | % 132.56/18.89 | | | | | | COMBINE_EQS: (322), (2975) imply: % 132.56/18.89 | | | | | | (2976) all_22_2 = e3 % 132.56/18.89 | | | | | | % 132.56/18.89 | | | | | | REDUCE: (347), (2975) imply: % 132.56/18.89 | | | | | | (2977) ~ (all_52_1 = e3) % 132.56/18.89 | | | | | | % 132.56/18.89 | | | | | | REDUCE: (350), (2975) imply: % 132.56/18.89 | | | | | | (2978) ~ (all_52_4 = e3) % 132.56/18.89 | | | | | | % 132.56/18.89 | | | | | | REDUCE: (352), (2975) imply: % 132.56/18.89 | | | | | | (2979) ~ (all_52_6 = e3) % 132.56/18.89 | | | | | | % 132.56/18.89 | | | | | | REDUCE: (354), (2975) imply: % 132.56/18.89 | | | | | | (2980) ~ (all_52_7 = e3) % 132.56/18.89 | | | | | | % 132.56/18.89 | | | | | | REDUCE: (356), (2975) imply: % 132.56/18.89 | | | | | | (2981) ~ (all_52_9 = e3) % 132.56/18.89 | | | | | | % 132.56/18.89 | | | | | | REDUCE: (358), (2975) imply: % 132.56/18.89 | | | | | | (2982) ~ (all_52_13 = e3) % 132.56/18.89 | | | | | | % 132.56/18.89 | | | | | | BETA: splitting (230) gives: % 132.56/18.89 | | | | | | % 132.56/18.89 | | | | | | Case 1: % 132.56/18.89 | | | | | | | % 132.56/18.89 | | | | | | | (2983) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & % 132.56/18.89 | | | | | | | op(e2, e2) = e3) % 132.56/18.89 | | | | | | | % 132.56/18.89 | | | | | | | BETA: splitting (2983) gives: % 132.56/18.89 | | | | | | | % 132.56/18.89 | | | | | | | Case 1: % 132.56/18.89 | | | | | | | | % 132.56/18.89 | | | | | | | | (2984) all_57_1 = e3 & op(e3, e2) = e3 % 132.56/18.89 | | | | | | | | % 132.56/18.89 | | | | | | | | ALPHA: (2984) implies: % 132.56/18.89 | | | | | | | | (2985) op(e3, e2) = e3 % 132.56/18.89 | | | | | | | | % 132.56/18.89 | | | | | | | | REF_CLOSE: (170), (2978), (2985), (function-axioms) are % 132.56/18.89 | | | | | | | | inconsistent by sub-proof #738. % 132.56/18.89 | | | | | | | | % 132.56/18.89 | | | | | | | Case 2: % 132.56/18.89 | | | | | | | | % 132.56/18.89 | | | | | | | | (2986) all_57_3 = e3 & op(e2, e2) = e3 % 132.56/18.89 | | | | | | | | % 132.56/18.89 | | | | | | | | ALPHA: (2986) implies: % 132.56/18.89 | | | | | | | | (2987) all_57_3 = e3 % 132.56/18.89 | | | | | | | | (2988) op(e2, e2) = e3 % 132.56/18.89 | | | | | | | | % 132.56/18.89 | | | | | | | | BETA: splitting (55) gives: % 132.56/18.89 | | | | | | | | % 132.56/18.89 | | | | | | | | Case 1: % 132.56/18.89 | | | | | | | | | % 132.56/18.89 | | | | | | | | | (2989) ~ (all_16_2 = e2) % 132.56/18.89 | | | | | | | | | % 132.56/18.89 | | | | | | | | | REDUCE: (327), (2989) imply: % 132.56/18.89 | | | | | | | | | (2990) ~ (all_10_2 = e2) % 132.56/18.89 | | | | | | | | | % 132.56/18.89 | | | | | | | | | BETA: splitting (61) gives: % 132.56/18.89 | | | | | | | | | % 132.56/18.89 | | | | | | | | | Case 1: % 132.56/18.89 | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | (2991) ~ (all_20_2 = e2) % 132.56/18.89 | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | REDUCE: (318), (2991) imply: % 132.56/18.89 | | | | | | | | | | (2992) ~ (all_4_2 = e2) % 132.56/18.89 | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | BETA: splitting (64) gives: % 132.56/18.89 | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | Case 1: % 132.56/18.89 | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | (2993) ~ (all_22_2 = e3) % 132.56/18.89 | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | REDUCE: (2976), (2993) imply: % 132.56/18.89 | | | | | | | | | | | (2994) $false % 132.56/18.89 | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | CLOSE: (2994) is inconsistent. % 132.56/18.89 | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | Case 2: % 132.56/18.89 | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | (2995) ( ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 & % 132.56/18.89 | | | | | | | | | | | $i(all_22_0)) | ( ~ (all_22_1 = e1) & op(e3, e3) % 132.56/18.89 | | | | | | | | | | | = all_22_1 & $i(all_22_1)) % 132.56/18.89 | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | BETA: splitting (73) gives: % 132.56/18.89 | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | Case 1: % 132.56/18.89 | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | (2996) ~ (all_28_2 = e3) % 132.56/18.89 | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | REDUCE: (316), (2996) imply: % 132.56/18.89 | | | | | | | | | | | | (2997) ~ (all_6_2 = e3) % 132.56/18.89 | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | BETA: splitting (79) gives: % 132.56/18.89 | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | Case 1: % 132.56/18.89 | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | (2998) ~ (all_32_2 = e1) % 132.56/18.89 | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | REDUCE: (312), (2998) imply: % 132.56/18.89 | | | | | | | | | | | | | (2999) ~ (all_10_2 = e1) % 132.56/18.89 | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | BETA: splitting (204) gives: % 132.56/18.89 | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | Case 1: % 132.56/18.89 | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | (3000) all_54_0 = e3 % 132.56/18.89 | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | COMBINE_EQS: (278), (3000) imply: % 132.56/18.89 | | | | | | | | | | | | | | (3001) all_10_2 = e3 % 132.56/18.89 | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | REDUCE: (338), (3001) imply: % 132.56/18.89 | | | | | | | | | | | | | | (3002) ~ (all_52_2 = e3) % 132.56/18.89 | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | REDUCE: (346), (3001) imply: % 132.56/18.89 | | | | | | | | | | | | | | (3003) ~ (all_52_12 = e3) % 132.56/18.89 | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | REDUCE: (45), (3001) imply: % 132.56/18.89 | | | | | | | | | | | | | | (3004) op(e3, e3) = e3 % 132.56/18.89 | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | BETA: splitting (206) gives: % 132.56/18.89 | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | Case 1: % 132.56/18.89 | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | (3005) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.56/18.89 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.89 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.56/18.89 | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.89 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.56/18.89 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.89 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.56/18.89 | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 132.56/18.89 | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.56/18.89 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.89 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.89 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.56/18.89 | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.56/18.89 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.89 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.56/18.89 | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | BETA: splitting (3005) gives: % 132.56/18.89 | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | Case 1: % 132.56/18.89 | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | (3006) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.56/18.89 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.89 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.56/18.89 | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.56/18.89 | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.89 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.56/18.89 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.89 | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.56/18.89 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.89 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.56/18.89 | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.56/18.89 | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.89 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.56/18.89 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 132.56/18.89 | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (3004), (3006), (function-axioms) are % 132.56/18.89 | | | | | | | | | | | | | | | | inconsistent by sub-proof #623. % 132.56/18.89 | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | Case 2: % 132.56/18.89 | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | (3007) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.56/18.89 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.89 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.56/18.89 | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.89 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.89 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.56/18.89 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.56/18.89 | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.56/18.89 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.89 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.89 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.89 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.56/18.89 | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.89 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.56/18.89 | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | REF_CLOSE: (168), (3003), (3004), (3007), (function-axioms) % 132.56/18.89 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #553. % 132.56/18.89 | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | End of split % 132.56/18.89 | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | Case 2: % 132.56/18.89 | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | (3008) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.56/18.89 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.89 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.56/18.89 | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.56/18.89 | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.56/18.89 | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.56/18.89 | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 132.56/18.89 | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 132.56/18.89 | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.89 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 132.56/18.89 | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 132.56/18.89 | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 132.56/18.89 | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 132.56/18.89 | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 132.56/18.89 | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 132.56/18.89 | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.56/18.89 | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 132.56/18.89 | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 132.56/18.89 | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 132.56/18.89 | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.89 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.56/18.89 | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 132.56/18.89 | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 132.56/18.89 | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 132.56/18.89 | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 132.56/18.89 | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.56/18.89 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.56/18.89 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.56/18.89 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.56/18.89 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.89 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.56/18.89 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.56/18.89 | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.56/18.89 | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | BETA: splitting (3008) gives: % 132.56/18.89 | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | Case 1: % 132.56/18.89 | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | (3009) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.56/18.89 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.89 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.89 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.89 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.56/18.89 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.89 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.56/18.89 | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.56/18.89 | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.56/18.89 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.56/18.89 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.56/18.89 | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.89 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.56/18.89 | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (2988), (2997), (3009), % 132.56/18.89 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.89 | | | | | | | | | | | | | | | | #324. % 132.56/18.89 | | | | | | | | | | | | | | | | % 132.56/18.89 | | | | | | | | | | | | | | | Case 2: % 132.56/18.89 | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | (3010) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.56/18.90 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.90 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 132.56/18.90 | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.90 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.90 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.56/18.90 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.56/18.90 | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.56/18.90 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.90 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.56/18.90 | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.90 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.56/18.90 | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.56/18.90 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.90 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.56/18.90 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.56/18.90 | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.56/18.90 | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.56/18.90 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.56/18.90 | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.56/18.90 | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.56/18.90 | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.56/18.90 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.56/18.90 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.56/18.90 | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.56/18.90 | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.56/18.90 | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.90 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.56/18.90 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.56/18.90 | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.56/18.90 | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.90 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.90 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.56/18.90 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.90 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.90 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.56/18.90 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.56/18.90 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.56/18.90 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.56/18.90 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.56/18.90 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.90 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.56/18.90 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.56/18.90 | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.56/18.90 | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | BETA: splitting (3010) gives: % 132.56/18.90 | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | Case 1: % 132.56/18.90 | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | (3011) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.56/18.90 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.56/18.90 | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 132.56/18.90 | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.90 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.56/18.90 | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.90 | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.56/18.90 | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | ALPHA: (3011) implies: % 132.56/18.90 | | | | | | | | | | | | | | | | | (3012) op(e2, e2) = e0 % 132.56/18.90 | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2988), (3012), (function-axioms) are % 132.56/18.90 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 132.56/18.90 | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | Case 2: % 132.56/18.90 | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | (3013) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.56/18.90 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.90 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.56/18.90 | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.90 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.56/18.90 | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.56/18.90 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.90 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.56/18.90 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.56/18.90 | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.56/18.90 | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.56/18.90 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.56/18.90 | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.56/18.90 | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.56/18.90 | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.56/18.90 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.56/18.90 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.56/18.90 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.56/18.90 | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.56/18.90 | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.90 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.56/18.90 | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.56/18.90 | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.56/18.90 | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.90 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.90 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.56/18.90 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.90 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.90 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.56/18.90 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.56/18.90 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.56/18.90 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.56/18.90 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.56/18.90 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.90 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.56/18.90 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.56/18.90 | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.56/18.90 | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | BETA: splitting (3013) gives: % 132.56/18.90 | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.90 | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | (3014) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 132.56/18.90 | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 132.56/18.90 | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 132.56/18.90 | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | ALPHA: (3014) implies: % 132.56/18.90 | | | | | | | | | | | | | | | | | | (3015) op(e1, e1) = e2 % 132.56/18.90 | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3015), (function-axioms) are % 132.56/18.90 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.56/18.90 | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.90 | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | (3016) op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.56/18.90 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 132.56/18.90 | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.56/18.90 | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.90 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.56/18.90 | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.56/18.90 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.90 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 132.56/18.90 | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.56/18.90 | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 132.56/18.90 | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | ALPHA: (3016) implies: % 132.56/18.90 | | | | | | | | | | | | | | | | | | (3017) op(e0, e0) = all_56_31 % 132.56/18.90 | | | | | | | | | | | | | | | | | | (3018) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.90 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 132.56/18.90 | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 132.56/18.90 | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 132.56/18.90 | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.90 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 132.56/18.90 | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 132.56/18.90 | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 132.56/18.90 | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 132.56/18.90 | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.56/18.90 | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 132.56/18.90 | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | (3019) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (2979), (3002), (3019), % 132.56/18.90 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.90 | | | | | | | | | | | | | | | | | | | #323. % 132.56/18.90 | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | (3020) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | BETA: splitting (3020) gives: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3021) all_57_8 = e3 & op(e1, e1) = e3 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | ALPHA: (3021) implies: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3022) op(e1, e1) = e3 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (2997), (3022), (function-axioms) are % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771. % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3023) all_57_11 = e3 & op(e1, e0) = e3 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | ALPHA: (3023) implies: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3024) op(e1, e0) = e3 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (36), (3017) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | gives: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3025) all_56_31 = all_4_2 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | e3, e0, e1, simplifying with (160), (3024) gives: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3026) all_52_14 = e3 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (3026) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3027) ~ (all_4_2 = e3) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | SIMP: (3027) implies: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3028) ~ (all_4_2 = e3) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (189), (245), (371), (2992), (3018), (3025), % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3028) are inconsistent by sub-proof #322. % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.90 | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | End of split % 132.56/18.90 | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | End of split % 132.56/18.90 | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | End of split % 132.56/18.90 | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | End of split % 132.56/18.90 | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | End of split % 132.56/18.90 | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | Case 2: % 132.56/18.90 | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | (3029) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 132.56/18.90 | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | REF_CLOSE: (278), (374), (2990), (2999), (3029) are % 132.56/18.90 | | | | | | | | | | | | | | inconsistent by sub-proof #777. % 132.56/18.90 | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | End of split % 132.56/18.90 | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | Case 2: % 132.56/18.90 | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | (3030) all_32_2 = e1 % 132.56/18.90 | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | COMBINE_EQS: (312), (3030) imply: % 132.56/18.90 | | | | | | | | | | | | | (3031) all_10_2 = e1 % 132.56/18.90 | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | SIMP: (3031) implies: % 132.56/18.90 | | | | | | | | | | | | | (3032) all_10_2 = e1 % 132.56/18.90 | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | REDUCE: (336), (3032) imply: % 132.56/18.90 | | | | | | | | | | | | | (3033) ~ (all_52_1 = e1) % 132.56/18.90 | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | REDUCE: (342), (3032) imply: % 132.56/18.90 | | | | | | | | | | | | | (3034) ~ (all_52_4 = e1) % 132.56/18.90 | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | REDUCE: (344), (3032) imply: % 132.56/18.90 | | | | | | | | | | | | | (3035) ~ (all_52_8 = e1) % 132.56/18.90 | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | REDUCE: (346), (3032) imply: % 132.56/18.90 | | | | | | | | | | | | | (3036) ~ (all_52_12 = e1) % 132.56/18.90 | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | REDUCE: (45), (3032) imply: % 132.56/18.90 | | | | | | | | | | | | | (3037) op(e3, e3) = e1 % 132.56/18.90 | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | BETA: splitting (2995) gives: % 132.56/18.90 | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | Case 1: % 132.56/18.90 | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | (3038) ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 & % 132.56/18.90 | | | | | | | | | | | | | | $i(all_22_0) % 132.56/18.90 | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | ALPHA: (3038) implies: % 132.56/18.90 | | | | | | | | | | | | | | (3039) ~ (all_22_0 = e0) % 132.56/18.90 | | | | | | | | | | | | | | (3040) op(e3, e2) = all_22_0 % 132.56/18.90 | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 132.56/18.90 | | | | | | | | | | | | | | all_22_0, e2, e3, simplifying with (170), (3040) % 132.56/18.90 | | | | | | | | | | | | | | gives: % 132.56/18.90 | | | | | | | | | | | | | | (3041) all_52_4 = all_22_0 % 132.56/18.90 | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | COMBINE_EQS: (271), (3041) imply: % 132.56/18.90 | | | | | | | | | | | | | | (3042) all_54_1 = all_22_0 % 132.56/18.90 | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | REDUCE: (134), (3041) imply: % 132.56/18.90 | | | | | | | | | | | | | | (3043) ~ (all_52_8 = all_22_0) % 132.56/18.90 | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | SIMP: (3043) implies: % 132.56/18.90 | | | | | | | | | | | | | | (3044) ~ (all_52_8 = all_22_0) % 132.56/18.90 | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | REDUCE: (133), (3041) imply: % 132.56/18.90 | | | | | | | | | | | | | | (3045) ~ (all_52_12 = all_22_0) % 132.56/18.90 | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | SIMP: (3045) implies: % 132.56/18.90 | | | | | | | | | | | | | | (3046) ~ (all_52_12 = all_22_0) % 132.56/18.90 | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | REDUCE: (2978), (3041) imply: % 132.56/18.90 | | | | | | | | | | | | | | (3047) ~ (all_22_0 = e3) % 132.56/18.90 | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | REDUCE: (3034), (3041) imply: % 132.56/18.90 | | | | | | | | | | | | | | (3048) ~ (all_22_0 = e1) % 132.56/18.90 | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | BETA: splitting (203) gives: % 132.56/18.90 | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | Case 1: % 132.56/18.90 | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | (3049) all_54_1 = e3 % 132.56/18.90 | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | COMBINE_EQS: (3042), (3049) imply: % 132.56/18.90 | | | | | | | | | | | | | | | (3050) all_22_0 = e3 % 132.56/18.90 | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | REDUCE: (3047), (3050) imply: % 132.56/18.90 | | | | | | | | | | | | | | | (3051) $false % 132.56/18.90 | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | CLOSE: (3051) is inconsistent. % 132.56/18.90 | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | Case 2: % 132.56/18.90 | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | (3052) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 132.56/18.90 | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | BETA: splitting (3052) gives: % 132.56/18.90 | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | Case 1: % 132.56/18.90 | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | (3053) all_54_1 = e2 % 132.56/18.90 | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | COMBINE_EQS: (3042), (3053) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | (3054) all_22_0 = e2 % 132.56/18.90 | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | REDUCE: (3044), (3054) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | (3055) ~ (all_52_8 = e2) % 132.56/18.90 | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | REDUCE: (3046), (3054) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | (3056) ~ (all_52_12 = e2) % 132.56/18.90 | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 132.56/18.90 | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | Case 1: % 132.56/18.90 | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | (3057) ~ (all_34_2 = e3) % 132.56/18.90 | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | REDUCE: (307), (3057) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | (3058) ~ (all_4_2 = e3) % 132.56/18.90 | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 132.56/18.90 | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.90 | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | (3059) all_54_15 = e3 % 132.56/18.90 | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3059) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | (3060) all_4_2 = e3 % 132.56/18.90 | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | REDUCE: (3058), (3060) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | (3061) $false % 132.56/18.90 | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | CLOSE: (3061) is inconsistent. % 132.56/18.90 | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.90 | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | (3062) ~ (all_54_15 = e3) % 132.56/18.90 | | | | | | | | | | | | | | | | | | (3063) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 132.56/18.90 | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | BETA: splitting (3063) gives: % 132.56/18.90 | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | (3064) all_54_15 = e2 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3064) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | (3065) all_4_2 = e2 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | REDUCE: (2992), (3065) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | (3066) $false % 132.56/18.90 | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | CLOSE: (3066) is inconsistent. % 132.56/18.90 | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | (3067) ~ (all_54_15 = e2) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | (3068) all_54_15 = e1 | all_54_15 = e0 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | BETA: splitting (3068) gives: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3069) all_54_15 = e1 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3069) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3070) all_4_2 = e1 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (3070) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3071) $false % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | CLOSE: (3071) is inconsistent. % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3072) all_54_15 = e0 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3072) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3073) all_4_2 = e0 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (3073) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3074) ~ (all_52_12 = e0) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (3073) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3075) ~ (all_52_13 = e0) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (3058), (3073) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3076) ~ (e3 = e0) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (2992), (3073) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3077) ~ (e2 = e0) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (3073) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3078) ~ (e1 = e0) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3073) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | (3079) op(e0, e0) = e0 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | (3080) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3080) gives: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | (3081) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (120), (169), (201), (269), (3036), (3037), % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | (3056), (3074), (3081), (function-axioms) are % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #318. % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | (3082) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3082) gives: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | (3083) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3083) implies: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | (3084) op(e3, e3) = e0 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3037), (3084), (function-axioms) are % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | (3085) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3085) implies: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | (3086) op(e2, e3) = e2 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | (3087) all_54_3 = e3 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (3087) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | (3088) all_52_12 = e3 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (3088) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | (3089) ~ (all_52_8 = e3) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (3088) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | (3090) ~ (all_52_13 = e3) % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | (3091) all_54_2 = e3 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3091) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | (3092) all_52_8 = e3 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3089), (3092) imply: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | (3093) $false % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3093) is inconsistent. % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | (3094) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.90 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3094) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (3095) all_54_2 = e2 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (3055), (3095) are inconsistent by % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #317. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (3096) all_54_2 = e1 | all_54_2 = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3096) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3097) all_54_2 = e1 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (3035), (3097) are inconsistent by % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #316. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3098) all_54_2 = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3098) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3099) all_52_8 = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3099) implies: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3100) all_52_8 = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (3100) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3101) ~ (all_52_9 = e0) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3101) implies: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3102) ~ (all_52_9 = e0) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3103) all_54_6 = e3 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (2981), (3103) are inconsistent by % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #315. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3104) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3104) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3105) all_54_6 = e2 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3105) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3106) all_52_9 = e2 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3106) implies: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3107) all_52_9 = e2 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (3107) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3108) ~ (all_52_1 = e2) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (3086), (3108), (function-axioms) are % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #779. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3109) all_54_6 = e1 | all_54_6 = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (117), (145), (167), (197), (259), (260), (2982), % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3075), (3086), (3102), (3109), (function-axioms) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #311. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (3110) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (3036), (3056), (3074), (3110) are % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (3111) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3111) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (3112) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (2988), (2997), (3112), % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | #324. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (3113) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3113) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | (3114) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3114) implies: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | (3115) op(e2, e2) = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2988), (3115), (function-axioms) are % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | (3116) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3116) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (3117) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3117) implies: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (3118) op(e1, e1) = e2 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3118), (function-axioms) are % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (3119) op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3119) implies: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (3120) op(e0, e0) = all_56_31 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (3121) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3121) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | (3122) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (3079), (3120), (3122), % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | #713. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | (3123) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3123) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (3124) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3124) implies: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (3125) op(e1, e1) = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3126) all_54_3 = e3 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (3126) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3127) all_52_12 = e3 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (3127) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3128) ~ (all_52_8 = e3) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3129) all_54_2 = e3 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3129) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3130) all_52_8 = e3 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3128), (3130) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3131) $false % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3131) is inconsistent. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3132) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (194), (270), (334), (361), (372), (2997), % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3035), (3055), (3125), (3132), (function-axioms) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #476. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3133) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (3036), (3056), (3074), (3133) are % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (3134) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3134) implies: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (3135) op(e0, e1) = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3136) all_54_3 = e3 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (3136) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3137) all_52_12 = e3 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (3137) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3138) ~ (all_52_8 = e3) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (3137) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3139) ~ (all_52_13 = e3) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (3137) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3140) ~ (all_52_14 = e3) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3140) implies: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3141) ~ (all_52_14 = e3) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3142) all_54_2 = e3 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3142) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3143) all_52_8 = e3 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3138), (3143) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3144) $false % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3144) is inconsistent. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3145) ~ (all_54_2 = e3) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3146) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3146) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3147) all_54_2 = e2 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3147) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3148) all_52_8 = e2 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3055), (3148) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3149) $false % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3149) is inconsistent. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3150) all_54_2 = e1 | all_54_2 = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3150) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3151) all_54_2 = e1 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3151) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3152) all_52_8 = e1 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3035), (3152) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3153) $false % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3153) is inconsistent. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3154) all_54_2 = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3154) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3155) all_52_8 = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (3155) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3156) ~ (all_52_9 = e0) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3156) implies: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3157) ~ (all_52_9 = e0) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (3155) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3158) ~ (all_6_2 = e0) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3158) implies: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3159) ~ (all_6_2 = e0) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3160) all_54_10 = e3 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (2997), (3160) are inconsistent by % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #742. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3161) ~ (all_54_10 = e3) % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3162) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3162) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3163) all_54_10 = e2 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (372), (3163) are inconsistent by sub-proof % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #741. % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3164) all_54_10 = e1 | all_54_10 = e0 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3164) gives: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3165) all_54_10 = e1 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (3165) imply: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3166) all_6_2 = e1 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3166) implies: % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3167) all_6_2 = e1 % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (3167) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3168) ~ (all_52_9 = e1) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2997), (3167) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3169) ~ (e3 = e1) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (3167) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3170) op(e1, e1) = e1 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3171) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3171) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3172) all_57_9 = e3 & op(e3, e0) = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3172) implies: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3173) all_57_9 = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3174) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (2981), (3138), (3174), % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #310. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3175) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3175) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3176) all_57_8 = e3 & op(e1, e1) = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3176) implies: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3177) op(e1, e1) = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (3170), (3177), (function-axioms) are % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3178) all_57_14 = e3 & op(e0, e1) = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3178) implies: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3179) op(e0, e1) = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3180) all_54_6 = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3180) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3181) all_52_9 = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2981), (3181) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3182) $false % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3182) is inconsistent. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3183) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3183) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3184) all_54_6 = e2 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3184) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3185) all_52_9 = e2 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (3185) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3186) ~ (all_52_1 = e2) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3187) all_54_4 = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3187) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3188) all_52_1 = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2977), (3188) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3189) $false % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3189) is inconsistent. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3190) ~ (all_54_4 = e3) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3191) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3191) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3192) all_54_4 = e2 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3192) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3193) all_52_1 = e2 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3186), (3193) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3194) $false % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3194) is inconsistent. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3195) all_54_4 = e1 | all_54_4 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3195) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3196) all_54_4 = e1 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3196) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3197) all_52_1 = e1 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3033), (3197) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3198) $false % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3198) is inconsistent. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3199) all_54_4 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3199) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3200) all_52_1 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e1, % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (3135), (3179) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3201) e3 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3173), (3201) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3202) all_57_9 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (164), (214), (2982), (3079), (3141), % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3202), (function-axioms) are inconsistent by % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #386. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3203) all_54_6 = e1 | all_54_6 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (3157), (3168), (3203) are inconsistent by % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #479. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3204) all_57_10 = e3 & op(e2, e0) = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2982), (3204), (function-axioms) are % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3205) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (160), (3079), (3141), (3205), % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #387. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3206) all_54_10 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (3159), (3206) are inconsistent by % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #506. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3207) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (3036), (3056), (3074), (3207) are % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | (3208) all_34_2 = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | (3209) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & % 132.56/18.92 | | | | | | | | | | | | | | | | | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3) % 132.56/18.92 | | | | | | | | | | | | | | | | | = all_34_1 & $i(all_34_1)) % 132.56/18.92 | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (3208) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | (3210) all_4_2 = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | SIMP: (3210) implies: % 132.56/18.92 | | | | | | | | | | | | | | | | | (3211) all_4_2 = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | REDUCE: (367), (3211) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | (3212) ~ (all_52_11 = e3) % 132.56/18.92 | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | REDUCE: (368), (3211) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | (3213) ~ (all_52_12 = e3) % 132.56/18.92 | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | REDUCE: (370), (3211) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | (3214) ~ (all_52_14 = e3) % 132.56/18.92 | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | REDUCE: (36), (3211) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | (3215) op(e0, e0) = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | (3216) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 132.56/18.92 | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | BETA: splitting (3216) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | (3217) all_57_6 = e3 & op(e1, e3) = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | ALPHA: (3217) implies: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | (3218) all_57_6 = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | (3219) op(e1, e3) = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | (3220) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3220) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | (3221) all_57_4 = e3 & op(e3, e1) = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3221) implies: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | (3222) all_57_4 = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | (3223) all_54_3 = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (3223) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | (3224) all_52_12 = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3213), (3224) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | (3225) $false % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3225) is inconsistent. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | (3226) ~ (all_54_3 = e3) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | (3227) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | (3228) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3228) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3229) all_57_6 = e2 & op(e1, e3) = e2 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3229) implies: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3230) all_57_6 = e2 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3218), (3230) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3231) e3 = e2 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (3231) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3232) $false % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3232) is inconsistent. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3233) all_57_7 = e2 & op(e1, e2) = e2 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3233) implies: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3234) all_57_7 = e2 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (227), (228), % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (232), (236), (238), (2978), (2988), (3037), % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3039), (3040), (3234), (function-axioms) are % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #308. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | (3235) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3235) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3236) all_57_8 = e2 & op(e1, e1) = e2 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3236) implies: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3237) op(e1, e1) = e2 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3237), (function-axioms) are % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3238) all_57_11 = e2 & op(e1, e0) = e2 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3238) implies: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3239) all_57_11 = e2 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | (3240) op(e1, e0) = e2 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | (3241) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3037), (3039), (3040), (3241), % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | #307. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | (3242) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3242) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (3243) all_57_4 = e0 & op(e3, e1) = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3222), (3243) are inconsistent by sub-proof % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | #384. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (3244) all_57_9 = e0 & op(e3, e0) = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3244) implies: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (3245) all_57_9 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3209) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3246) ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_0) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3246) implies: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3247) ~ (all_34_0 = e2) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3248) op(e3, e0) = all_34_0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3249) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3249) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3250) all_57_9 = e1 & op(e3, e0) = e1 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3250) implies: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3251) all_57_9 = e1 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3245), (3251) are inconsistent by sub-proof % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #383. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3252) all_57_10 = e1 & op(e2, e0) = e1 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3252) implies: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3253) op(e2, e0) = e1 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3227) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3254) all_54_3 = e2 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (3254) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3255) all_52_12 = e2 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3056), (3255) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3256) $false % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3256) is inconsistent. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3257) all_54_3 = e1 | all_54_3 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3257) gives: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3258) all_54_3 = e1 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (3258) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3259) all_52_12 = e1 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3036), (3259) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3260) $false % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3260) is inconsistent. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3261) all_54_3 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (3261) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3262) all_52_12 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (3262) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3263) ~ (all_52_13 = e0) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3263) implies: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3264) ~ (all_52_13 = e0) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3213), (3262) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3265) ~ (e3 = e0) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (3262) imply: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3266) op(e3, e0) = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (110), (160), (163), (164), (168), % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (208), (212), (214), (366), (2982), (2988), % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3037), (3213), (3214), (3219), (3239), (3240), % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3247), (3248), (3253), (3264), (3266), % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #631. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3267) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (3215), (3240), (3267), % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #557. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3268) ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 & % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_1) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3268) implies: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3269) ~ (all_34_1 = e1) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3270) op(e3, e3) = all_34_1 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3037), (3269), (3270), (function-axioms) are % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #626. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | (3271) all_57_5 = e3 & op(e2, e1) = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2981), (3271), (function-axioms) are % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | (3272) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (2997), (3212), (3272), % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | #651. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | (3273) all_57_7 = e3 & op(e1, e2) = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | ALPHA: (3273) implies: % 132.56/18.92 | | | | | | | | | | | | | | | | | | | (3274) op(e1, e2) = e3 % 132.56/18.92 | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2979), (3274), (function-axioms) are % 132.56/18.92 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654. % 132.56/18.92 | | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | (3275) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 132.56/18.92 | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 132.56/18.92 | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (2997), (3214), (3275), % 132.56/18.92 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.92 | | | | | | | | | | | | | | | | | | #653. % 132.56/18.92 | | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | (3276) all_54_1 = e1 | all_54_1 = e0 % 132.56/18.92 | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | | REF_CLOSE: (3039), (3042), (3048), (3276) are inconsistent by % 132.56/18.92 | | | | | | | | | | | | | | | | sub-proof #306. % 132.56/18.92 | | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | (3277) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & % 132.56/18.92 | | | | | | | | | | | | | | $i(all_22_1) % 132.56/18.92 | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | | REF_CLOSE: (3037), (3277), (function-axioms) are inconsistent % 132.56/18.92 | | | | | | | | | | | | | | by sub-proof #305. % 132.56/18.92 | | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | End of split % 132.56/18.92 | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | Case 2: % 132.56/18.92 | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | (3278) all_28_2 = e3 % 132.56/18.92 | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | COMBINE_EQS: (316), (3278) imply: % 132.56/18.92 | | | | | | | | | | | | (3279) all_6_2 = e3 % 132.56/18.92 | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | SIMP: (3279) implies: % 132.56/18.92 | | | | | | | | | | | | (3280) all_6_2 = e3 % 132.56/18.92 | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | REDUCE: (348), (3280) imply: % 132.56/18.92 | | | | | | | | | | | | (3281) ~ (all_52_2 = e3) % 132.56/18.92 | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | REDUCE: (361), (3280) imply: % 132.56/18.92 | | | | | | | | | | | | (3282) ~ (all_52_8 = e3) % 132.56/18.92 | | | | | | | | | | | | % 132.56/18.92 | | | | | | | | | | | | REDUCE: (364), (3280) imply: % 132.56/18.93 | | | | | | | | | | | | (3283) ~ (all_52_11 = e3) % 132.56/18.93 | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | REDUCE: (39), (3280) imply: % 132.56/18.93 | | | | | | | | | | | | (3284) op(e1, e1) = e3 % 132.56/18.93 | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | BETA: splitting (79) gives: % 132.56/18.93 | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | Case 1: % 132.56/18.93 | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | (3285) ~ (all_32_2 = e1) % 132.56/18.93 | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | REDUCE: (312), (3285) imply: % 132.56/18.93 | | | | | | | | | | | | | (3286) ~ (all_10_2 = e1) % 132.56/18.93 | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | BETA: splitting (204) gives: % 132.56/18.93 | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | Case 1: % 132.56/18.93 | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | (3287) all_54_0 = e3 % 132.56/18.93 | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | COMBINE_EQS: (278), (3287) imply: % 132.56/18.93 | | | | | | | | | | | | | | (3288) all_10_2 = e3 % 132.56/18.93 | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | SIMP: (3288) implies: % 132.56/18.93 | | | | | | | | | | | | | | (3289) all_10_2 = e3 % 132.56/18.93 | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | REDUCE: (340), (3289) imply: % 132.56/18.93 | | | | | | | | | | | | | | (3290) ~ (all_52_3 = e3) % 132.56/18.93 | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | REDUCE: (346), (3289) imply: % 132.56/18.93 | | | | | | | | | | | | | | (3291) ~ (all_52_12 = e3) % 132.56/18.93 | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | REDUCE: (45), (3289) imply: % 132.56/18.93 | | | | | | | | | | | | | | (3292) op(e3, e3) = e3 % 132.56/18.93 | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | BETA: splitting (211) gives: % 132.56/18.93 | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | Case 1: % 132.56/18.93 | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | (3293) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 132.56/18.93 | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 132.56/18.93 | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | BETA: splitting (3293) gives: % 132.56/18.93 | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | Case 1: % 132.56/18.93 | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | (3294) all_57_12 = e3 & op(e0, e3) = e3 % 132.56/18.93 | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3290), (3294), (function-axioms) are % 132.56/18.93 | | | | | | | | | | | | | | | | inconsistent by sub-proof #628. % 132.56/18.93 | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | Case 2: % 132.56/18.93 | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | (3295) all_57_13 = e3 & op(e0, e2) = e3 % 132.56/18.93 | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | REF_CLOSE: (158), (2980), (3295), (function-axioms) are % 132.56/18.93 | | | | | | | | | | | | | | | | inconsistent by sub-proof #556. % 132.56/18.93 | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | End of split % 132.56/18.93 | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | Case 2: % 132.56/18.93 | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | (3296) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 132.56/18.93 | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 132.56/18.93 | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | BETA: splitting (3296) gives: % 132.56/18.93 | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | Case 1: % 132.56/18.93 | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | (3297) all_57_14 = e3 & op(e0, e1) = e3 % 132.56/18.93 | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | REF_CLOSE: (157), (3283), (3297), (function-axioms) are % 132.56/18.93 | | | | | | | | | | | | | | | | inconsistent by sub-proof #652. % 132.56/18.93 | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | Case 2: % 132.56/18.93 | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | (3298) all_57_15 = e3 & op(e0, e0) = e3 % 132.56/18.93 | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | ALPHA: (3298) implies: % 132.56/18.93 | | | | | | | | | | | | | | | | (3299) op(e0, e0) = e3 % 132.56/18.93 | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 132.56/18.93 | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | Case 1: % 132.56/18.93 | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | (3300) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.56/18.93 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.93 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.56/18.93 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.56/18.93 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.93 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.56/18.93 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.56/18.93 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.93 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.93 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.56/18.93 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.93 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.56/18.93 | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | BETA: splitting (3300) gives: % 132.56/18.93 | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.93 | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | (3301) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.56/18.93 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.93 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.56/18.93 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 132.56/18.93 | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (3292), (3301), (function-axioms) are % 132.56/18.93 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623. % 132.56/18.93 | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.93 | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | (3302) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.93 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.56/18.93 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.93 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.56/18.93 | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | BETA: splitting (3302) gives: % 132.56/18.93 | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3303) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | ALPHA: (3303) implies: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3304) op(e3, e0) = e3 % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (3291), (3304), (function-axioms) are % 132.56/18.93 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #733. % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3305) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | ALPHA: (3305) implies: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3306) ~ (all_56_1 = e3) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3307) op(e3, e3) = all_56_1 % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_1, % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (3292), (3307) gives: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3308) all_56_1 = e3 % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | REDUCE: (3306), (3308) imply: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3309) $false % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | CLOSE: (3309) is inconsistent. % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | End of split % 132.56/18.93 | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | End of split % 132.56/18.93 | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | Case 2: % 132.56/18.93 | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | (3310) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.56/18.93 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.93 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.56/18.93 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.56/18.93 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.56/18.93 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.56/18.93 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 132.56/18.93 | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 132.56/18.93 | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.93 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 132.56/18.93 | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 132.56/18.93 | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 132.56/18.93 | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 132.56/18.93 | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 132.56/18.93 | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 132.56/18.93 | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.56/18.93 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 132.56/18.93 | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 132.56/18.93 | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 132.56/18.93 | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.93 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.56/18.93 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 132.56/18.93 | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 132.56/18.93 | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 132.56/18.93 | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 132.56/18.93 | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.56/18.93 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.56/18.93 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.56/18.93 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.56/18.93 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.93 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.56/18.93 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.56/18.93 | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.56/18.93 | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | BETA: splitting (3310) gives: % 132.56/18.93 | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.93 | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | (3311) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.93 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.56/18.93 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.56/18.93 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.56/18.93 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.56/18.93 | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | BETA: splitting (3311) gives: % 132.56/18.93 | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3312) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | ALPHA: (3312) implies: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3313) ~ (all_56_1 = e3) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3314) op(e3, e3) = all_56_1 % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3292), (3313), (3314), (function-axioms) are % 132.56/18.93 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #766. % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3315) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | ALPHA: (3315) implies: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3316) op(e2, e2) = e1 % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2988), (3316), (function-axioms) are % 132.56/18.93 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | End of split % 132.56/18.93 | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.93 | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | (3317) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.93 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.56/18.93 | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.56/18.93 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.93 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.56/18.93 | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.56/18.93 | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.56/18.93 | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.56/18.93 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.56/18.93 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.56/18.93 | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.56/18.93 | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.56/18.93 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.93 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.56/18.93 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.56/18.93 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.56/18.93 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.56/18.93 | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.56/18.93 | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | BETA: splitting (3317) gives: % 132.56/18.93 | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3318) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | ALPHA: (3318) implies: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3319) op(e2, e2) = e0 % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2988), (3319), (function-axioms) are % 132.56/18.93 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (3320) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.56/18.93 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.56/18.93 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.56/18.93 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.56/18.93 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.56/18.93 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.56/18.93 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | BETA: splitting (3320) gives: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (3321) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | ALPHA: (3321) implies: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (3322) op(e1, e1) = e2 % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3322), (function-axioms) are % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (3323) op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | ALPHA: (3323) implies: % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (3324) op(e0, e0) = all_56_31 % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (3325) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (371), (2992), (3284), (3292), (3299), % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | (3324), (3325), (function-axioms) are inconsistent % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | by sub-proof #751. % 132.56/18.93 | | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.93 | | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | | End of split % 132.56/18.93 | | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | | End of split % 132.56/18.93 | | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | | End of split % 132.56/18.93 | | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | | End of split % 132.56/18.93 | | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | End of split % 132.56/18.93 | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | Case 2: % 132.56/18.93 | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | (3326) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 132.56/18.93 | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | REF_CLOSE: (278), (374), (2990), (3286), (3326) are % 132.56/18.93 | | | | | | | | | | | | | | inconsistent by sub-proof #777. % 132.56/18.93 | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | End of split % 132.56/18.93 | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | Case 2: % 132.56/18.93 | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | (3327) all_32_2 = e1 % 132.56/18.93 | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | COMBINE_EQS: (312), (3327) imply: % 132.56/18.93 | | | | | | | | | | | | | (3328) all_10_2 = e1 % 132.56/18.93 | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | SIMP: (3328) implies: % 132.56/18.93 | | | | | | | | | | | | | (3329) all_10_2 = e1 % 132.56/18.93 | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | REDUCE: (338), (3329) imply: % 132.56/18.93 | | | | | | | | | | | | | (3330) ~ (all_52_2 = e1) % 132.56/18.93 | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | REDUCE: (342), (3329) imply: % 132.56/18.93 | | | | | | | | | | | | | (3331) ~ (all_52_4 = e1) % 132.56/18.93 | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | REDUCE: (344), (3329) imply: % 132.56/18.93 | | | | | | | | | | | | | (3332) ~ (all_52_8 = e1) % 132.56/18.93 | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | REDUCE: (346), (3329) imply: % 132.56/18.93 | | | | | | | | | | | | | (3333) ~ (all_52_12 = e1) % 132.56/18.93 | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | REDUCE: (45), (3329) imply: % 132.56/18.93 | | | | | | | | | | | | | (3334) op(e3, e3) = e1 % 132.56/18.93 | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | BETA: splitting (2995) gives: % 132.56/18.93 | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | Case 1: % 132.56/18.93 | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | (3335) ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 & % 132.56/18.93 | | | | | | | | | | | | | | $i(all_22_0) % 132.56/18.93 | | | | | | | | | | | | | | % 132.56/18.93 | | | | | | | | | | | | | | ALPHA: (3335) implies: % 132.56/18.93 | | | | | | | | | | | | | | (3336) ~ (all_22_0 = e0) % 132.56/18.94 | | | | | | | | | | | | | | (3337) op(e3, e2) = all_22_0 % 132.56/18.94 | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | BETA: splitting (237) gives: % 132.56/18.94 | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | (3338) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 132.56/18.94 | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 132.56/18.94 | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | BETA: splitting (3338) gives: % 132.56/18.94 | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | (3339) all_57_0 = e3 & op(e3, e3) = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | ALPHA: (3339) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | (3340) op(e3, e3) = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3334), (3340), (function-axioms) are % 132.56/18.94 | | | | | | | | | | | | | | | | inconsistent by sub-proof #775. % 132.56/18.94 | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | (3341) all_57_2 = e3 & op(e2, e3) = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | ALPHA: (3341) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | (3342) op(e2, e3) = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | REF_CLOSE: (167), (2977), (3342), (function-axioms) are % 132.56/18.94 | | | | | | | | | | | | | | | | inconsistent by sub-proof #763. % 132.56/18.94 | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | End of split % 132.56/18.94 | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | (3343) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 132.56/18.94 | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 132.56/18.94 | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | BETA: splitting (3343) gives: % 132.56/18.94 | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | (3344) all_57_6 = e3 & op(e1, e3) = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3281), (3344), (function-axioms) are % 132.56/18.94 | | | | | | | | | | | | | | | | inconsistent by sub-proof #761. % 132.56/18.94 | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | (3345) all_57_12 = e3 & op(e0, e3) = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | ALPHA: (3345) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | (3346) all_57_12 = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | (3347) op(e0, e3) = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | (3348) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 132.56/18.94 | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (2978), (3334), (3348), % 132.56/18.94 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.94 | | | | | | | | | | | | | | | | | #737. % 132.56/18.94 | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | (3349) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 132.56/18.94 | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | BETA: splitting (3349) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3350) all_57_4 = e3 & op(e3, e1) = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | ALPHA: (3350) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3351) op(e3, e1) = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3282), (3351), (function-axioms) are % 132.56/18.94 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #705. % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3352) all_57_9 = e3 & op(e3, e0) = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | ALPHA: (3352) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3353) all_57_9 = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3354) op(e3, e0) = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3, % 132.56/18.94 | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (3347) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3355) all_52_3 = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 132.56/18.94 | | | | | | | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (3354) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3356) all_52_12 = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 132.56/18.94 | | | | | | | | | | | | | | | | | | all_22_0, e2, e3, simplifying with (170), (3337) % 132.56/18.94 | | | | | | | | | | | | | | | | | | gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3357) all_52_4 = all_22_0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (3357) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3358) all_54_1 = all_22_0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | REDUCE: (140), (3355) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3359) ~ (all_52_7 = e3) % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | REDUCE: (139), (3355) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3360) ~ (all_52_11 = e3) % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | REDUCE: (135), (3357) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3361) ~ (all_52_7 = all_22_0) % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | SIMP: (3361) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3362) ~ (all_52_7 = all_22_0) % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | REDUCE: (134), (3357) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3363) ~ (all_52_8 = all_22_0) % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | SIMP: (3363) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3364) ~ (all_52_8 = all_22_0) % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | REDUCE: (2978), (3357) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3365) ~ (all_22_0 = e3) % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | REDUCE: (3331), (3357) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3366) ~ (all_22_0 = e1) % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | REDUCE: (113), (3356) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3367) ~ (all_52_13 = e3) % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | REDUCE: (368), (3356) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3368) ~ (all_4_2 = e3) % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | SIMP: (3368) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | | | (3369) ~ (all_4_2 = e3) % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | (3370) all_54_15 = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (3369), (3370) are inconsistent by % 132.56/18.94 | | | | | | | | | | | | | | | | | | | sub-proof #601. % 132.56/18.94 | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | (3371) ~ (all_54_15 = e3) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | (3372) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | (3373) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3334), (3336), (3337), (3373), % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | #307. % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | (3374) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3374) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | (3375) all_57_4 = e0 & op(e3, e1) = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3375) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | (3376) all_57_4 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | (3377) all_54_1 = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3358), (3377) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | (3378) all_22_0 = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3365), (3378) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | (3379) $false % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3379) is inconsistent. % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | (3380) ~ (all_54_1 = e3) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | (3381) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3381) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | (3382) all_54_1 = e2 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3358), (3382) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | (3383) all_22_0 = e2 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3362), (3383) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | (3384) ~ (all_52_7 = e2) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3364), (3383) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | (3385) ~ (all_52_8 = e2) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3365), (3383) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | (3386) ~ (e3 = e2) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3372) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | (3387) all_54_15 = e2 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (2992), (3387) are inconsistent by % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #748. % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | (3388) ~ (all_54_15 = e2) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | (3389) all_54_15 = e1 | all_54_15 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | (3390) all_54_2 = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3390) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | (3391) all_52_8 = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3282), (3391) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | (3392) $false % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3392) is inconsistent. % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | (3393) ~ (all_54_2 = e3) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | (3394) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (3395) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3395) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3396) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (3282), (3334), (3396), % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | #552. % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3397) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3397) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3398) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3398) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3399) op(e3, e3) = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3334), (3399), (function-axioms) are % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3400) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3400) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3401) op(e2, e3) = e2 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3389) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3402) all_54_15 = e1 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (3402) are inconsistent by sub-proof % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #747. % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3403) all_54_15 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3403) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3404) all_4_2 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3404) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3405) all_4_2 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (3405) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3406) ~ (all_52_7 = e0) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (3405) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3407) ~ (all_52_13 = e0) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3408) all_54_13 = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (3408) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3409) all_52_7 = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3409) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3410) all_52_7 = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2980), (3410) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3411) $false % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3411) is inconsistent. % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3412) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3412) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3413) all_54_13 = e2 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (3384), (3413) are inconsistent by % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #472. % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3414) all_54_13 = e1 | all_54_13 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3414) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3415) all_54_13 = e1 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (3415) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3416) all_52_7 = e1 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3416) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3417) all_52_7 = e1 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (3417) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3418) ~ (all_52_11 = e1) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3418) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3419) ~ (all_52_11 = e1) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3394) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3420) all_54_2 = e2 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3420) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3421) all_52_8 = e2 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3385), (3421) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3422) $false % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3422) is inconsistent. % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3423) all_54_2 = e1 | all_54_2 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3423) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3424) all_54_2 = e1 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3424) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3425) all_52_8 = e1 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3332), (3425) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3426) $false % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3426) is inconsistent. % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3427) all_54_2 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3427) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3428) all_52_8 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (3428) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3429) ~ (all_52_9 = e0) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3429) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3430) ~ (all_52_9 = e0) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (3428) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3431) ~ (all_52_11 = e0) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3431) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3432) ~ (all_52_11 = e0) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3433) all_54_14 = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (3283), (3433) are inconsistent by % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #760. % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3434) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3434) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3435) all_54_14 = e2 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (3435) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3436) all_52_11 = e2 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3436) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3437) all_52_11 = e2 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (3437) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3438) ~ (all_52_9 = e2) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3439) all_54_6 = e3 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (2981), (3439) are inconsistent by % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #315. % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3440) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3440) gives: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3441) all_54_6 = e2 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3441) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3442) all_52_9 = e2 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3442) implies: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3443) all_52_9 = e2 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3438), (3443) imply: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3444) $false % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3444) is inconsistent. % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3445) all_54_6 = e1 | all_54_6 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (117), (145), (167), (197), (259), (260), (2982), % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3401), (3407), (3430), (3445), (function-axioms) % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #311. % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3446) all_54_14 = e1 | all_54_14 = e0 % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (3419), (3432), (3446) are inconsistent by % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #755. % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.56/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3447) all_54_13 = e0 % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (3406), (3447) are inconsistent by % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #471. % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (3448) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3448) gives: % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3449) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (163), (2988), (3330), (3449), % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | #304. % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3450) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3450) gives: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3451) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3451) implies: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3452) op(e2, e2) = e0 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2988), (3452), (function-axioms) are % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3453) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3453) gives: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3454) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3454) implies: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3455) op(e1, e1) = e2 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3455), (function-axioms) are % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3456) op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3456) implies: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3457) op(e0, e0) = all_56_31 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3458) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3459) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3459) gives: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3460) all_57_0 = e2 & op(e3, e3) = e2 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3460) implies: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3461) op(e3, e3) = e2 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3334), (3461), (function-axioms) are % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743. % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3462) all_57_1 = e2 & op(e3, e2) = e2 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3462) implies: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3463) all_57_1 = e2 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3389) gives: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3464) all_54_15 = e1 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (3464) are inconsistent by sub-proof % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #747. % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3465) all_54_15 = e0 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3465) imply: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3466) all_4_2 = e0 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3466) implies: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3467) all_4_2 = e0 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3369), (3467) imply: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3468) ~ (e3 = e0) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2992), (3467) imply: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3469) ~ (e2 = e0) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (3467) imply: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3470) ~ (e1 = e0) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3467) imply: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3471) op(e0, e0) = e0 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (210), (227), (228), % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2987), (3284), (3346), (3457), (3458), (3463), % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3471), (function-axioms) are inconsistent by % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #300. % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3472) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3472) gives: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3473) all_57_4 = e2 & op(e3, e1) = e2 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3376), (3473) are inconsistent by sub-proof % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #689. % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3474) all_57_9 = e2 & op(e3, e0) = e2 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3474) implies: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3475) all_57_9 = e2 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3353), (3475) imply: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3476) e3 = e2 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (3476) imply: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3477) $false % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3477) is inconsistent. % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | (3478) all_54_1 = e1 | all_54_1 = e0 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3336), (3358), (3366), (3478) are inconsistent by % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #306. % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | (3479) all_57_9 = e0 & op(e3, e0) = e0 % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3353), (3479) are inconsistent by sub-proof % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | #299. % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | Case 2: % 132.91/18.95 | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | (3480) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & % 132.91/18.95 | | | | | | | | | | | | | | $i(all_22_1) % 132.91/18.95 | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | REF_CLOSE: (3334), (3480), (function-axioms) are inconsistent % 132.91/18.95 | | | | | | | | | | | | | | by sub-proof #305. % 132.91/18.95 | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | End of split % 132.91/18.95 | | | | | | | | | | % 132.91/18.95 | | | | | | | | | Case 2: % 132.91/18.95 | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | (3481) all_20_2 = e2 % 132.91/18.95 | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | COMBINE_EQS: (318), (3481) imply: % 132.91/18.95 | | | | | | | | | | (3482) all_4_2 = e2 % 132.91/18.95 | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | SIMP: (3482) implies: % 132.91/18.95 | | | | | | | | | | (3483) all_4_2 = e2 % 132.91/18.95 | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | COMBINE_EQS: (331), (3483) imply: % 132.91/18.95 | | | | | | | | | | (3484) all_26_2 = e2 % 132.91/18.95 | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | REDUCE: (367), (3483) imply: % 132.91/18.95 | | | | | | | | | | (3485) ~ (all_52_11 = e2) % 132.91/18.95 | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | REDUCE: (368), (3483) imply: % 132.91/18.95 | | | | | | | | | | (3486) ~ (all_52_12 = e2) % 132.91/18.95 | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | REDUCE: (369), (3483) imply: % 132.91/18.95 | | | | | | | | | | (3487) ~ (all_52_13 = e2) % 132.91/18.95 | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | REDUCE: (370), (3483) imply: % 132.91/18.95 | | | | | | | | | | (3488) ~ (all_52_14 = e2) % 132.91/18.95 | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | REDUCE: (36), (3483) imply: % 132.91/18.95 | | | | | | | | | | (3489) op(e0, e0) = e2 % 132.91/18.95 | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | BETA: splitting (70) gives: % 132.91/18.95 | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | Case 1: % 132.91/18.95 | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | (3490) ~ (all_26_2 = e2) % 132.91/18.95 | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | REDUCE: (3484), (3490) imply: % 132.91/18.95 | | | | | | | | | | | (3491) $false % 132.91/18.95 | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | CLOSE: (3491) is inconsistent. % 132.91/18.95 | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | Case 2: % 132.91/18.95 | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | (3492) ( ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 & % 132.91/18.95 | | | | | | | | | | | $i(all_26_0)) | ( ~ (all_26_1 = e3) & op(e2, e2) % 132.91/18.95 | | | | | | | | | | | = all_26_1 & $i(all_26_1)) % 132.91/18.95 | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | BETA: splitting (3492) gives: % 132.91/18.95 | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | Case 1: % 132.91/18.95 | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | (3493) ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 & % 132.91/18.95 | | | | | | | | | | | | $i(all_26_0) % 132.91/18.95 | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | ALPHA: (3493) implies: % 132.91/18.95 | | | | | | | | | | | | (3494) ~ (all_26_0 = e1) % 132.91/18.95 | | | | | | | | | | | | (3495) op(e2, e0) = all_26_0 % 132.91/18.95 | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 132.91/18.95 | | | | | | | | | | | | all_26_0, e0, e2, simplifying with (164), (3495) % 132.91/18.95 | | | | | | | | | | | | gives: % 132.91/18.95 | | | | | | | | | | | | (3496) all_52_13 = all_26_0 % 132.91/18.95 | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | COMBINE_EQS: (259), (3496) imply: % 132.91/18.95 | | | | | | | | | | | | (3497) all_54_7 = all_26_0 % 132.91/18.95 | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | REDUCE: (113), (3496) imply: % 132.91/18.95 | | | | | | | | | | | | (3498) ~ (all_52_12 = all_26_0) % 132.91/18.95 | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | REDUCE: (110), (3496) imply: % 132.91/18.95 | | | | | | | | | | | | (3499) ~ (all_52_14 = all_26_0) % 132.91/18.95 | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | SIMP: (3499) implies: % 132.91/18.95 | | | | | | | | | | | | (3500) ~ (all_52_14 = all_26_0) % 132.91/18.95 | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | REDUCE: (2982), (3496) imply: % 132.91/18.95 | | | | | | | | | | | | (3501) ~ (all_26_0 = e3) % 132.91/18.95 | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | REDUCE: (3487), (3496) imply: % 132.91/18.95 | | | | | | | | | | | | (3502) ~ (all_26_0 = e2) % 132.91/18.95 | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | BETA: splitting (197) gives: % 132.91/18.95 | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | Case 1: % 132.91/18.95 | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | (3503) all_54_7 = e3 % 132.91/18.95 | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | COMBINE_EQS: (3497), (3503) imply: % 132.91/18.95 | | | | | | | | | | | | | (3504) all_26_0 = e3 % 132.91/18.95 | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | REDUCE: (3501), (3504) imply: % 132.91/18.95 | | | | | | | | | | | | | (3505) $false % 132.91/18.95 | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | CLOSE: (3505) is inconsistent. % 132.91/18.95 | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | Case 2: % 132.91/18.95 | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | (3506) ~ (all_54_7 = e3) % 132.91/18.95 | | | | | | | | | | | | | (3507) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 132.91/18.95 | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | BETA: splitting (3507) gives: % 132.91/18.95 | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | Case 1: % 132.91/18.95 | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | (3508) all_54_7 = e2 % 132.91/18.95 | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | COMBINE_EQS: (3497), (3508) imply: % 132.91/18.95 | | | | | | | | | | | | | | (3509) all_26_0 = e2 % 132.91/18.95 | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | REDUCE: (3502), (3509) imply: % 132.91/18.95 | | | | | | | | | | | | | | (3510) $false % 132.91/18.95 | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | CLOSE: (3510) is inconsistent. % 132.91/18.95 | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | Case 2: % 132.91/18.95 | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | (3511) ~ (all_54_7 = e2) % 132.91/18.95 | | | | | | | | | | | | | | (3512) all_54_7 = e1 | all_54_7 = e0 % 132.91/18.95 | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | BETA: splitting (3512) gives: % 132.91/18.95 | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | Case 1: % 132.91/18.95 | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | (3513) all_54_7 = e1 % 132.91/18.95 | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | COMBINE_EQS: (3497), (3513) imply: % 132.91/18.95 | | | | | | | | | | | | | | | (3514) all_26_0 = e1 % 132.91/18.95 | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | REDUCE: (3494), (3514) imply: % 132.91/18.95 | | | | | | | | | | | | | | | (3515) $false % 132.91/18.95 | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | CLOSE: (3515) is inconsistent. % 132.91/18.95 | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | Case 2: % 132.91/18.95 | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | (3516) all_54_7 = e0 % 132.91/18.95 | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | COMBINE_EQS: (3497), (3516) imply: % 132.91/18.95 | | | | | | | | | | | | | | | (3517) all_26_0 = e0 % 132.91/18.95 | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | REDUCE: (3498), (3517) imply: % 132.91/18.95 | | | | | | | | | | | | | | | (3518) ~ (all_52_12 = e0) % 132.91/18.95 | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | REDUCE: (3500), (3517) imply: % 132.91/18.95 | | | | | | | | | | | | | | | (3519) ~ (all_52_14 = e0) % 132.91/18.95 | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | REDUCE: (3501), (3517) imply: % 132.91/18.95 | | | | | | | | | | | | | | | (3520) ~ (e3 = e0) % 132.91/18.95 | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | REDUCE: (3502), (3517) imply: % 132.91/18.95 | | | | | | | | | | | | | | | (3521) ~ (e2 = e0) % 132.91/18.95 | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | REDUCE: (3494), (3517) imply: % 132.91/18.95 | | | | | | | | | | | | | | | (3522) ~ (e1 = e0) % 132.91/18.95 | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | REDUCE: (3495), (3517) imply: % 132.91/18.95 | | | | | | | | | | | | | | | (3523) op(e2, e0) = e0 % 132.91/18.95 | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 132.91/18.95 | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | Case 1: % 132.91/18.95 | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | (3524) all_57_15 = e0 & op(e0, e0) = e0 % 132.91/18.95 | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | ALPHA: (3524) implies: % 132.91/18.95 | | | | | | | | | | | | | | | | (3525) op(e0, e0) = e0 % 132.91/18.95 | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3489), (3525), (function-axioms) are % 132.91/18.95 | | | | | | | | | | | | | | | | inconsistent by sub-proof #714. % 132.91/18.95 | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | Case 2: % 132.91/18.95 | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | (3526) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 132.91/18.95 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 132.91/18.95 | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 132.91/18.95 | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 132.91/18.95 | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 132.91/18.95 | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | ALPHA: (3526) implies: % 132.91/18.95 | | | | | | | | | | | | | | | | (3527) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 132.91/18.95 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, % 132.91/18.95 | | | | | | | | | | | | | | | | e0) = e0) % 132.91/18.95 | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | BETA: splitting (3527) gives: % 132.91/18.95 | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | Case 1: % 132.91/18.95 | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | (3528) all_57_9 = e0 & op(e3, e0) = e0 % 132.91/18.95 | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | ALPHA: (3528) implies: % 132.91/18.95 | | | | | | | | | | | | | | | | | (3529) all_57_9 = e0 % 132.91/18.95 | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (208), (212), % 132.91/18.95 | | | | | | | | | | | | | | | | | (214), (223), (224), (225), (2982), (2987), % 132.91/18.95 | | | | | | | | | | | | | | | | | (2988), (3489), (3523), (3529), (function-axioms) % 132.91/18.95 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #291. % 132.91/18.95 | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | Case 2: % 132.91/18.95 | | | | | | | | | | | | | | | | | % 132.91/18.95 | | | | | | | | | | | | | | | | | (3530) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = % 132.91/18.95 | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 132.91/18.95 | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | BETA: splitting (3530) gives: % 132.91/18.96 | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.96 | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | (3531) all_57_10 = e0 & op(e2, e0) = e0 % 132.91/18.96 | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | ALPHA: (3531) implies: % 132.91/18.96 | | | | | | | | | | | | | | | | | | (3532) all_57_10 = e0 % 132.91/18.96 | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives: % 132.91/18.96 | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | (3533) ~ (all_22_2 = e3) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | REDUCE: (2976), (3533) imply: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | (3534) $false % 132.91/18.96 | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | CLOSE: (3534) is inconsistent. % 132.91/18.96 | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | (3535) ( ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | $i(all_22_0)) | ( ~ (all_22_1 = e1) & op(e3, e3) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | = all_22_1 & $i(all_22_1)) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3536) ~ (all_28_2 = e3) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | REDUCE: (316), (3536) imply: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3537) ~ (all_6_2 = e3) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3538) ~ (all_32_2 = e1) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | REDUCE: (312), (3538) imply: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3539) ~ (all_10_2 = e1) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | (3540) all_54_0 = e3 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (3540) imply: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | (3541) all_10_2 = e3 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (3541) imply: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | (3542) ~ (all_52_12 = e3) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (3541) imply: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | (3543) op(e3, e3) = e3 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3544) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3544) gives: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (3545) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3545) gives: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (3546) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3546) implies: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (3547) op(e3, e3) = e2 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (91), (118), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (145), (146), (149), (157), (158), (163), (164), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (165), (167), (170), (190), (197), (200), (206), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (208), (209), (210), (211), (212), (214), (217), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (221), (223), (224), (225), (227), (228), (231), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (232), (233), (234), (237), (238), (246), (259), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (268), (332), (362), (364), (372), (2977), (2978), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (2980), (2981), (2982), (2987), (2988), (3487), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (3489), (3494), (3495), (3547), (function-axioms) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #267. % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (3548) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3548) implies: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | (3549) op(e3, e3) = e1 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3543), (3549), (function-axioms) are % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #775. % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (3550) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (3542), (3543), (3550), (function-axioms) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #553. % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3551) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3551) gives: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (3552) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (2988), (3537), (3552), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | #324. % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (3553) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (39), (91), (157), (190), (246), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (332), (364), (372), (2988), (3485), (3489), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | (3523), (3553), (function-axioms) are inconsistent % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #265. % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | (3554) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (374), (2990), (3539), (3554) are % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #777. % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3555) all_32_2 = e1 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (312), (3555) imply: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3556) all_10_2 = e1 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | SIMP: (3556) implies: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3557) all_10_2 = e1 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | REDUCE: (338), (3557) imply: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3558) ~ (all_52_2 = e1) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (3557) imply: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3559) ~ (all_52_12 = e1) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2990), (3557) imply: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3560) ~ (e2 = e1) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (39), (45), (91), (118), (120), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (133), (145), (146), (149), (157), (158), (163), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (164), (165), (167), (169), (170), (190), (197), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (200), (201), (204), (206), (208), (209), (210), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (211), (212), (214), (217), (221), (223), (224), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (225), (227), (228), (231), (232), (233), (234), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (237), (238), (246), (259), (268), (269), (278), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (332), (346), (362), (364), (372), (374), (2977), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (2980), (2981), (2982), (2987), (2988), (2990), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3485), (3486), (3487), (3489), (3494), (3495), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3518), (3523), (3532), (3535), (3558), (3559), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | #261. % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3561) all_28_2 = e3 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (3561) imply: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3562) all_6_2 = e3 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | SIMP: (3562) implies: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3563) all_6_2 = e3 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (3563) imply: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3564) ~ (all_52_14 = e3) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3565) all_54_11 = e3 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (3564), (3565) are inconsistent by % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | sub-proof #260. % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | (3566) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3566) gives: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | (3567) all_54_11 = e2 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (3488), (3567) are inconsistent by % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | sub-proof #259. % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | (3568) ~ (all_54_11 = e2) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | (3569) all_54_11 = e1 | all_54_11 = e0 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3569) gives: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3570) all_54_11 = e1 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (3570) imply: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3571) all_52_14 = e1 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3571) implies: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3572) all_52_14 = e1 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (3572) imply: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3573) ~ (all_52_2 = e1) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (3572) imply: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3574) ~ (all_52_12 = e1) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3488), (3572) imply: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3575) ~ (e2 = e1) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (39), (45), (91), (118), (120), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (133), (145), (146), (149), (157), (158), (163), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (164), (165), (167), (169), (170), (190), (197), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (200), (201), (204), (206), (208), (209), (210), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (211), (212), (214), (217), (221), (223), (224), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (225), (227), (228), (231), (232), (233), (234), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (237), (238), (246), (259), (268), (269), (278), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (332), (346), (362), (364), (372), (374), (2977), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (2980), (2981), (2982), (2987), (2988), (2990), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3485), (3486), (3487), (3489), (3494), (3495), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3518), (3523), (3532), (3535), (3573), (3574), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | #261. % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | (3576) all_54_11 = e0 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (3519), (3576) are inconsistent by % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #258. % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.96 | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | (3577) all_57_11 = e0 & op(e1, e0) = e0 % 132.91/18.96 | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | ALPHA: (3577) implies: % 132.91/18.96 | | | | | | | | | | | | | | | | | | (3578) all_57_11 = e0 % 132.91/18.96 | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 132.91/18.96 | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | (3579) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | BETA: splitting (3579) gives: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3580) all_57_9 = e3 & op(e3, e0) = e3 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | ALPHA: (3580) implies: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3581) all_57_9 = e3 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (212), (3489), (3523), (3578), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3581), (function-axioms) are inconsistent by % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | sub-proof #257. % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | (3582) all_57_10 = e3 & op(e2, e0) = e3 % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2982), (3582), (function-axioms) are % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749. % 132.91/18.96 | | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.96 | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | (3583) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 132.91/18.96 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 132.91/18.96 | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (3489), (3578), (3583), % 132.91/18.96 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/18.96 | | | | | | | | | | | | | | | | | | | #255. % 132.91/18.96 | | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | Case 2: % 132.91/18.96 | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | (3584) ~ (all_26_1 = e3) & op(e2, e2) = all_26_1 & % 132.91/18.96 | | | | | | | | | | | | $i(all_26_1) % 132.91/18.96 | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | ALPHA: (3584) implies: % 132.91/18.96 | | | | | | | | | | | | (3585) ~ (all_26_1 = e3) % 132.91/18.96 | | | | | | | | | | | | (3586) op(e2, e2) = all_26_1 % 132.91/18.96 | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | | REF_CLOSE: (2988), (3585), (3586), (function-axioms) are % 132.91/18.96 | | | | | | | | | | | | inconsistent by sub-proof #334. % 132.91/18.96 | | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | | % 132.91/18.96 | | | | | | | | | End of split % 132.91/18.96 | | | | | | | | | % 132.91/18.96 | | | | | | | | Case 2: % 132.91/18.96 | | | | | | | | | % 132.91/18.96 | | | | | | | | | (3587) all_16_2 = e2 % 132.91/18.96 | | | | | | | | | % 132.91/18.96 | | | | | | | | | COMBINE_EQS: (327), (3587) imply: % 132.91/18.96 | | | | | | | | | (3588) all_10_2 = e2 % 132.91/18.96 | | | | | | | | | % 132.91/18.96 | | | | | | | | | REDUCE: (336), (3588) imply: % 132.91/18.96 | | | | | | | | | (3589) ~ (all_52_1 = e2) % 132.91/18.96 | | | | | | | | | % 132.91/18.96 | | | | | | | | | REDUCE: (342), (3588) imply: % 132.91/18.96 | | | | | | | | | (3590) ~ (all_52_4 = e2) % 132.91/18.96 | | | | | | | | | % 132.91/18.96 | | | | | | | | | REDUCE: (344), (3588) imply: % 132.91/18.96 | | | | | | | | | (3591) ~ (all_52_8 = e2) % 132.91/18.96 | | | | | | | | | % 132.91/18.96 | | | | | | | | | REDUCE: (346), (3588) imply: % 132.91/18.96 | | | | | | | | | (3592) ~ (all_52_12 = e2) % 132.91/18.96 | | | | | | | | | % 132.91/18.96 | | | | | | | | | REDUCE: (45), (3588) imply: % 132.91/18.96 | | | | | | | | | (3593) op(e3, e3) = e2 % 132.91/18.96 | | | | | | | | | % 132.91/18.96 | | | | | | | | | BETA: splitting (61) gives: % 132.91/18.96 | | | | | | | | | % 132.91/18.96 | | | | | | | | | Case 1: % 132.91/18.96 | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | (3594) ~ (all_20_2 = e2) % 132.91/18.96 | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | REDUCE: (318), (3594) imply: % 132.91/18.96 | | | | | | | | | | (3595) ~ (all_4_2 = e2) % 132.91/18.96 | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | BETA: splitting (73) gives: % 132.91/18.96 | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | Case 1: % 132.91/18.96 | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | (3596) ~ (all_28_2 = e3) % 132.91/18.96 | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | REDUCE: (316), (3596) imply: % 132.91/18.96 | | | | | | | | | | | (3597) ~ (all_6_2 = e3) % 132.91/18.96 | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | BETA: splitting (206) gives: % 132.91/18.96 | | | | | | | | | | | % 132.91/18.96 | | | | | | | | | | | Case 1: % 132.91/18.96 | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | (3598) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.91/18.97 | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.91/18.97 | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.91/18.97 | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.91/18.97 | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.91/18.97 | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.91/18.97 | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.91/18.97 | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.91/18.97 | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.91/18.97 | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.91/18.97 | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.91/18.97 | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/18.97 | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.91/18.97 | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 132.91/18.97 | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.91/18.97 | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.91/18.97 | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.91/18.97 | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.91/18.97 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.97 | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.91/18.97 | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.91/18.97 | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.91/18.97 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/18.97 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.97 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.97 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.91/18.97 | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.97 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.91/18.97 | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | BETA: splitting (3598) gives: % 132.91/18.97 | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | Case 1: % 132.91/18.97 | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | (3599) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.91/18.97 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.91/18.97 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.91/18.97 | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.91/18.97 | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.91/18.97 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.91/18.97 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.91/18.97 | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.91/18.97 | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.91/18.97 | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.91/18.97 | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.91/18.97 | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/18.97 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.91/18.97 | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 132.91/18.97 | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | REF_CLOSE: (6), (170), (2978), (3593), (3599), % 132.91/18.97 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/18.97 | | | | | | | | | | | | | #254. % 132.91/18.97 | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | Case 2: % 132.91/18.97 | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | (3600) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.91/18.97 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.91/18.97 | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.91/18.97 | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.91/18.97 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.97 | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.91/18.97 | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.91/18.97 | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.91/18.97 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/18.97 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.97 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.97 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.91/18.97 | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.97 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.91/18.97 | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | BETA: splitting (3600) gives: % 132.91/18.97 | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | Case 1: % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | (3601) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.91/18.97 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.91/18.97 | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 132.91/18.97 | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.91/18.97 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.91/18.97 | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | ALPHA: (3601) implies: % 132.91/18.97 | | | | | | | | | | | | | | (3602) op(e3, e3) = e0 % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | REF_CLOSE: (5), (3593), (3602), (function-axioms) are % 132.91/18.97 | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | Case 2: % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | (3603) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.91/18.97 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 132.91/18.97 | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.97 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.97 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 132.91/18.97 | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | ALPHA: (3603) implies: % 132.91/18.97 | | | | | | | | | | | | | | (3604) op(e2, e3) = e2 % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2, % 132.91/18.97 | | | | | | | | | | | | | | e3, e2, simplifying with (167), (3604) gives: % 132.91/18.97 | | | | | | | | | | | | | | (3605) all_52_1 = e2 % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | REDUCE: (3589), (3605) imply: % 132.91/18.97 | | | | | | | | | | | | | | (3606) $false % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | CLOSE: (3606) is inconsistent. % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | End of split % 132.91/18.97 | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | End of split % 132.91/18.97 | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | Case 2: % 132.91/18.97 | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | (3607) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.91/18.97 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/18.97 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.97 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.97 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.91/18.97 | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.97 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.91/18.97 | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.91/18.97 | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.91/18.97 | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.91/18.97 | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.91/18.97 | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.91/18.97 | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.91/18.97 | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 132.91/18.97 | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 132.91/18.97 | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.91/18.97 | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 132.91/18.97 | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.91/18.97 | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 132.91/18.97 | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.91/18.97 | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 132.91/18.97 | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 132.91/18.97 | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.91/18.97 | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.91/18.97 | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 132.91/18.97 | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 132.91/18.97 | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.91/18.97 | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 132.91/18.97 | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 132.91/18.97 | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 132.91/18.97 | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 132.91/18.97 | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.97 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 132.91/18.97 | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.91/18.97 | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.97 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 132.91/18.97 | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 132.91/18.97 | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 132.91/18.97 | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.91/18.97 | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.91/18.97 | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.91/18.97 | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.91/18.97 | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 132.91/18.97 | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 132.91/18.97 | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 132.91/18.97 | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.91/18.97 | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 132.91/18.97 | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 132.91/18.97 | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 132.91/18.97 | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.91/18.97 | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.91/18.97 | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.91/18.97 | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.91/18.97 | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/18.97 | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.91/18.97 | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.91/18.97 | | | | | | | | | | | | & $i(all_56_29)))) % 132.91/18.97 | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | BETA: splitting (3607) gives: % 132.91/18.97 | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | Case 1: % 132.91/18.97 | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | (3608) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.91/18.97 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/18.97 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.97 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.97 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.91/18.97 | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.97 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.91/18.97 | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.91/18.97 | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.91/18.97 | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.91/18.97 | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.91/18.97 | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.91/18.97 | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.91/18.97 | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.91/18.97 | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | REF_CLOSE: (8), (39), (2988), (3597), (3608), % 132.91/18.97 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/18.97 | | | | | | | | | | | | | #324. % 132.91/18.97 | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | Case 2: % 132.91/18.97 | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | (3609) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.91/18.97 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.91/18.97 | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 132.91/18.97 | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 132.91/18.97 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.97 | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.91/18.97 | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.91/18.97 | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.91/18.97 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.91/18.97 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.91/18.97 | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.91/18.97 | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.91/18.97 | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.91/18.97 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.91/18.97 | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.91/18.97 | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.91/18.97 | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.91/18.97 | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.91/18.97 | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.91/18.97 | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.91/18.97 | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.91/18.97 | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.91/18.97 | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.91/18.97 | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.91/18.97 | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.91/18.97 | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.91/18.97 | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.91/18.97 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.91/18.97 | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.91/18.97 | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.91/18.97 | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.91/18.97 | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.91/18.97 | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.91/18.97 | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.91/18.97 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.97 | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.91/18.97 | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.91/18.97 | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.91/18.97 | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.91/18.97 | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.91/18.97 | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/18.97 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.91/18.97 | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.91/18.97 | | | | | | | | | | | | | & $i(all_56_29)))) % 132.91/18.97 | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | BETA: splitting (3609) gives: % 132.91/18.97 | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | Case 1: % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | (3610) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.91/18.97 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.91/18.97 | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 132.91/18.97 | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.91/18.97 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.91/18.97 | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | ALPHA: (3610) implies: % 132.91/18.97 | | | | | | | | | | | | | | (3611) op(e2, e2) = e0 % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e0, e2, % 132.91/18.97 | | | | | | | | | | | | | | e2, simplifying with (2988), (3611) gives: % 132.91/18.97 | | | | | | | | | | | | | | (3612) e3 = e0 % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | REDUCE: (7), (3612) imply: % 132.91/18.97 | | | | | | | | | | | | | | (3613) $false % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | CLOSE: (3613) is inconsistent. % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | Case 2: % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | (3614) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.91/18.97 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.91/18.97 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.91/18.97 | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.91/18.97 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.91/18.97 | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.91/18.97 | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.91/18.97 | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.91/18.97 | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.91/18.97 | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.91/18.97 | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.91/18.97 | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.91/18.97 | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.91/18.97 | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.91/18.97 | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.91/18.97 | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.91/18.97 | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.91/18.97 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.91/18.97 | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.91/18.97 | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.91/18.97 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.91/18.97 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.91/18.97 | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.91/18.97 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.91/18.97 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.91/18.97 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.91/18.97 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.91/18.97 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/18.97 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.91/18.97 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.91/18.97 | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | BETA: splitting (3614) gives: % 132.91/18.97 | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | Case 1: % 132.91/18.97 | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | (3615) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.91/18.97 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 132.91/18.97 | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.91/18.97 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.91/18.97 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 132.91/18.97 | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 132.91/18.97 | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | ALPHA: (3615) implies: % 132.91/18.97 | | | | | | | | | | | | | | | (3616) op(e1, e1) = e2 % 132.91/18.97 | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3616), (function-axioms) are % 132.91/18.97 | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.91/18.97 | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | Case 2: % 132.91/18.97 | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | (3617) op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.91/18.97 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.91/18.97 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 132.91/18.97 | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.91/18.97 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 132.91/18.97 | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.91/18.97 | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 132.91/18.97 | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 132.91/18.97 | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.91/18.97 | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.91/18.97 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.91/18.97 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.91/18.97 | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.91/18.97 | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.91/18.97 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.91/18.97 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.91/18.97 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.91/18.97 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 132.91/18.97 | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 132.91/18.97 | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 132.91/18.97 | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 132.91/18.97 | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 132.91/18.97 | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.91/18.97 | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_29))) % 132.91/18.97 | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | ALPHA: (3617) implies: % 132.91/18.97 | | | | | | | | | | | | | | | (3618) op(e0, e0) = all_56_31 % 132.91/18.97 | | | | | | | | | | | | | | | (3619) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.91/18.97 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/18.97 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.97 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.97 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 132.91/18.97 | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 132.91/18.97 | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 132.91/18.97 | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 132.91/18.97 | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 132.91/18.97 | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 132.91/18.97 | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.91/18.97 | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.91/18.97 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.91/18.97 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 132.91/18.97 | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.91/18.97 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 132.91/18.97 | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.91/18.97 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.91/18.97 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 132.91/18.97 | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 132.91/18.97 | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 132.91/18.97 | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 132.91/18.97 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.91/18.97 | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 132.91/18.97 | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (36), (3618) % 132.91/18.97 | | | | | | | | | | | | | | | gives: % 132.91/18.97 | | | | | | | | | | | | | | | (3620) all_56_31 = all_4_2 % 132.91/18.97 | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 132.91/18.97 | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | Case 1: % 132.91/18.97 | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | (3621) ~ (all_34_2 = e3) % 132.91/18.97 | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | REDUCE: (307), (3621) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | (3622) ~ (all_4_2 = e3) % 132.91/18.97 | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | REF_CLOSE: (189), (245), (371), (3595), (3619), (3620), % 132.91/18.97 | | | | | | | | | | | | | | | | (3622) are inconsistent by sub-proof #322. % 132.91/18.97 | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | Case 2: % 132.91/18.97 | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | (3623) all_34_2 = e3 % 132.91/18.97 | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (3623) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | (3624) all_4_2 = e3 % 132.91/18.97 | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | SIMP: (3624) implies: % 132.91/18.97 | | | | | | | | | | | | | | | | (3625) all_4_2 = e3 % 132.91/18.97 | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (3625) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | (3626) all_44_2 = e3 % 132.91/18.97 | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | COMBINE_EQS: (3620), (3625) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | (3627) all_56_31 = e3 % 132.91/18.97 | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | REDUCE: (368), (3625) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | (3628) ~ (all_52_12 = e3) % 132.91/18.97 | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | REDUCE: (36), (3625) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | (3629) op(e0, e0) = e3 % 132.91/18.97 | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | BETA: splitting (97) gives: % 132.91/18.97 | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | Case 1: % 132.91/18.97 | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | (3630) ~ (all_44_2 = e3) % 132.91/18.97 | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | REDUCE: (3626), (3630) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | (3631) $false % 132.91/18.97 | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | CLOSE: (3631) is inconsistent. % 132.91/18.97 | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | Case 2: % 132.91/18.97 | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | (3632) ( ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 & % 132.91/18.97 | | | | | | | | | | | | | | | | | $i(all_44_0)) | ( ~ (all_44_1 = e2) & op(e3, e3) % 132.91/18.97 | | | | | | | | | | | | | | | | | = all_44_1 & $i(all_44_1)) % 132.91/18.97 | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | BETA: splitting (3632) gives: % 132.91/18.97 | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.97 | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | (3633) ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 & % 132.91/18.97 | | | | | | | | | | | | | | | | | | $i(all_44_0) % 132.91/18.97 | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | ALPHA: (3633) implies: % 132.91/18.97 | | | | | | | | | | | | | | | | | | (3634) ~ (all_44_0 = e1) % 132.91/18.97 | | | | | | | | | | | | | | | | | | (3635) op(e3, e0) = all_44_0 % 132.91/18.97 | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 132.91/18.97 | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | (3636) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 132.91/18.97 | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | BETA: splitting (3636) gives: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3637) all_57_4 = e3 & op(e3, e1) = e3 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | ALPHA: (3637) implies: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3638) all_57_4 = e3 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3639) op(e3, e1) = e3 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | all_44_0, e0, e3, simplifying with (168), (3635) % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | gives: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3640) all_52_12 = all_44_0 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3, % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (3639) gives: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3641) all_52_8 = e3 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (3640) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3642) all_54_3 = all_44_0 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (3640) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3643) ~ (all_52_4 = all_44_0) % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (3641) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3644) ~ (all_52_11 = e3) % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | SIMP: (3644) implies: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3645) ~ (all_52_11 = e3) % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | REDUCE: (3628), (3640) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3646) ~ (all_44_0 = e3) % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | REDUCE: (3592), (3640) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | (3647) ~ (all_44_0 = e2) % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | (3648) all_54_3 = e3 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3642), (3648) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | (3649) all_44_0 = e3 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3646), (3649) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | (3650) $false % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | CLOSE: (3650) is inconsistent. % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | (3651) ~ (all_54_3 = e3) % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | (3652) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3652) gives: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | (3653) all_54_3 = e2 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3642), (3653) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | (3654) all_44_0 = e2 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3647), (3654) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | (3655) $false % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3655) is inconsistent. % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | (3656) ~ (all_54_3 = e2) % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | (3657) all_54_3 = e1 | all_54_3 = e0 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3657) gives: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3658) all_54_3 = e1 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3642), (3658) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3659) all_44_0 = e1 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3634), (3659) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3660) $false % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3660) is inconsistent. % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3661) all_54_3 = e0 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3642), (3661) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3662) all_44_0 = e0 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3643), (3662) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3663) ~ (all_52_4 = e0) % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3646), (3662) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3664) ~ (e3 = e0) % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3647), (3662) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3665) ~ (e2 = e0) % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3634), (3662) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3666) ~ (e1 = e0) % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3635), (3662) imply: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | (3667) op(e3, e0) = e0 % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3619) gives: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.97 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3668) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3668) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3669) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3669) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3670) ~ (all_56_25 = e0) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3671) op(e3, e0) = all_56_25 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3667), (3670), (3671), (function-axioms) are % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #642. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3672) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3672) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3673) all_56_31 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3627), (3673) imply: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3674) e3 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3674) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3675) e3 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3638), (3675) imply: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3676) all_57_4 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (238), (2978), (3593), (3676), (function-axioms) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #278. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3677) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3677) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3678) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3678) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3679) ~ (all_56_23 = e1) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3680) op(e0, e1) = all_56_23 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3681) op(e1, e1) = e0 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3682) all_54_1 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (2978), (3682) are inconsistent by % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #740. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3683) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (100), (157), (190), (246), (271), (295), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (364), (3590), (3629), (3645), (3663), (3679), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3680), (3681), (3683), (function-axioms) are % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #607. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3684) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3684) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3685) all_56_31 = e1 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3627), (3685) are inconsistent by sub-proof % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | #253. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | (3686) all_57_5 = e3 & op(e2, e1) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2981), (3686), (function-axioms) are % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | (3687) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | BETA: splitting (3687) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | (3688) all_57_8 = e3 & op(e1, e1) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | ALPHA: (3688) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | (3689) op(e1, e1) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (3597), (3689), (function-axioms) are % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | (3690) all_57_14 = e3 & op(e0, e1) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | ALPHA: (3690) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | (3691) all_57_14 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | (3692) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3692) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | (3693) all_57_12 = e2 & op(e0, e3) = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3693) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | (3694) all_57_12 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | (3593), (3694), (function-axioms) are inconsistent % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #290. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | (3695) all_57_13 = e2 & op(e0, e2) = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3695) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | (3696) all_57_13 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | (3697) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3697) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3698) all_57_0 = e3 & op(e3, e3) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3698) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3699) op(e3, e3) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3593), (3699), (function-axioms) are % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #778. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3700) all_57_2 = e3 & op(e2, e3) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3700) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3701) all_57_2 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3702) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (2978), (3593), (3702), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | #282. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3703) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3703) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3704) all_57_4 = e3 & op(e3, e1) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (170), (219), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (221), (232), (234), (238), (372), (2978), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3593), (3691), (3704), (function-axioms) are % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #251. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3705) all_57_9 = e3 & op(e3, e0) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3705) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3706) all_57_9 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3707) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3707) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3708) all_57_4 = e2 & op(e3, e1) = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3708) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3709) all_57_4 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (232), (234), (3593), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3706), (3709), (function-axioms) are inconsistent % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #279. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3710) all_57_5 = e2 & op(e2, e1) = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3710) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3711) all_57_5 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (223), (224), (2987), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3701), (3711) are inconsistent by sub-proof #368. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3712) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (158), (170), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (208), (209), (211), (232), (234), (238), (372), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2978), (2980), (3593), (3696), (3706), (3712), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | #249. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | (3713) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3713) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3714) all_57_6 = e3 & op(e1, e3) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3714) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3715) all_57_6 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3716) all_57_15 = e0 & op(e0, e0) = e0 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3716) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3717) op(e0, e0) = e0 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3629), (3717), (function-axioms) are % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #715. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3718) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3718) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3719) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3720) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (2978), (3593), (3720), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | #282. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3721) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3721) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3722) all_57_4 = e3 & op(e3, e1) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (170), (219), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (221), (232), (234), (238), (372), (2978), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3593), (3691), (3722), (function-axioms) are % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #251. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3723) all_57_9 = e3 & op(e3, e0) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3723) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3724) all_57_9 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (158), (170), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (208), (209), (211), (213), (221), (223), (224), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (233), (234), (237), (238), (372), (2978), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2980), (2987), (2988), (3593), (3629), (3691), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3696), (3715), (3719), (3724), (function-axioms) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #246. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3725) all_57_12 = e3 & op(e0, e3) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3725) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | (3726) all_57_12 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3727) all_57_15 = e0 & op(e0, e0) = e0 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3727) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3728) all_57_15 = e0 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3729) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (3696), (3726), (3729) are inconsistent % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #245. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3730) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3730) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3731) all_57_14 = e1 & op(e0, e1) = e1 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3731) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3732) all_57_14 = e1 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3691), (3732) are inconsistent by sub-proof % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | #561. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3733) all_57_15 = e1 & op(e0, e0) = e1 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3733) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3734) all_57_15 = e1 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3728), (3734) imply: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3735) e1 = e0 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (3735) imply: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3736) $false % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3736) is inconsistent. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3737) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3737) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | (3738) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3739) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (2978), (3593), (3739), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | #282. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (3740) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3740) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3741) all_57_4 = e3 & op(e3, e1) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (170), (219), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (221), (232), (234), (238), (372), (2978), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3593), (3691), (3741), (function-axioms) are % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #251. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3742) all_57_9 = e3 & op(e3, e0) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3742) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3743) all_57_9 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3744) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3744) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3745) all_57_6 = e3 & op(e1, e3) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3745) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3746) all_57_6 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (158), (170), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208), (209), (211), (213), (221), (223), (224), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (233), (234), (237), (238), (372), (2978), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2980), (2987), (2988), (3593), (3629), (3691), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3696), (3738), (3743), (3746), (function-axioms) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #246. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3747) all_57_7 = e3 & op(e1, e2) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3747) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3748) op(e1, e2) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2979), (3748), (function-axioms) are % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3749) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3749) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3750) all_57_8 = e3 & op(e1, e1) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3750) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3751) op(e1, e1) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (3597), (3751), (function-axioms) are % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3752) all_57_11 = e3 & op(e1, e0) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3752) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3753) all_57_11 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3754) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3754) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3755) all_57_4 = e2 & op(e3, e1) = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3755) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3756) all_57_4 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3757) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (2978), (3593), (3757), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #282. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3740) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3758) all_57_4 = e3 & op(e3, e1) = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3758) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3759) all_57_4 = e3 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3756), (3759) imply: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3760) e3 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3726), (3760) imply: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3761) all_57_12 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3593), (3761), (function-axioms) are inconsistent % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #290. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (232), (234), (3593), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3743), (3756), (function-axioms) are inconsistent % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #279. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3762) all_57_5 = e2 & op(e2, e1) = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3762) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3763) all_57_5 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3764) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3764) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3765) all_57_6 = e2 & op(e1, e3) = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3765) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3766) all_57_6 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (231), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (237), (2987), (3593), (3763), (3766), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #366. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3767) all_57_7 = e2 & op(e1, e2) = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3767) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3768) all_57_7 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (227), (228), (2987), % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3696), (3768) are inconsistent by sub-proof #287. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3769) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3769) gives: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3770) all_57_8 = e2 & op(e1, e1) = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3770) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3771) op(e1, e1) = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3771), (function-axioms) are % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3772) all_57_11 = e2 & op(e1, e0) = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3772) implies: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3773) all_57_11 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3753), (3773) imply: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3774) e3 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3743), (3774) imply: % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3775) all_57_9 = e2 % 132.91/18.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234), % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (2978), (3593), (3775), (function-axioms) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #250. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3776) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3776) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3777) all_57_8 = e2 & op(e1, e1) = e2 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3777) implies: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3778) op(e1, e1) = e2 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3778), (function-axioms) are % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3779) all_57_14 = e2 & op(e0, e1) = e2 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3779) implies: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3780) all_57_14 = e2 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (3696), (3726), (3738), (3780) are % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #410. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | (3781) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3781) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (3782) all_57_14 = e2 & op(e0, e1) = e2 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3691), (3782) are inconsistent by sub-proof % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | #397. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (3783) all_57_15 = e2 & op(e0, e0) = e2 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3783) implies: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (3784) op(e0, e0) = e2 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3629), (3784), (function-axioms) are % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | (3785) ~ (all_44_1 = e2) & op(e3, e3) = all_44_1 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | $i(all_44_1) % 132.91/18.99 | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | REF_CLOSE: (3593), (3785), (function-axioms) are inconsistent % 132.91/18.99 | | | | | | | | | | | | | | | | | | by sub-proof #431. % 132.91/18.99 | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | (3786) all_28_2 = e3 % 132.91/18.99 | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | COMBINE_EQS: (316), (3786) imply: % 132.91/18.99 | | | | | | | | | | | (3787) all_6_2 = e3 % 132.91/18.99 | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | COMBINE_EQS: (302), (3787) imply: % 132.91/18.99 | | | | | | | | | | | (3788) all_36_2 = e3 % 132.91/18.99 | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | REDUCE: (348), (3787) imply: % 132.91/18.99 | | | | | | | | | | | (3789) ~ (all_52_2 = e3) % 132.91/18.99 | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | REDUCE: (361), (3787) imply: % 132.91/18.99 | | | | | | | | | | | (3790) ~ (all_52_8 = e3) % 132.91/18.99 | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | REDUCE: (39), (3787) imply: % 132.91/18.99 | | | | | | | | | | | (3791) op(e1, e1) = e3 % 132.91/18.99 | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | BETA: splitting (85) gives: % 132.91/18.99 | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | (3792) ~ (all_36_2 = e3) % 132.91/18.99 | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | REDUCE: (3788), (3792) imply: % 132.91/18.99 | | | | | | | | | | | | (3793) $false % 132.91/18.99 | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | CLOSE: (3793) is inconsistent. % 132.91/18.99 | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | (3794) ( ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 & % 132.91/18.99 | | | | | | | | | | | | $i(all_36_0)) | ( ~ (all_36_1 = e2) & op(e3, e3) % 132.91/18.99 | | | | | | | | | | | | = all_36_1 & $i(all_36_1)) % 132.91/18.99 | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | BETA: splitting (3794) gives: % 132.91/18.99 | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | (3795) ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 & % 132.91/18.99 | | | | | | | | | | | | | $i(all_36_0) % 132.91/18.99 | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | ALPHA: (3795) implies: % 132.91/18.99 | | | | | | | | | | | | | (3796) ~ (all_36_0 = e0) % 132.91/18.99 | | | | | | | | | | | | | (3797) op(e3, e1) = all_36_0 % 132.91/18.99 | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | BETA: splitting (237) gives: % 132.91/18.99 | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | (3798) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 132.91/18.99 | | | | | | | | | | | | | | & op(e2, e3) = e3) % 132.91/18.99 | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | BETA: splitting (3798) gives: % 132.91/18.99 | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | (3799) all_57_0 = e3 & op(e3, e3) = e3 % 132.91/18.99 | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | ALPHA: (3799) implies: % 132.91/18.99 | | | | | | | | | | | | | | | (3800) op(e3, e3) = e3 % 132.91/18.99 | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | REF_CLOSE: (9), (3593), (3800), (function-axioms) are % 132.91/18.99 | | | | | | | | | | | | | | | inconsistent by sub-proof #778. % 132.91/18.99 | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | (3801) all_57_2 = e3 & op(e2, e3) = e3 % 132.91/18.99 | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | ALPHA: (3801) implies: % 132.91/18.99 | | | | | | | | | | | | | | | (3802) op(e2, e3) = e3 % 132.91/18.99 | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | REF_CLOSE: (167), (2977), (3802), (function-axioms) are % 132.91/18.99 | | | | | | | | | | | | | | | inconsistent by sub-proof #763. % 132.91/18.99 | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | (3803) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 132.91/18.99 | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 132.91/18.99 | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | BETA: splitting (3803) gives: % 132.91/18.99 | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | (3804) all_57_6 = e3 & op(e1, e3) = e3 % 132.91/18.99 | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | REF_CLOSE: (163), (3789), (3804), (function-axioms) are % 132.91/18.99 | | | | | | | | | | | | | | | inconsistent by sub-proof #761. % 132.91/18.99 | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | (3805) all_57_12 = e3 & op(e0, e3) = e3 % 132.91/18.99 | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | ALPHA: (3805) implies: % 132.91/18.99 | | | | | | | | | | | | | | | (3806) all_57_12 = e3 % 132.91/18.99 | | | | | | | | | | | | | | | (3807) op(e0, e3) = e3 % 132.91/18.99 | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 132.91/18.99 | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | (3808) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 132.91/18.99 | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 132.91/18.99 | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (2978), (3593), (3808), % 132.91/18.99 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/18.99 | | | | | | | | | | | | | | | | #282. % 132.91/18.99 | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | (3809) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 132.91/18.99 | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 132.91/18.99 | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | BETA: splitting (3809) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | (3810) all_57_4 = e3 & op(e3, e1) = e3 % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3790), (3797), (3810), (function-axioms) % 132.91/18.99 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #379. % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | (3811) all_57_9 = e3 & op(e3, e0) = e3 % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | ALPHA: (3811) implies: % 132.91/18.99 | | | | | | | | | | | | | | | | | (3812) all_57_9 = e3 % 132.91/18.99 | | | | | | | | | | | | | | | | | (3813) op(e3, e0) = e3 % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3, % 132.91/18.99 | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (3807) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | (3814) all_52_3 = e3 % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 132.91/18.99 | | | | | | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (3813) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | (3815) all_52_12 = e3 % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 132.91/18.99 | | | | | | | | | | | | | | | | | all_36_0, e1, e3, simplifying with (169), (3797) % 132.91/18.99 | | | | | | | | | | | | | | | | | gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | (3816) all_52_8 = all_36_0 % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3816) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | (3817) all_54_2 = all_36_0 % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | REDUCE: (140), (3814) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | (3818) ~ (all_52_7 = e3) % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | REDUCE: (139), (3814) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | (3819) ~ (all_52_11 = e3) % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | SIMP: (3819) implies: % 132.91/18.99 | | | | | | | | | | | | | | | | | (3820) ~ (all_52_11 = e3) % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | REDUCE: (134), (3816) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | (3821) ~ (all_52_4 = all_36_0) % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | REDUCE: (123), (3816) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | (3822) ~ (all_52_9 = all_36_0) % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | SIMP: (3822) implies: % 132.91/18.99 | | | | | | | | | | | | | | | | | (3823) ~ (all_52_9 = all_36_0) % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | REDUCE: (121), (3816) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | (3824) ~ (all_52_11 = all_36_0) % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | SIMP: (3824) implies: % 132.91/18.99 | | | | | | | | | | | | | | | | | (3825) ~ (all_52_11 = all_36_0) % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | REDUCE: (3790), (3816) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | (3826) ~ (all_36_0 = e3) % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | REDUCE: (3591), (3816) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | (3827) ~ (all_36_0 = e2) % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | REDUCE: (368), (3815) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | (3828) ~ (all_4_2 = e3) % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | SIMP: (3828) implies: % 132.91/18.99 | | | | | | | | | | | | | | | | | (3829) ~ (all_4_2 = e3) % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | (3830) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 132.91/18.99 | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | BETA: splitting (3830) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | (3831) all_57_0 = e0 & op(e3, e3) = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | ALPHA: (3831) implies: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | (3832) op(e3, e3) = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3593), (3832), (function-axioms) are % 132.91/18.99 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | (3833) all_57_1 = e0 & op(e3, e2) = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | ALPHA: (3833) implies: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | (3834) all_57_1 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | (3835) op(e3, e2) = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | (3836) all_54_15 = e3 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (3829), (3836) are inconsistent by % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | sub-proof #601. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | (3837) ~ (all_54_15 = e3) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | (3838) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | (3839) all_54_2 = e3 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3817), (3839) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | (3840) all_36_0 = e3 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3826), (3840) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | (3841) $false % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | CLOSE: (3841) is inconsistent. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | (3842) ~ (all_54_2 = e3) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | (3843) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (3844) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3844) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (3845) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (2978), (3593), (3845), % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | #254. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (3846) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (3589), (3593), (3846), % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | #443. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (3847) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3847) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (3848) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3848) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | (3849) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3849) implies: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | (3850) op(e1, e3) = e1 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3843) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | (3851) all_54_2 = e2 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3817), (3827), (3851) are inconsistent by % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #244. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | (3852) all_54_2 = e1 | all_54_2 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3838) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (3853) all_54_15 = e2 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (3595), (3853) are inconsistent by % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #748. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (3854) all_54_15 = e1 | all_54_15 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3854) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3855) all_54_15 = e1 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (3855) are inconsistent by sub-proof % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | #747. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3856) all_54_15 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3856) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3857) all_4_2 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3857) implies: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3858) all_4_2 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (3858) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3859) ~ (all_52_11 = e0) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3852) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3860) all_54_2 = e1 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3817), (3860) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3861) all_36_0 = e1 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3861) implies: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3862) all_36_0 = e1 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3823), (3862) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3863) ~ (all_52_9 = e1) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3825), (3862) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3864) ~ (all_52_11 = e1) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3865) all_54_14 = e3 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (3820), (3865) are inconsistent by % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #760. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3866) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3866) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3867) all_54_14 = e2 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (3867) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3868) all_52_11 = e2 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3868) implies: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3869) all_52_11 = e2 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (3869) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3870) ~ (all_52_9 = e2) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3871) all_54_6 = e3 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3871) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3872) all_52_9 = e3 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2981), (3872) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3873) $false % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3873) is inconsistent. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3874) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3874) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3875) all_54_6 = e2 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3875) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3876) all_52_9 = e2 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3870), (3876) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3877) $false % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3877) is inconsistent. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3878) all_54_6 = e1 | all_54_6 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3878) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3879) all_54_6 = e1 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3879) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3880) all_52_9 = e1 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3863), (3880) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3881) $false % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3881) is inconsistent. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3882) all_54_6 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3882) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3883) all_52_9 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (3883) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3884) ~ (all_52_1 = e0) % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3885) all_54_4 = e3 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3885) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3886) all_52_1 = e3 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2977), (3886) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3887) $false % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3887) is inconsistent. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3888) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3888) gives: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3889) all_54_4 = e2 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3889) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3890) all_52_1 = e2 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3589), (3890) imply: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3891) $false % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3891) is inconsistent. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3892) all_54_4 = e1 | all_54_4 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (163), (268), (3850), (3884), (3892), % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #243. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3893) all_54_14 = e1 | all_54_14 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (3859), (3864), (3893) are inconsistent by % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #755. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3894) all_54_2 = e0 % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3796), (3817), (3894) are inconsistent by % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #242. % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/18.99 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | (3895) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3895) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | (3896) op(e2, e2) = e1 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2988), (3896), (function-axioms) are % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | (3897) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3897) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | (3898) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3898) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | (3899) op(e2, e2) = e0 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2988), (3899), (function-axioms) are % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | (3900) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3900) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (3901) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3901) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (3902) op(e1, e1) = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (3902), (function-axioms) are % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (3903) op(e0, e0) = all_56_31 & $i(all_56_31) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3903) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (3904) op(e0, e0) = all_56_31 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (3905) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (3906) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (3593), (3835), (3906), % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | #241. % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (3907) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3907) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3908) all_57_4 = e1 & op(e3, e1) = e1 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3908) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3909) all_57_4 = e1 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3843) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3910) all_54_2 = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3817), (3827), (3910) are inconsistent by % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #244. % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3911) ~ (all_54_2 = e2) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3912) all_54_2 = e1 | all_54_2 = e0 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3912) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3913) all_54_2 = e1 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3817), (3913) imply: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3914) all_36_0 = e1 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3914) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3915) all_36_0 = e1 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3825), (3915) imply: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3916) ~ (all_52_11 = e1) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3826), (3915) imply: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3917) ~ (e3 = e1) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3827), (3915) imply: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3918) ~ (e2 = e1) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3919) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3919) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3920) all_57_12 = e1 & op(e0, e3) = e1 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3920) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3921) all_57_12 = e1 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3806), (3921) are inconsistent by sub-proof % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #591. % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3922) all_57_13 = e1 & op(e0, e2) = e1 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3922) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3923) all_57_13 = e1 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3924) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3924) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3925) all_57_12 = e2 & op(e0, e3) = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3925) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3926) all_57_12 = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237), % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3593), (3926), (function-axioms) are inconsistent % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #290. % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3927) all_57_13 = e2 & op(e0, e2) = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3927) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3928) all_57_13 = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3923), (3928) are inconsistent by sub-proof % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #567. % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3929) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3929) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3930) all_57_14 = e2 & op(e0, e1) = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3930) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3931) all_57_14 = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3932) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3932) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3933) all_57_1 = e2 & op(e3, e2) = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3933) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3934) all_57_1 = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234), % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (2978), (3593), (3812), (3934), % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #237. % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3935) all_57_3 = e2 & op(e2, e2) = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234), % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (2978), (2987), (3593), (3812), (3935), % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #236. % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3936) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3936) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3937) all_57_7 = e2 & op(e1, e2) = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3937) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3938) all_57_7 = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3838) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3939) all_54_15 = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (3595), (3939) are inconsistent by % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #748. % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3940) ~ (all_54_15 = e2) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3941) all_54_15 = e1 | all_54_15 = e0 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3942) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3942) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3943) all_57_4 = e0 & op(e3, e1) = e0 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3943) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3944) all_57_4 = e0 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (170), (203), (234), (271), (2978), % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3590), (3593), (3796), (3812), (3817), (3821), % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3827), (3843), (3944), (function-axioms) are % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #234. % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3945) all_57_5 = e0 & op(e2, e1) = e0 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3945) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3946) all_57_5 = e0 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3941) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3947) all_54_15 = e1 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (3947) are inconsistent by sub-proof % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #747. % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3948) all_54_15 = e0 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3948) imply: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3949) all_4_2 = e0 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3949) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3950) all_4_2 = e0 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (3950) imply: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3951) ~ (all_52_11 = e0) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3829), (3950) imply: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3952) ~ (e3 = e0) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3595), (3950) imply: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3953) ~ (e2 = e0) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (3950) imply: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3954) ~ (e1 = e0) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3950) imply: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3955) op(e0, e0) = e0 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3956) all_54_14 = e3 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (3820), (3956) are inconsistent by % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #760. % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3957) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3958) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3958) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3959) all_57_2 = e2 & op(e2, e3) = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3959) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3960) all_57_2 = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (231), (233), (3593), % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3806), (3960), (function-axioms) are inconsistent % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #489. % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3961) all_57_3 = e2 & op(e2, e2) = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234), % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (2978), (2987), (3593), (3812), (3961), % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #236. % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3962) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3962) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3963) all_57_5 = e2 & op(e2, e1) = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3963) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3964) all_57_5 = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3946), (3964) are inconsistent by sub-proof % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #372. % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3965) all_57_10 = e2 & op(e2, e0) = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3965) implies: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3966) all_57_10 = e2 % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3905) gives: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 132.91/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3967) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3967) gives: % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3968) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3968) implies: % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3969) all_56_31 = e3 % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3904), (3969) imply: % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3970) op(e0, e0) = e3 % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3955), (3970), (function-axioms) are % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #715. % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3971) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3971) implies: % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3972) all_56_31 = e2 % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3904), (3972) imply: % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3973) op(e0, e0) = e2 % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (158), (170), % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208), (209), (210), (211), (221), (223), (224), % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (228), (231), (232), (233), (234), (237), % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (372), (2978), (2980), (2987), (3593), % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3938), (3966), (3973), (function-axioms) are % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #269. % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3974) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3974) gives: % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3975) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3975) implies: % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3976) op(e1, e1) = e0 % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3791), (3976), (function-axioms) are % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3977) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3977) implies: % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3978) op(e0, e1) = e0 % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (246), (3916), (3951), (3957), (3978), % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #351. % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3979) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3979) gives: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3980) all_57_8 = e0 & op(e1, e1) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3980) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3981) op(e1, e1) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3791), (3981), (function-axioms) are % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3982) all_57_14 = e0 & op(e0, e1) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3982) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3983) op(e0, e1) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (190), (245), (246), (367), (371), (3820), % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3916), (3941), (3983), (function-axioms) are % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #233. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3984) all_57_13 = e2 & op(e0, e2) = e2 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3984) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3985) all_57_13 = e2 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (208), (209), (3806), % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3931), (3985) are inconsistent by sub-proof #409. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3986) all_57_15 = e2 & op(e0, e0) = e2 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3986) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3987) op(e0, e0) = e2 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3988) all_57_15 = e0 & op(e0, e0) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3988) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3989) op(e0, e0) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3987), (3989), (function-axioms) are % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #714. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3990) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3990) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3991) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3991) gives: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3992) all_57_12 = e0 & op(e0, e3) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3806), (3992) are inconsistent by sub-proof % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #436. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3993) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3993) gives: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3994) all_57_13 = e0 & op(e0, e2) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3994) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3995) all_57_13 = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3923), (3995) imply: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3996) e1 = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3909), (3996) imply: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3997) all_57_4 = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (170), (203), (234), (271), (2978), % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3590), (3593), (3796), (3812), (3817), (3821), % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3827), (3843), (3997), (function-axioms) are % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #234. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3998) all_57_14 = e0 & op(e0, e1) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3998) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3999) op(e0, e1) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (190), (245), (246), (367), (371), (3595), % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3820), (3838), (3916), (3999), (function-axioms) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #232. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4000) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4000) gives: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4001) all_57_14 = e1 & op(e0, e1) = e1 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4001) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4002) all_57_14 = e1 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4003) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4003) gives: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4004) all_57_4 = e2 & op(e3, e1) = e2 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4004) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4005) all_57_4 = e2 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (234), (3593), (3812), (3834), % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4005), (function-axioms) are inconsistent by % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #280. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4006) all_57_5 = e2 & op(e2, e1) = e2 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4006) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4007) all_57_5 = e2 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4008) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4008) gives: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4009) all_57_4 = e0 & op(e3, e1) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4009) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4010) all_57_4 = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (170), (203), (234), (271), (2978), % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3590), (3593), (3796), (3812), (3817), (3821), % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3827), (3843), (4010), (function-axioms) are % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #234. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4011) all_57_5 = e0 & op(e2, e1) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4011) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4012) all_57_5 = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4007), (4012) are inconsistent by sub-proof % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #372. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4013) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4013) gives: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4014) all_57_8 = e0 & op(e1, e1) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4014) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4015) op(e1, e1) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3791), (4015), (function-axioms) are % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4016) all_57_14 = e0 & op(e0, e1) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4016) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4017) all_57_14 = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4002), (4017) imply: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4018) e1 = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3909), (4018) imply: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4019) all_57_4 = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (39), (220), (3791), (4007), % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4017), (4019), (function-axioms) are inconsistent % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #230. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4020) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (372), (4002), (4020), % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #559. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4021) all_57_15 = e1 & op(e0, e0) = e1 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4021) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4022) op(e0, e0) = e1 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3838) gives: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4023) all_54_15 = e2 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (3595), (4023) are inconsistent by % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #748. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4024) all_54_15 = e1 | all_54_15 = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3905) gives: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4025) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4025) gives: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4026) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4026) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4027) all_56_31 = e3 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3904), (4027) imply: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4028) op(e0, e0) = e3 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4022), (4028), (function-axioms) are % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4029) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4029) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4030) all_56_31 = e2 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3904), (4030) imply: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4031) op(e0, e0) = e2 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4022), (4031), (function-axioms) are % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4032) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4032) gives: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4033) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4033) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4034) op(e1, e1) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3791), (4034), (function-axioms) are % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4035) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4035) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4036) op(e0, e1) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (190), (245), (246), (367), (371), (3820), % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3916), (4024), (4036), (function-axioms) are % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #233. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4037) all_54_2 = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3796), (3817), (4037) are inconsistent by % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #242. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4038) all_57_9 = e1 & op(e3, e0) = e1 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4038) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4039) all_57_9 = e1 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3812), (4039) are inconsistent by sub-proof % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | #690. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | (4040) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 133.16/19.01 | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | BETA: splitting (4040) gives: % 133.16/19.01 | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | (4041) all_57_4 = e0 & op(e3, e1) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | ALPHA: (4041) implies: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | (4042) all_57_4 = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | (4043) all_54_2 = e3 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3817), (4043) imply: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | (4044) all_36_0 = e3 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | REDUCE: (3826), (4044) imply: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | (4045) $false % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | CLOSE: (4045) is inconsistent. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | (4046) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (170), (203), (234), (271), (2978), % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | (3590), (3593), (3796), (3812), (3817), (3821), % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | (3827), (4042), (4046), (function-axioms) are % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #234. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | (4047) all_57_9 = e0 & op(e3, e0) = e0 % 133.16/19.01 | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3812), (4047) are inconsistent by sub-proof % 133.16/19.01 | | | | | | | | | | | | | | | | | | | #299. % 133.16/19.01 | | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | (4048) ~ (all_36_1 = e2) & op(e3, e3) = all_36_1 & % 133.16/19.01 | | | | | | | | | | | | | $i(all_36_1) % 133.16/19.01 | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | | REF_CLOSE: (3593), (4048), (function-axioms) are inconsistent % 133.16/19.01 | | | | | | | | | | | | | by sub-proof #342. % 133.16/19.01 | | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | % 133.16/19.01 | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | (4049) all_20_2 = e2 % 133.16/19.01 | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | COMBINE_EQS: (318), (4049) imply: % 133.16/19.01 | | | | | | | | | | (4050) all_4_2 = e2 % 133.16/19.01 | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | COMBINE_EQS: (331), (4050) imply: % 133.16/19.01 | | | | | | | | | | (4051) all_26_2 = e2 % 133.16/19.01 | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | REDUCE: (369), (4050) imply: % 133.16/19.01 | | | | | | | | | | (4052) ~ (all_52_13 = e2) % 133.16/19.01 | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | REDUCE: (36), (4050) imply: % 133.16/19.01 | | | | | | | | | | (4053) op(e0, e0) = e2 % 133.16/19.01 | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | BETA: splitting (70) gives: % 133.16/19.01 | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | (4054) ~ (all_26_2 = e2) % 133.16/19.01 | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | REDUCE: (4051), (4054) imply: % 133.16/19.01 | | | | | | | | | | | (4055) $false % 133.16/19.01 | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | CLOSE: (4055) is inconsistent. % 133.16/19.01 | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | (4056) ( ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 & % 133.16/19.01 | | | | | | | | | | | $i(all_26_0)) | ( ~ (all_26_1 = e3) & op(e2, e2) % 133.16/19.01 | | | | | | | | | | | = all_26_1 & $i(all_26_1)) % 133.16/19.01 | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | BETA: splitting (4056) gives: % 133.16/19.01 | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | (4057) ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 & % 133.16/19.01 | | | | | | | | | | | | $i(all_26_0) % 133.16/19.01 | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | ALPHA: (4057) implies: % 133.16/19.01 | | | | | | | | | | | | (4058) ~ (all_26_0 = e1) % 133.16/19.01 | | | | | | | | | | | | (4059) op(e2, e0) = all_26_0 % 133.16/19.01 | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (91), (118), % 133.16/19.01 | | | | | | | | | | | | (145), (146), (149), (157), (158), (163), (164), % 133.16/19.01 | | | | | | | | | | | | (165), (167), (170), (190), (197), (200), (206), % 133.16/19.01 | | | | | | | | | | | | (208), (209), (210), (211), (212), (214), (217), % 133.16/19.01 | | | | | | | | | | | | (221), (223), (224), (225), (227), (228), (231), % 133.16/19.01 | | | | | | | | | | | | (232), (233), (234), (237), (238), (246), (259), % 133.16/19.01 | | | | | | | | | | | | (268), (332), (362), (364), (372), (2977), (2978), % 133.16/19.01 | | | | | | | | | | | | (2980), (2981), (2982), (2987), (2988), (3593), % 133.16/19.01 | | | | | | | | | | | | (4052), (4053), (4058), (4059), (function-axioms) % 133.16/19.01 | | | | | | | | | | | | are inconsistent by sub-proof #267. % 133.16/19.01 | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | Case 2: % 133.16/19.01 | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | (4060) ~ (all_26_1 = e3) & op(e2, e2) = all_26_1 & % 133.16/19.01 | | | | | | | | | | | | $i(all_26_1) % 133.16/19.01 | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | ALPHA: (4060) implies: % 133.16/19.01 | | | | | | | | | | | | (4061) ~ (all_26_1 = e3) % 133.16/19.01 | | | | | | | | | | | | (4062) op(e2, e2) = all_26_1 % 133.16/19.01 | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | | REF_CLOSE: (2988), (4061), (4062), (function-axioms) are % 133.16/19.01 | | | | | | | | | | | | inconsistent by sub-proof #334. % 133.16/19.01 | | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | | % 133.16/19.01 | | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | | % 133.16/19.01 | | | | | | | | | End of split % 133.16/19.01 | | | | | | | | | % 133.16/19.01 | | | | | | | | End of split % 133.16/19.01 | | | | | | | | % 133.16/19.01 | | | | | | | End of split % 133.16/19.01 | | | | | | | % 133.16/19.01 | | | | | | Case 2: % 133.16/19.01 | | | | | | | % 133.16/19.01 | | | | | | | (4063) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & % 133.16/19.01 | | | | | | | op(e0, e2) = e3) % 133.16/19.01 | | | | | | | % 133.16/19.01 | | | | | | | REF_CLOSE: (158), (162), (2979), (2980), (4063), (function-axioms) % 133.16/19.01 | | | | | | | are inconsistent by sub-proof #555. % 133.16/19.01 | | | | | | | % 133.16/19.01 | | | | | | End of split % 133.16/19.01 | | | | | | % 133.16/19.01 | | | | | End of split % 133.16/19.01 | | | | | % 133.16/19.01 | | | | Case 2: % 133.16/19.01 | | | | | % 133.16/19.01 | | | | | (4064) all_10_2 = e0 % 133.16/19.01 | | | | | % 133.16/19.01 | | | | | COMBINE_EQS: (319), (4064) imply: % 133.16/19.01 | | | | | (4065) all_24_2 = e0 % 133.16/19.01 | | | | | % 133.16/19.01 | | | | | REDUCE: (336), (4064) imply: % 133.16/19.01 | | | | | (4066) ~ (all_52_1 = e0) % 133.16/19.01 | | | | | % 133.16/19.01 | | | | | REDUCE: (340), (4064) imply: % 133.16/19.01 | | | | | (4067) ~ (all_52_3 = e0) % 133.16/19.01 | | | | | % 133.16/19.01 | | | | | REDUCE: (342), (4064) imply: % 133.16/19.01 | | | | | (4068) ~ (all_52_4 = e0) % 133.16/19.01 | | | | | % 133.16/19.01 | | | | | REDUCE: (344), (4064) imply: % 133.16/19.01 | | | | | (4069) ~ (all_52_8 = e0) % 133.16/19.01 | | | | | % 133.16/19.01 | | | | | REDUCE: (346), (4064) imply: % 133.16/19.01 | | | | | (4070) ~ (all_52_12 = e0) % 133.16/19.01 | | | | | % 133.16/19.01 | | | | | REDUCE: (45), (4064) imply: % 133.16/19.01 | | | | | (4071) op(e3, e3) = e0 % 133.16/19.01 | | | | | % 133.16/19.01 | | | | | BETA: splitting (52) gives: % 133.16/19.01 | | | | | % 133.16/19.01 | | | | | Case 1: % 133.16/19.01 | | | | | | % 133.16/19.01 | | | | | | (4072) ~ (all_14_2 = e3) % 133.16/19.01 | | | | | | % 133.16/19.01 | | | | | | REDUCE: (329), (4072) imply: % 133.16/19.01 | | | | | | (4073) ~ (all_8_2 = e3) % 133.16/19.01 | | | | | | % 133.16/19.01 | | | | | | BETA: splitting (61) gives: % 133.16/19.01 | | | | | | % 133.16/19.01 | | | | | | Case 1: % 133.16/19.01 | | | | | | | % 133.16/19.01 | | | | | | | (4074) ~ (all_20_2 = e2) % 133.16/19.01 | | | | | | | % 133.16/19.01 | | | | | | | REDUCE: (318), (4074) imply: % 133.16/19.01 | | | | | | | (4075) ~ (all_4_2 = e2) % 133.16/19.01 | | | | | | | % 133.16/19.01 | | | | | | | BETA: splitting (73) gives: % 133.16/19.01 | | | | | | | % 133.16/19.01 | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | % 133.16/19.01 | | | | | | | | (4076) ~ (all_28_2 = e3) % 133.16/19.01 | | | | | | | | % 133.16/19.01 | | | | | | | | REDUCE: (316), (4076) imply: % 133.16/19.01 | | | | | | | | (4077) ~ (all_6_2 = e3) % 133.16/19.01 | | | | | | | | % 133.16/19.01 | | | | | | | | BETA: splitting (76) gives: % 133.16/19.01 | | | | | | | | % 133.16/19.01 | | | | | | | | Case 1: % 133.16/19.01 | | | | | | | | | % 133.16/19.01 | | | | | | | | | (4078) ~ (all_30_2 = e0) % 133.16/19.01 | | | | | | | | | % 133.16/19.01 | | | | | | | | | REDUCE: (309), (4078) imply: % 133.16/19.02 | | | | | | | | | (4079) ~ (all_8_2 = e0) % 133.16/19.02 | | | | | | | | | % 133.16/19.02 | | | | | | | | | BETA: splitting (199) gives: % 133.16/19.02 | | | | | | | | | % 133.16/19.02 | | | | | | | | | Case 1: % 133.16/19.02 | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | (4080) all_54_5 = e3 % 133.16/19.02 | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | REF_CLOSE: (267), (4073), (4080) are inconsistent by % 133.16/19.02 | | | | | | | | | | sub-proof #554. % 133.16/19.02 | | | | | | | | | | % 133.16/19.02 | | | | | | | | | Case 2: % 133.16/19.02 | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | (4081) ~ (all_54_5 = e3) % 133.16/19.02 | | | | | | | | | | (4082) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 133.16/19.02 | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | BETA: splitting (4082) gives: % 133.16/19.02 | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | Case 1: % 133.16/19.02 | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | (4083) all_54_5 = e2 % 133.16/19.02 | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | COMBINE_EQS: (267), (4083) imply: % 133.16/19.02 | | | | | | | | | | | (4084) all_8_2 = e2 % 133.16/19.02 | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | SIMP: (4084) implies: % 133.16/19.02 | | | | | | | | | | | (4085) all_8_2 = e2 % 133.16/19.02 | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | REDUCE: (356), (4085) imply: % 133.16/19.02 | | | | | | | | | | | (4086) ~ (all_52_9 = e2) % 133.16/19.02 | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | REDUCE: (358), (4085) imply: % 133.16/19.02 | | | | | | | | | | | (4087) ~ (all_52_13 = e2) % 133.16/19.02 | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | BETA: splitting (82) gives: % 133.16/19.02 | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | Case 1: % 133.16/19.02 | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | (4088) ~ (all_34_2 = e3) % 133.16/19.02 | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | REDUCE: (307), (4088) imply: % 133.16/19.02 | | | | | | | | | | | | (4089) ~ (all_4_2 = e3) % 133.16/19.02 | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | BETA: splitting (189) gives: % 133.16/19.02 | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | Case 1: % 133.16/19.02 | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | (4090) all_54_15 = e3 % 133.16/19.02 | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | REF_CLOSE: (245), (4089), (4090) are inconsistent by % 133.16/19.02 | | | | | | | | | | | | | sub-proof #601. % 133.16/19.02 | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | Case 2: % 133.16/19.02 | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | (4091) ~ (all_54_15 = e3) % 133.16/19.02 | | | | | | | | | | | | | (4092) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 133.16/19.02 | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | BETA: splitting (4092) gives: % 133.16/19.02 | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | Case 1: % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | (4093) all_54_15 = e2 % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | REF_CLOSE: (245), (4075), (4093) are inconsistent by % 133.16/19.02 | | | | | | | | | | | | | | sub-proof #748. % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | Case 2: % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | (4094) ~ (all_54_15 = e2) % 133.16/19.02 | | | | | | | | | | | | | | (4095) all_54_15 = e1 | all_54_15 = e0 % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | BETA: splitting (4095) gives: % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | Case 1: % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | (4096) all_54_15 = e1 % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (4096) are inconsistent by sub-proof % 133.16/19.02 | | | | | | | | | | | | | | | #747. % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | Case 2: % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | (4097) all_54_15 = e0 % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | COMBINE_EQS: (245), (4097) imply: % 133.16/19.02 | | | | | | | | | | | | | | | (4098) all_4_2 = e0 % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | SIMP: (4098) implies: % 133.16/19.02 | | | | | | | | | | | | | | | (4099) all_4_2 = e0 % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | REDUCE: (4089), (4099) imply: % 133.16/19.02 | | | | | | | | | | | | | | | (4100) ~ (e3 = e0) % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | REDUCE: (4075), (4099) imply: % 133.16/19.02 | | | | | | | | | | | | | | | (4101) ~ (e2 = e0) % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | REDUCE: (371), (4099) imply: % 133.16/19.02 | | | | | | | | | | | | | | | (4102) ~ (e1 = e0) % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | REDUCE: (36), (4099) imply: % 133.16/19.02 | | | | | | | | | | | | | | | (4103) op(e0, e0) = e0 % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | Case 1: % 133.16/19.02 | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | (4104) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.16/19.02 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.16/19.02 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.16/19.02 | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.16/19.02 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.16/19.02 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.16/19.02 | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.16/19.02 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.16/19.02 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.16/19.02 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.16/19.02 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.16/19.02 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.16/19.02 | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | BETA: splitting (4104) gives: % 133.16/19.02 | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | Case 1: % 133.16/19.02 | | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | | (4105) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.16/19.02 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.16/19.02 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.16/19.02 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.16/19.02 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.16/19.02 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.16/19.02 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.16/19.02 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.16/19.02 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.16/19.02 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.16/19.02 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.16/19.02 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.16/19.02 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.16/19.02 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.16/19.02 | | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (4071), (4105), (function-axioms) are % 133.16/19.02 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #229. % 133.16/19.02 | | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | Case 2: % 133.16/19.02 | | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | | (4106) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.16/19.02 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.16/19.02 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.16/19.02 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.16/19.02 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.16/19.02 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.16/19.02 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.16/19.02 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.16/19.02 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.16/19.02 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.16/19.02 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.16/19.02 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.16/19.02 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.16/19.02 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.16/19.02 | | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | | BETA: splitting (4106) gives: % 133.16/19.02 | | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.02 | | | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | | | (4107) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.16/19.02 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.16/19.02 | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 133.16/19.02 | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.16/19.02 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.16/19.02 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.16/19.02 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.16/19.02 | | | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | | | ALPHA: (4107) implies: % 133.16/19.02 | | | | | | | | | | | | | | | | | | (4108) ~ (all_56_31 = e0) % 133.16/19.02 | | | | | | | | | | | | | | | | | | (4109) op(e0, e0) = all_56_31 % 133.16/19.02 | | | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4103), (4108), (4109), (function-axioms) are % 133.16/19.02 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #712. % 133.16/19.02 | | | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.02 | | | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | | | (4110) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.16/19.02 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.16/19.02 | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.16/19.02 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.16/19.02 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 133.16/19.02 | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.16/19.02 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.16/19.02 | | | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | | | ALPHA: (4110) implies: % 133.16/19.02 | | | | | | | | | | | | | | | | | | (4111) op(e2, e2) = e3 % 133.16/19.02 | | | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (4073), (4111), (function-axioms) are % 133.16/19.02 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228. % 133.16/19.02 | | | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | | End of split % 133.16/19.02 | | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | End of split % 133.16/19.02 | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | Case 2: % 133.16/19.02 | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | (4112) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.16/19.02 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.16/19.02 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.16/19.02 | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.16/19.02 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.16/19.02 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.16/19.02 | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.16/19.02 | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.16/19.02 | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.16/19.02 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.16/19.02 | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.16/19.02 | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.16/19.02 | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.16/19.02 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.16/19.02 | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.16/19.02 | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.16/19.02 | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.16/19.02 | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.16/19.02 | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.16/19.02 | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.16/19.02 | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.16/19.02 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.16/19.02 | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.16/19.02 | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.16/19.02 | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.16/19.02 | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.16/19.02 | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.16/19.02 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.16/19.02 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.16/19.02 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.16/19.02 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.16/19.02 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.16/19.02 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.16/19.02 | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.16/19.02 | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (164), (165), (372), (4077), % 133.16/19.02 | | | | | | | | | | | | | | | | (4086), (4087), (4103), (4112), (function-axioms) % 133.16/19.02 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #708. % 133.16/19.02 | | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | End of split % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | End of split % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | End of split % 133.16/19.02 | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | End of split % 133.16/19.02 | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | Case 2: % 133.16/19.02 | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | (4113) all_34_2 = e3 % 133.16/19.02 | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | COMBINE_EQS: (307), (4113) imply: % 133.16/19.02 | | | | | | | | | | | | (4114) all_4_2 = e3 % 133.16/19.02 | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | SIMP: (4114) implies: % 133.16/19.02 | | | | | | | | | | | | (4115) all_4_2 = e3 % 133.16/19.02 | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | REDUCE: (367), (4115) imply: % 133.16/19.02 | | | | | | | | | | | | (4116) ~ (all_52_11 = e3) % 133.16/19.02 | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | REDUCE: (368), (4115) imply: % 133.16/19.02 | | | | | | | | | | | | (4117) ~ (all_52_12 = e3) % 133.16/19.02 | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | REDUCE: (36), (4115) imply: % 133.16/19.02 | | | | | | | | | | | | (4118) op(e0, e0) = e3 % 133.16/19.02 | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | BETA: splitting (206) gives: % 133.16/19.02 | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | Case 1: % 133.16/19.02 | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | (4119) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.16/19.02 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.16/19.02 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.16/19.02 | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.16/19.02 | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.16/19.02 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.16/19.02 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.16/19.02 | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.16/19.02 | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.16/19.02 | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.16/19.02 | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.16/19.02 | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.16/19.02 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.16/19.02 | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.16/19.02 | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.16/19.02 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.16/19.02 | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.16/19.02 | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.16/19.02 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.16/19.02 | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.16/19.02 | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.16/19.02 | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.16/19.02 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.16/19.02 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.16/19.02 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.16/19.02 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.16/19.02 | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.16/19.02 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.16/19.02 | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | BETA: splitting (4119) gives: % 133.16/19.02 | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | Case 1: % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | (4120) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.16/19.02 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.16/19.02 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.16/19.02 | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.16/19.02 | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.16/19.02 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.16/19.02 | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.16/19.02 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.16/19.02 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.16/19.02 | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.16/19.02 | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.16/19.02 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (4071), (4120), (function-axioms) are % 133.16/19.02 | | | | | | | | | | | | | | inconsistent by sub-proof #229. % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | Case 2: % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | (4121) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.16/19.02 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.16/19.02 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.16/19.02 | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.16/19.02 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.16/19.02 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.16/19.02 | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.16/19.02 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.16/19.02 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.16/19.02 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.16/19.02 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.16/19.02 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | BETA: splitting (4121) gives: % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | Case 1: % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | (4122) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.16/19.02 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.16/19.02 | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 133.16/19.02 | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.16/19.02 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.16/19.02 | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | ALPHA: (4122) implies: % 133.16/19.02 | | | | | | | | | | | | | | | (4123) op(e3, e0) = e3 % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | REF_CLOSE: (168), (4117), (4123), (function-axioms) are % 133.16/19.02 | | | | | | | | | | | | | | | inconsistent by sub-proof #733. % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | Case 2: % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | (4124) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.16/19.02 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.16/19.02 | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.16/19.02 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.16/19.02 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 133.16/19.02 | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | ALPHA: (4124) implies: % 133.16/19.02 | | | | | | | | | | | | | | | (4125) op(e2, e2) = e3 % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | REF_CLOSE: (42), (4073), (4125), (function-axioms) are % 133.16/19.02 | | | | | | | | | | | | | | | inconsistent by sub-proof #228. % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | End of split % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | End of split % 133.16/19.02 | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | Case 2: % 133.16/19.02 | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | (4126) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.16/19.02 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.16/19.02 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.16/19.02 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.16/19.02 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.16/19.02 | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.16/19.02 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.16/19.02 | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.16/19.02 | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.16/19.02 | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.16/19.02 | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.16/19.02 | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.16/19.02 | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.16/19.02 | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.16/19.02 | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.16/19.02 | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.16/19.02 | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.16/19.02 | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.16/19.02 | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.16/19.02 | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.16/19.02 | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.16/19.02 | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.16/19.02 | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.16/19.02 | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.16/19.02 | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.16/19.02 | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.16/19.02 | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.16/19.02 | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.16/19.02 | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.16/19.02 | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.16/19.02 | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.16/19.02 | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.16/19.02 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.16/19.02 | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.16/19.02 | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.16/19.02 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.16/19.02 | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.16/19.02 | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.16/19.02 | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.16/19.02 | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.16/19.02 | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.16/19.02 | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.16/19.02 | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.16/19.02 | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.16/19.02 | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.16/19.02 | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.16/19.02 | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.16/19.02 | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.16/19.02 | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.16/19.02 | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.16/19.02 | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.16/19.02 | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.16/19.02 | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.16/19.02 | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.16/19.02 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.16/19.02 | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.16/19.02 | | | | | | | | | | | | | & $i(all_56_29)))) % 133.16/19.02 | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | BETA: splitting (4126) gives: % 133.16/19.02 | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | Case 1: % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | (4127) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.16/19.02 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.16/19.02 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.16/19.02 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.16/19.02 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.16/19.02 | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.16/19.02 | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.16/19.02 | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.16/19.02 | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.16/19.02 | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.16/19.02 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.16/19.02 | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | REF_CLOSE: (39), (165), (4077), (4086), (4127), % 133.16/19.02 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.16/19.02 | | | | | | | | | | | | | | #769. % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | Case 2: % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | (4128) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.16/19.02 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.16/19.02 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.16/19.02 | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.16/19.02 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.16/19.02 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.16/19.02 | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.16/19.02 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.16/19.02 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.16/19.02 | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.16/19.02 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.16/19.02 | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.16/19.02 | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.16/19.02 | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.16/19.02 | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.16/19.02 | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.16/19.02 | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.16/19.02 | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.16/19.02 | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.16/19.02 | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.16/19.02 | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.16/19.02 | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.16/19.02 | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.16/19.02 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.16/19.02 | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.16/19.02 | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.16/19.02 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.16/19.02 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.16/19.02 | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.16/19.02 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.16/19.02 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.16/19.02 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.16/19.02 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.16/19.02 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.16/19.02 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.16/19.02 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.16/19.02 | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | BETA: splitting (4128) gives: % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | Case 1: % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | (4129) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.16/19.02 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.16/19.02 | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.16/19.02 | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.16/19.02 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.16/19.02 | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | ALPHA: (4129) implies: % 133.16/19.02 | | | | | | | | | | | | | | | (4130) op(e2, e0) = e2 % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | REF_CLOSE: (164), (4087), (4130), (function-axioms) are % 133.16/19.02 | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | Case 2: % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | (4131) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.16/19.02 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.16/19.02 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.16/19.02 | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.16/19.02 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.16/19.02 | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.16/19.02 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.16/19.02 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.16/19.02 | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.16/19.02 | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.16/19.02 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.16/19.02 | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.16/19.02 | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.16/19.02 | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.16/19.02 | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.16/19.02 | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.16/19.02 | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.16/19.02 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.16/19.02 | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.16/19.02 | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.16/19.02 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.16/19.02 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.16/19.02 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.16/19.02 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.16/19.02 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.16/19.02 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.16/19.02 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.16/19.02 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.16/19.02 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.16/19.02 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.16/19.02 | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (42), (100), (157), (158), (159), % 133.16/19.02 | | | | | | | | | | | | | | | (190), (199), (246), (267), (295), (354), (364), % 133.16/19.02 | | | | | | | | | | | | | | | (372), (373), (4067), (4073), (4116), (4118), % 133.16/19.02 | | | | | | | | | | | | | | | (4131), (function-axioms) are inconsistent by % 133.16/19.02 | | | | | | | | | | | | | | | sub-proof #226. % 133.16/19.02 | | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | | End of split % 133.16/19.02 | | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | | End of split % 133.16/19.02 | | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | | End of split % 133.16/19.02 | | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | End of split % 133.16/19.02 | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | Case 2: % 133.16/19.02 | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | (4132) all_54_5 = e1 | all_54_5 = e0 % 133.16/19.02 | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | | REF_CLOSE: (267), (373), (4079), (4132) are inconsistent by % 133.16/19.02 | | | | | | | | | | | sub-proof #624. % 133.16/19.02 | | | | | | | | | | | % 133.16/19.02 | | | | | | | | | | End of split % 133.16/19.02 | | | | | | | | | | % 133.16/19.02 | | | | | | | | | End of split % 133.16/19.02 | | | | | | | | | % 133.16/19.02 | | | | | | | | Case 2: % 133.16/19.02 | | | | | | | | | % 133.16/19.02 | | | | | | | | | (4133) all_30_2 = e0 % 133.16/19.02 | | | | | | | | | % 133.16/19.02 | | | | | | | | | COMBINE_EQS: (309), (4133) imply: % 133.16/19.02 | | | | | | | | | (4134) all_8_2 = e0 % 133.16/19.02 | | | | | | | | | % 133.16/19.02 | | | | | | | | | SIMP: (4134) implies: % 133.16/19.02 | | | | | | | | | (4135) all_8_2 = e0 % 133.16/19.02 | | | | | | | | | % 133.16/19.03 | | | | | | | | | COMBINE_EQS: (301), (4135) imply: % 133.16/19.03 | | | | | | | | | (4136) all_42_2 = e0 % 133.16/19.03 | | | | | | | | | % 133.16/19.03 | | | | | | | | | REDUCE: (352), (4135) imply: % 133.16/19.03 | | | | | | | | | (4137) ~ (all_52_6 = e0) % 133.16/19.03 | | | | | | | | | % 133.16/19.03 | | | | | | | | | REDUCE: (354), (4135) imply: % 133.16/19.03 | | | | | | | | | (4138) ~ (all_52_7 = e0) % 133.16/19.03 | | | | | | | | | % 133.16/19.03 | | | | | | | | | REDUCE: (356), (4135) imply: % 133.16/19.03 | | | | | | | | | (4139) ~ (all_52_9 = e0) % 133.16/19.03 | | | | | | | | | % 133.16/19.03 | | | | | | | | | REDUCE: (4073), (4135) imply: % 133.16/19.03 | | | | | | | | | (4140) ~ (e3 = e0) % 133.16/19.03 | | | | | | | | | % 133.16/19.03 | | | | | | | | | REDUCE: (373), (4135) imply: % 133.16/19.03 | | | | | | | | | (4141) ~ (e1 = e0) % 133.16/19.03 | | | | | | | | | % 133.16/19.03 | | | | | | | | | BETA: splitting (223) gives: % 133.16/19.03 | | | | | | | | | % 133.16/19.03 | | | | | | | | | Case 1: % 133.16/19.03 | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | (4142) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 % 133.16/19.03 | | | | | | | | | | & op(e2, e2) = e0) % 133.16/19.03 | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | BETA: splitting (4142) gives: % 133.16/19.03 | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | Case 1: % 133.16/19.03 | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | (4143) all_57_2 = e0 & op(e2, e3) = e0 % 133.16/19.03 | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | REF_CLOSE: (167), (4066), (4143), (function-axioms) are % 133.16/19.03 | | | | | | | | | | | inconsistent by sub-proof #225. % 133.16/19.03 | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | Case 2: % 133.16/19.03 | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | (4144) all_57_3 = e0 & op(e2, e2) = e0 % 133.16/19.03 | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | ALPHA: (4144) implies: % 133.16/19.03 | | | | | | | | | | | (4145) all_57_3 = e0 % 133.16/19.03 | | | | | | | | | | | (4146) op(e2, e2) = e0 % 133.16/19.03 | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | BETA: splitting (82) gives: % 133.16/19.03 | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | Case 1: % 133.16/19.03 | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | (4147) ~ (all_34_2 = e3) % 133.16/19.03 | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | REDUCE: (307), (4147) imply: % 133.16/19.03 | | | | | | | | | | | | (4148) ~ (all_4_2 = e3) % 133.16/19.03 | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | BETA: splitting (189) gives: % 133.16/19.03 | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | Case 1: % 133.16/19.03 | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | (4149) all_54_15 = e3 % 133.16/19.03 | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | COMBINE_EQS: (245), (4149) imply: % 133.16/19.03 | | | | | | | | | | | | | (4150) all_4_2 = e3 % 133.16/19.03 | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | REDUCE: (4148), (4150) imply: % 133.16/19.03 | | | | | | | | | | | | | (4151) $false % 133.16/19.03 | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | CLOSE: (4151) is inconsistent. % 133.16/19.03 | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | Case 2: % 133.16/19.03 | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | (4152) ~ (all_54_15 = e3) % 133.16/19.03 | | | | | | | | | | | | | (4153) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 133.16/19.03 | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | BETA: splitting (4153) gives: % 133.16/19.03 | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | Case 1: % 133.16/19.03 | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | (4154) all_54_15 = e2 % 133.16/19.03 | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | COMBINE_EQS: (245), (4154) imply: % 133.16/19.03 | | | | | | | | | | | | | | (4155) all_4_2 = e2 % 133.16/19.03 | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | REDUCE: (4075), (4155) imply: % 133.16/19.03 | | | | | | | | | | | | | | (4156) $false % 133.16/19.03 | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | CLOSE: (4156) is inconsistent. % 133.16/19.03 | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | Case 2: % 133.16/19.03 | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | (4157) ~ (all_54_15 = e2) % 133.16/19.03 | | | | | | | | | | | | | | (4158) all_54_15 = e1 | all_54_15 = e0 % 133.16/19.03 | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | BETA: splitting (4158) gives: % 133.16/19.03 | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | Case 1: % 133.16/19.03 | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | (4159) all_54_15 = e1 % 133.16/19.03 | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | COMBINE_EQS: (245), (4159) imply: % 133.16/19.03 | | | | | | | | | | | | | | | (4160) all_4_2 = e1 % 133.16/19.03 | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | REDUCE: (371), (4160) imply: % 133.16/19.03 | | | | | | | | | | | | | | | (4161) $false % 133.16/19.03 | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | CLOSE: (4161) is inconsistent. % 133.16/19.03 | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | Case 2: % 133.16/19.03 | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | (4162) all_54_15 = e0 % 133.16/19.03 | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | COMBINE_EQS: (245), (4162) imply: % 133.16/19.03 | | | | | | | | | | | | | | | (4163) all_4_2 = e0 % 133.16/19.03 | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | REDUCE: (4075), (4163) imply: % 133.16/19.03 | | | | | | | | | | | | | | | (4164) ~ (e2 = e0) % 133.16/19.03 | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | REDUCE: (36), (4163) imply: % 133.16/19.03 | | | | | | | | | | | | | | | (4165) op(e0, e0) = e0 % 133.16/19.03 | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 133.16/19.03 | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | Case 1: % 133.16/19.03 | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | (4166) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 133.16/19.03 | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 133.16/19.03 | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | BETA: splitting (4166) gives: % 133.16/19.03 | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | Case 1: % 133.16/19.03 | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | (4167) all_57_4 = e0 & op(e3, e1) = e0 % 133.16/19.03 | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4069), (4167), (function-axioms) are % 133.16/19.03 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #224. % 133.16/19.03 | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | Case 2: % 133.16/19.03 | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | (4168) all_57_5 = e0 & op(e2, e1) = e0 % 133.16/19.03 | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4139), (4168), (function-axioms) are % 133.16/19.03 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #455. % 133.16/19.03 | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | End of split % 133.16/19.03 | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | Case 2: % 133.16/19.03 | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | (4169) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 133.16/19.03 | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 133.16/19.03 | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | BETA: splitting (4169) gives: % 133.16/19.03 | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | Case 1: % 133.16/19.03 | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | (4170) all_57_8 = e0 & op(e1, e1) = e0 % 133.16/19.03 | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | ALPHA: (4170) implies: % 133.16/19.03 | | | | | | | | | | | | | | | | | (4171) op(e1, e1) = e0 % 133.16/19.03 | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.16/19.03 | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.03 | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | (4172) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.16/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.16/19.03 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.16/19.03 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.16/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.16/19.03 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.16/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.16/19.03 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.16/19.03 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.16/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.16/19.03 | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.16/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.16/19.03 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.16/19.03 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.16/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.16/19.03 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.16/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.16/19.03 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.16/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.16/19.03 | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | BETA: splitting (4172) gives: % 133.16/19.03 | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.03 | | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | | (4173) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.16/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.16/19.03 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.16/19.03 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.16/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.16/19.03 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.16/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.16/19.03 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.16/19.03 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.16/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.16/19.03 | | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | | BETA: splitting (4173) gives: % 133.16/19.03 | | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | | Case 1: % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | (4174) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | ALPHA: (4174) implies: % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | (4175) op(e3, e3) = e2 % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4071), (4175), (function-axioms) are % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | (4176) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | ALPHA: (4176) implies: % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | (4177) op(e3, e3) = e1 % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (39), (168), (169), (170), (206), % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | (232), (245), (368), (371), (372), (4068), (4075), % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | (4077), (4146), (4148), (4153), (4177), % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | #594. % 133.16/19.03 | | | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | | End of split % 133.16/19.03 | | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.03 | | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | | (4178) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.16/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.16/19.03 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.16/19.03 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.16/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.16/19.03 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.16/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.16/19.03 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.16/19.03 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.16/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.16/19.03 | | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4146), (4165), (4178), (function-axioms) are % 133.16/19.03 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #223. % 133.16/19.03 | | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | | End of split % 133.16/19.03 | | | | | | | | | | | | | | | | | | % 133.16/19.03 | | | | | | | | | | | | | | | | | Case 2: % 133.16/19.03 | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | (4179) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.03 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.03 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.03 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.03 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.03 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.26/19.03 | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.26/19.03 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.03 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.26/19.03 | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.26/19.03 | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.26/19.03 | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.26/19.03 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.26/19.03 | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.26/19.03 | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.26/19.03 | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.03 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.26/19.03 | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.26/19.03 | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.26/19.03 | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.03 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.03 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.03 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.03 | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.03 | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | BETA: splitting (4179) gives: % 133.26/19.03 | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | (4180) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.03 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.03 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | BETA: splitting (4180) gives: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (4181) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | ALPHA: (4181) implies: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (4182) op(e1, e1) = e3 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4171), (4182), (function-axioms) are % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (4183) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | ALPHA: (4183) implies: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (4184) op(e2, e2) = e1 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4146), (4184), (function-axioms) are % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.03 | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | (4185) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.03 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.26/19.03 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.03 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.03 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.03 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.03 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (372), (4165), (4185), % 133.26/19.03 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.03 | | | | | | | | | | | | | | | | | | | #596. % 133.26/19.03 | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | End of split % 133.26/19.03 | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | End of split % 133.26/19.03 | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | Case 2: % 133.26/19.03 | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | (4186) all_57_14 = e0 & op(e0, e1) = e0 % 133.26/19.03 | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | ALPHA: (4186) implies: % 133.26/19.03 | | | | | | | | | | | | | | | | | (4187) all_57_14 = e0 % 133.26/19.03 | | | | | | | | | | | | | | | | | (4188) op(e0, e1) = e0 % 133.26/19.03 | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.26/19.03 | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.03 | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | (4189) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.26/19.03 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.26/19.03 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.03 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.03 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.03 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.26/19.03 | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | BETA: splitting (4189) gives: % 133.26/19.03 | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | (4190) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.26/19.03 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.26/19.03 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | BETA: splitting (4190) gives: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (4191) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (168), (170), % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (220), (221), (222), (232), (372), (4068), (4070), % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (4187), (4188), (4191), (function-axioms) are % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #222. % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (4192) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | ALPHA: (4192) implies: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | (4193) op(e3, e3) = e1 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | (4194) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4194) gives: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | (4195) all_57_12 = e1 & op(e0, e3) = e1 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4195) implies: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | (4196) all_57_12 = e1 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (235), (237), % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | (4193), (4196), (function-axioms) are inconsistent % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #583. % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | (4197) all_57_13 = e1 & op(e0, e2) = e1 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4197) implies: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | (4198) all_57_13 = e1 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | (4199) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4199) gives: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | (4200) all_57_12 = e2 & op(e0, e3) = e2 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4200) implies: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | (4201) all_57_12 = e2 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | (4202) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4202) gives: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4203) all_57_12 = e3 & op(e0, e3) = e3 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4203) implies: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4204) all_57_12 = e3 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4201), (4204) are inconsistent by sub-proof % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | #518. % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4205) all_57_13 = e3 & op(e0, e2) = e3 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4205) implies: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4206) all_57_13 = e3 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4198), (4206) imply: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4207) e3 = e1 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (4207) imply: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4208) $false % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4208) is inconsistent. % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | (4209) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4209) gives: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4210) all_57_14 = e3 & op(e0, e1) = e3 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4187), (4210) are inconsistent by sub-proof % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | #661. % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4211) all_57_15 = e3 & op(e0, e0) = e3 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4211) implies: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (4212) op(e0, e0) = e3 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4165), (4212), (function-axioms) are % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #715. % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | (4213) all_57_13 = e2 & op(e0, e2) = e2 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4213) implies: % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | (4214) all_57_13 = e2 % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4198), (4214) are inconsistent by sub-proof % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | #567. % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.03 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | (4215) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4215) gives: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (4216) all_57_14 = e2 & op(e0, e1) = e2 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4216) implies: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (4217) op(e0, e1) = e2 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4188), (4217), (function-axioms) are % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660. % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (4218) all_57_15 = e2 & op(e0, e0) = e2 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4218) implies: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (4219) op(e0, e0) = e2 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4165), (4219), (function-axioms) are % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #714. % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | (4220) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4220) gives: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | (4221) all_57_14 = e1 & op(e0, e1) = e1 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4221) implies: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | (4222) all_57_14 = e1 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4187), (4222) are inconsistent by sub-proof % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | #221. % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | (4223) all_57_15 = e1 & op(e0, e0) = e1 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4223) implies: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | (4224) op(e0, e0) = e1 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4165), (4224), (function-axioms) are % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #220. % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.04 | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | (4225) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.04 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4146), (4165), (4225), (function-axioms) are % 133.26/19.04 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #223. % 133.26/19.04 | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | End of split % 133.26/19.04 | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | (4226) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.04 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.04 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.04 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.04 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.26/19.04 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.26/19.04 | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.26/19.04 | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.26/19.04 | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.26/19.04 | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.26/19.04 | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.26/19.04 | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.26/19.04 | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.04 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.04 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.04 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.04 | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.04 | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | BETA: splitting (4226) gives: % 133.26/19.04 | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | (4227) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (4077), (4146), (4227), % 133.26/19.04 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.04 | | | | | | | | | | | | | | | | | | | #621. % 133.26/19.04 | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | (4228) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.04 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.26/19.04 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.04 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.04 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (372), (4165), (4228), % 133.26/19.04 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.04 | | | | | | | | | | | | | | | | | | | #596. % 133.26/19.04 | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | End of split % 133.26/19.04 | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | End of split % 133.26/19.04 | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | End of split % 133.26/19.04 | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | End of split % 133.26/19.04 | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | End of split % 133.26/19.04 | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | End of split % 133.26/19.04 | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | End of split % 133.26/19.04 | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | (4229) all_34_2 = e3 % 133.26/19.04 | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | COMBINE_EQS: (307), (4229) imply: % 133.26/19.04 | | | | | | | | | | | | (4230) all_4_2 = e3 % 133.26/19.04 | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | SIMP: (4230) implies: % 133.26/19.04 | | | | | | | | | | | | (4231) all_4_2 = e3 % 133.26/19.04 | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | REDUCE: (360), (4231) imply: % 133.26/19.04 | | | | | | | | | | | | (4232) ~ (all_52_7 = e3) % 133.26/19.04 | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | REDUCE: (367), (4231) imply: % 133.26/19.04 | | | | | | | | | | | | (4233) ~ (all_52_11 = e3) % 133.26/19.04 | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | REDUCE: (368), (4231) imply: % 133.26/19.04 | | | | | | | | | | | | (4234) ~ (all_52_12 = e3) % 133.26/19.04 | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | REDUCE: (370), (4231) imply: % 133.26/19.04 | | | | | | | | | | | | (4235) ~ (all_52_14 = e3) % 133.26/19.04 | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | REDUCE: (36), (4231) imply: % 133.26/19.04 | | | | | | | | | | | | (4236) op(e0, e0) = e3 % 133.26/19.04 | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | BETA: splitting (94) gives: % 133.26/19.04 | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | (4237) ~ (all_42_2 = e0) % 133.26/19.04 | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | REDUCE: (4136), (4237) imply: % 133.26/19.04 | | | | | | | | | | | | | (4238) $false % 133.26/19.04 | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | CLOSE: (4238) is inconsistent. % 133.26/19.04 | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | (4239) ( ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 & % 133.26/19.04 | | | | | | | | | | | | | $i(all_42_0)) | ( ~ (all_42_1 = e3) & op(e0, e0) % 133.26/19.04 | | | | | | | | | | | | | = all_42_1 & $i(all_42_1)) % 133.26/19.04 | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | BETA: splitting (4239) gives: % 133.26/19.04 | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | (4240) ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 & % 133.26/19.04 | | | | | | | | | | | | | | $i(all_42_0) % 133.26/19.04 | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | ALPHA: (4240) implies: % 133.26/19.04 | | | | | | | | | | | | | | (4241) ~ (all_42_0 = e1) % 133.26/19.04 | | | | | | | | | | | | | | (4242) op(e0, e2) = all_42_0 % 133.26/19.04 | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | BETA: splitting (208) gives: % 133.26/19.04 | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | (4243) all_57_15 = e0 & op(e0, e0) = e0 % 133.26/19.04 | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | ALPHA: (4243) implies: % 133.26/19.04 | | | | | | | | | | | | | | | (4244) op(e0, e0) = e0 % 133.26/19.04 | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | REF_CLOSE: (7), (4236), (4244), (function-axioms) are % 133.26/19.04 | | | | | | | | | | | | | | | inconsistent by sub-proof #715. % 133.26/19.04 | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | (4245) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 133.26/19.04 | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 133.26/19.04 | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 133.26/19.04 | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 133.26/19.04 | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 133.26/19.04 | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | ALPHA: (4245) implies: % 133.26/19.04 | | | | | | | | | | | | | | | (4246) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 133.26/19.04 | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 133.26/19.04 | | | | | | | | | | | | | | | e1) = e0) % 133.26/19.04 | | | | | | | | | | | | | | | (4247) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 133.26/19.04 | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, % 133.26/19.04 | | | | | | | | | | | | | | | e0) = e0) % 133.26/19.04 | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | BETA: splitting (4247) gives: % 133.26/19.04 | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | (4248) all_57_9 = e0 & op(e3, e0) = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4070), (4248), (function-axioms) are % 133.26/19.04 | | | | | | | | | | | | | | | | inconsistent by sub-proof #618. % 133.26/19.04 | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | (4249) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = % 133.26/19.04 | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 133.26/19.04 | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | BETA: splitting (4249) gives: % 133.26/19.04 | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | (4250) all_57_10 = e0 & op(e2, e0) = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | ALPHA: (4250) implies: % 133.26/19.04 | | | | | | | | | | | | | | | | | (4251) all_57_10 = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | (4252) op(e2, e0) = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (226), % 133.26/19.04 | | | | | | | | | | | | | | | | | (4145), (4146), (4251), (4252), (function-axioms) % 133.26/19.04 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #446. % 133.26/19.04 | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | (4253) all_57_11 = e0 & op(e1, e0) = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | ALPHA: (4253) implies: % 133.26/19.04 | | | | | | | | | | | | | | | | | (4254) op(e1, e0) = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, % 133.26/19.04 | | | | | | | | | | | | | | | | | all_42_0, e2, e0, simplifying with (158), (4242) % 133.26/19.04 | | | | | | | | | | | | | | | | | gives: % 133.26/19.04 | | | | | | | | | | | | | | | | | (4255) all_52_7 = all_42_0 % 133.26/19.04 | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 133.26/19.04 | | | | | | | | | | | | | | | | | e0, e0, e1, simplifying with (160), (4254) gives: % 133.26/19.04 | | | | | | | | | | | | | | | | | (4256) all_52_14 = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (4255) imply: % 133.26/19.04 | | | | | | | | | | | | | | | | | (4257) all_54_13 = all_42_0 % 133.26/19.04 | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | REDUCE: (4232), (4255) imply: % 133.26/19.04 | | | | | | | | | | | | | | | | | (4258) ~ (all_42_0 = e3) % 133.26/19.04 | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | REDUCE: (4138), (4255) imply: % 133.26/19.04 | | | | | | | | | | | | | | | | | (4259) ~ (all_42_0 = e0) % 133.26/19.04 | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | REDUCE: (366), (4256) imply: % 133.26/19.04 | | | | | | | | | | | | | | | | | (4260) ~ (all_6_2 = e0) % 133.26/19.04 | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | SIMP: (4260) implies: % 133.26/19.04 | | | | | | | | | | | | | | | | | (4261) ~ (all_6_2 = e0) % 133.26/19.04 | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 133.26/19.04 | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | (4262) all_54_10 = e3 % 133.26/19.04 | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (4077), (4262) are inconsistent by % 133.26/19.04 | | | | | | | | | | | | | | | | | | sub-proof #742. % 133.26/19.04 | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | (4263) ~ (all_54_10 = e3) % 133.26/19.04 | | | | | | | | | | | | | | | | | | (4264) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 133.26/19.04 | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | (4265) all_54_13 = e3 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4257), (4258), (4265) are inconsistent by % 133.26/19.04 | | | | | | | | | | | | | | | | | | | sub-proof #617. % 133.26/19.04 | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | (4266) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | BETA: splitting (4246) gives: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | (4267) all_57_12 = e0 & op(e0, e3) = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | ALPHA: (4267) implies: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | (4268) op(e0, e3) = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4067), (4268), (function-axioms) are % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219. % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | (4269) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4269) gives: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | (4270) all_57_13 = e0 & op(e0, e2) = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4270) implies: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | (4271) op(e0, e2) = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (4138), (4271), (function-axioms) are % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | (4272) all_57_14 = e0 & op(e0, e1) = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4272) implies: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | (4273) all_57_14 = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | (4274) op(e0, e1) = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4264) gives: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | (4275) all_54_10 = e2 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (372), (4275) are inconsistent by sub-proof % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | #741. % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | (4276) ~ (all_54_10 = e2) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | (4277) all_54_10 = e1 | all_54_10 = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4277) gives: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | (4278) all_54_10 = e1 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (4278) imply: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | (4279) all_6_2 = e1 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4279) implies: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | (4280) all_6_2 = e1 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4077), (4280) imply: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | (4281) ~ (e3 = e1) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (4280) imply: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | (4282) ~ (e2 = e1) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (4280) imply: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | (4283) op(e1, e1) = e1 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (4284) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4284) gives: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | (4285) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4285) gives: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (4286) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (168), (170), % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (221), (222), (232), (372), (4068), (4070), % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (4273), (4274), (4286), (function-axioms) are % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #222. % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (4287) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4287) implies: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | (4288) op(e3, e3) = e1 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4071), (4288), (function-axioms) are % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | (4289) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (4146), (4234), (4289), % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | #622. % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (4290) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4290) gives: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.04 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (4291) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (39), (4146), (4283), (4291), % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | #508. % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (4292) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4292) gives: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (4293) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4293) implies: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (4294) ~ (all_56_15 = e2) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (4295) op(e0, e2) = all_56_15 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4241), (4242), (4257), (4259), (4266), (4294), % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (4295), (function-axioms) are inconsistent by % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #539. % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (4296) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (42), (100), (157), (158), (159), % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (190), (199), (246), (267), (295), (354), (364), % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (373), (4067), (4073), (4233), (4236), % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (4296), (function-axioms) are inconsistent by % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #226. % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | (4297) all_54_10 = e0 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (4261), (4297) are inconsistent by % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #506. % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | (4298) ~ (all_42_1 = e3) & op(e0, e0) = all_42_1 & % 133.26/19.05 | | | | | | | | | | | | | | $i(all_42_1) % 133.26/19.05 | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | REF_CLOSE: (4236), (4298), (function-axioms) are inconsistent % 133.26/19.05 | | | | | | | | | | | | | | by sub-proof #602. % 133.26/19.05 | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | % 133.26/19.05 | | | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | (4299) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = % 133.26/19.05 | | | | | | | | | | e0 & op(e2, e0) = e0) % 133.26/19.05 | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | BETA: splitting (4299) gives: % 133.26/19.05 | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | (4300) all_57_5 = e0 & op(e2, e1) = e0 % 133.26/19.05 | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | REF_CLOSE: (165), (4139), (4300), (function-axioms) are % 133.26/19.05 | | | | | | | | | | | inconsistent by sub-proof #455. % 133.26/19.05 | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | (4301) all_57_10 = e0 & op(e2, e0) = e0 % 133.26/19.05 | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | ALPHA: (4301) implies: % 133.26/19.05 | | | | | | | | | | | (4302) all_57_10 = e0 % 133.26/19.05 | | | | | | | | | | | (4303) op(e2, e0) = e0 % 133.26/19.05 | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | BETA: splitting (227) gives: % 133.26/19.05 | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | (4304) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 133.26/19.05 | | | | | | | | | | | | & op(e2, e2) = e0) % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (224), (225), % 133.26/19.05 | | | | | | | | | | | | (226), (4068), (4302), (4303), (4304), % 133.26/19.05 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.05 | | | | | | | | | | | | #445. % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | (4305) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 133.26/19.05 | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | REF_CLOSE: (158), (162), (4137), (4138), (4305), % 133.26/19.05 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.05 | | | | | | | | | | | | #504. % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | % 133.26/19.05 | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | % 133.26/19.05 | | | | | | | | End of split % 133.26/19.05 | | | | | | | | % 133.26/19.05 | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | % 133.26/19.05 | | | | | | | | (4306) all_28_2 = e3 % 133.26/19.05 | | | | | | | | (4307) ( ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 & % 133.26/19.05 | | | | | | | | $i(all_28_0)) | ( ~ (all_28_1 = e0) & op(e3, e3) = % 133.26/19.05 | | | | | | | | all_28_1 & $i(all_28_1)) % 133.26/19.05 | | | | | | | | % 133.26/19.05 | | | | | | | | COMBINE_EQS: (316), (4306) imply: % 133.26/19.05 | | | | | | | | (4308) all_6_2 = e3 % 133.26/19.05 | | | | | | | | % 133.26/19.05 | | | | | | | | SIMP: (4308) implies: % 133.26/19.05 | | | | | | | | (4309) all_6_2 = e3 % 133.26/19.05 | | | | | | | | % 133.26/19.05 | | | | | | | | REDUCE: (361), (4309) imply: % 133.26/19.05 | | | | | | | | (4310) ~ (all_52_8 = e3) % 133.26/19.05 | | | | | | | | % 133.26/19.05 | | | | | | | | REDUCE: (362), (4309) imply: % 133.26/19.05 | | | | | | | | (4311) ~ (all_52_9 = e3) % 133.26/19.05 | | | | | | | | % 133.26/19.05 | | | | | | | | REDUCE: (364), (4309) imply: % 133.26/19.05 | | | | | | | | (4312) ~ (all_52_11 = e3) % 133.26/19.05 | | | | | | | | % 133.26/19.05 | | | | | | | | REDUCE: (39), (4309) imply: % 133.26/19.05 | | | | | | | | (4313) op(e1, e1) = e3 % 133.26/19.05 | | | | | | | | % 133.26/19.05 | | | | | | | | BETA: splitting (4307) gives: % 133.26/19.05 | | | | | | | | % 133.26/19.05 | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | % 133.26/19.05 | | | | | | | | | (4314) ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 & % 133.26/19.05 | | | | | | | | | $i(all_28_0) % 133.26/19.05 | | | | | | | | | % 133.26/19.05 | | | | | | | | | ALPHA: (4314) implies: % 133.26/19.05 | | | | | | | | | (4315) ~ (all_28_0 = e2) % 133.26/19.05 | | | | | | | | | (4316) op(e3, e1) = all_28_0 % 133.26/19.05 | | | | | | | | | % 133.26/19.05 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 133.26/19.05 | | | | | | | | | all_28_0, e1, e3, simplifying with (169), (4316) % 133.26/19.05 | | | | | | | | | gives: % 133.26/19.05 | | | | | | | | | (4317) all_52_8 = all_28_0 % 133.26/19.05 | | | | | | | | | % 133.26/19.05 | | | | | | | | | COMBINE_EQS: (270), (4317) imply: % 133.26/19.05 | | | | | | | | | (4318) all_54_2 = all_28_0 % 133.26/19.05 | | | | | | | | | % 133.26/19.05 | | | | | | | | | REDUCE: (134), (4317) imply: % 133.26/19.05 | | | | | | | | | (4319) ~ (all_52_4 = all_28_0) % 133.26/19.05 | | | | | | | | | % 133.26/19.05 | | | | | | | | | REDUCE: (123), (4317) imply: % 133.26/19.05 | | | | | | | | | (4320) ~ (all_52_9 = all_28_0) % 133.26/19.05 | | | | | | | | | % 133.26/19.05 | | | | | | | | | SIMP: (4320) implies: % 133.26/19.05 | | | | | | | | | (4321) ~ (all_52_9 = all_28_0) % 133.26/19.05 | | | | | | | | | % 133.26/19.05 | | | | | | | | | REDUCE: (121), (4317) imply: % 133.26/19.05 | | | | | | | | | (4322) ~ (all_52_11 = all_28_0) % 133.26/19.05 | | | | | | | | | % 133.26/19.05 | | | | | | | | | SIMP: (4322) implies: % 133.26/19.05 | | | | | | | | | (4323) ~ (all_52_11 = all_28_0) % 133.26/19.05 | | | | | | | | | % 133.26/19.05 | | | | | | | | | REDUCE: (120), (4317) imply: % 133.26/19.05 | | | | | | | | | (4324) ~ (all_52_12 = all_28_0) % 133.26/19.05 | | | | | | | | | % 133.26/19.05 | | | | | | | | | SIMP: (4324) implies: % 133.26/19.05 | | | | | | | | | (4325) ~ (all_52_12 = all_28_0) % 133.26/19.05 | | | | | | | | | % 133.26/19.05 | | | | | | | | | REDUCE: (4310), (4317) imply: % 133.26/19.05 | | | | | | | | | (4326) ~ (all_28_0 = e3) % 133.26/19.05 | | | | | | | | | % 133.26/19.05 | | | | | | | | | REDUCE: (4069), (4317) imply: % 133.26/19.05 | | | | | | | | | (4327) ~ (all_28_0 = e0) % 133.26/19.05 | | | | | | | | | % 133.26/19.05 | | | | | | | | | BETA: splitting (202) gives: % 133.26/19.05 | | | | | | | | | % 133.26/19.05 | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | (4328) all_54_2 = e3 % 133.26/19.05 | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | COMBINE_EQS: (4318), (4328) imply: % 133.26/19.05 | | | | | | | | | | (4329) all_28_0 = e3 % 133.26/19.05 | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | REDUCE: (4326), (4329) imply: % 133.26/19.05 | | | | | | | | | | (4330) $false % 133.26/19.05 | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | CLOSE: (4330) is inconsistent. % 133.26/19.05 | | | | | | | | | | % 133.26/19.05 | | | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | (4331) ~ (all_54_2 = e3) % 133.26/19.05 | | | | | | | | | | (4332) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 133.26/19.05 | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | BETA: splitting (4332) gives: % 133.26/19.05 | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | (4333) all_54_2 = e2 % 133.26/19.05 | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | COMBINE_EQS: (4318), (4333) imply: % 133.26/19.05 | | | | | | | | | | | (4334) all_28_0 = e2 % 133.26/19.05 | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | REDUCE: (4315), (4334) imply: % 133.26/19.05 | | | | | | | | | | | (4335) $false % 133.26/19.05 | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | CLOSE: (4335) is inconsistent. % 133.26/19.05 | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | (4336) ~ (all_54_2 = e2) % 133.26/19.05 | | | | | | | | | | | (4337) all_54_2 = e1 | all_54_2 = e0 % 133.26/19.05 | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | BETA: splitting (4337) gives: % 133.26/19.05 | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | (4338) all_54_2 = e1 % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | COMBINE_EQS: (4318), (4338) imply: % 133.26/19.05 | | | | | | | | | | | | (4339) all_28_0 = e1 % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | REDUCE: (4319), (4339) imply: % 133.26/19.05 | | | | | | | | | | | | (4340) ~ (all_52_4 = e1) % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | REDUCE: (4321), (4339) imply: % 133.26/19.05 | | | | | | | | | | | | (4341) ~ (all_52_9 = e1) % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | REDUCE: (4323), (4339) imply: % 133.26/19.05 | | | | | | | | | | | | (4342) ~ (all_52_11 = e1) % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | REDUCE: (4325), (4339) imply: % 133.26/19.05 | | | | | | | | | | | | (4343) ~ (all_52_12 = e1) % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | REDUCE: (4326), (4339) imply: % 133.26/19.05 | | | | | | | | | | | | (4344) ~ (e3 = e1) % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | REDUCE: (4315), (4339) imply: % 133.26/19.05 | | | | | | | | | | | | (4345) ~ (e2 = e1) % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | REDUCE: (4316), (4339) imply: % 133.26/19.05 | | | | | | | | | | | | (4346) op(e3, e1) = e1 % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | BETA: splitting (220) gives: % 133.26/19.05 | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | (4347) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 133.26/19.05 | | | | | | | | | | | | | & op(e2, e1) = e1) % 133.26/19.05 | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | BETA: splitting (4347) gives: % 133.26/19.05 | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | (4348) all_57_4 = e1 & op(e3, e1) = e1 % 133.26/19.05 | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | ALPHA: (4348) implies: % 133.26/19.05 | | | | | | | | | | | | | | (4349) all_57_4 = e1 % 133.26/19.05 | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | BETA: splitting (76) gives: % 133.26/19.05 | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | (4350) ~ (all_30_2 = e0) % 133.26/19.05 | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | REDUCE: (309), (4350) imply: % 133.26/19.05 | | | | | | | | | | | | | | | (4351) ~ (all_8_2 = e0) % 133.26/19.05 | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | BETA: splitting (199) gives: % 133.26/19.05 | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | (4352) all_54_5 = e3 % 133.26/19.05 | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | REF_CLOSE: (267), (4073), (4352) are inconsistent by % 133.26/19.05 | | | | | | | | | | | | | | | | sub-proof #554. % 133.26/19.05 | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | (4353) ~ (all_54_5 = e3) % 133.26/19.05 | | | | | | | | | | | | | | | | (4354) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 133.26/19.05 | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | BETA: splitting (4354) gives: % 133.26/19.05 | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | (4355) all_54_5 = e2 % 133.26/19.05 | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (4355) imply: % 133.26/19.05 | | | | | | | | | | | | | | | | | (4356) all_8_2 = e2 % 133.26/19.05 | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | SIMP: (4356) implies: % 133.26/19.05 | | | | | | | | | | | | | | | | | (4357) all_8_2 = e2 % 133.26/19.05 | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | REDUCE: (350), (4357) imply: % 133.26/19.05 | | | | | | | | | | | | | | | | | (4358) ~ (all_52_4 = e2) % 133.26/19.05 | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | REDUCE: (356), (4357) imply: % 133.26/19.05 | | | | | | | | | | | | | | | | | (4359) ~ (all_52_9 = e2) % 133.26/19.05 | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | REDUCE: (358), (4357) imply: % 133.26/19.05 | | | | | | | | | | | | | | | | | (4360) ~ (all_52_13 = e2) % 133.26/19.05 | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | REDUCE: (4073), (4357) imply: % 133.26/19.05 | | | | | | | | | | | | | | | | | (4361) ~ (e3 = e2) % 133.26/19.05 | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 133.26/19.05 | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | (4362) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 133.26/19.05 | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 133.26/19.05 | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | BETA: splitting (4362) gives: % 133.26/19.05 | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | (4363) all_57_4 = e2 & op(e3, e1) = e2 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4315), (4316), (4363), (function-axioms) are % 133.26/19.05 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #218. % 133.26/19.05 | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | (4364) all_57_5 = e2 & op(e2, e1) = e2 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | ALPHA: (4364) implies: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | (4365) op(e2, e1) = e2 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4359), (4365), (function-axioms) are % 133.26/19.05 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770. % 133.26/19.05 | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | (4366) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 133.26/19.05 | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | BETA: splitting (4366) gives: % 133.26/19.05 | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | (4367) all_57_8 = e2 & op(e1, e1) = e2 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | ALPHA: (4367) implies: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | (4368) op(e1, e1) = e2 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (4368), (function-axioms) are % 133.26/19.05 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 133.26/19.05 | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | (4369) all_57_14 = e2 & op(e0, e1) = e2 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | ALPHA: (4369) implies: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | (4370) op(e0, e1) = e2 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (4371) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4371) gives: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | (4372) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4372) gives: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (4373) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4373) implies: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (4374) op(e3, e3) = e2 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4071), (4374), (function-axioms) are % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (4375) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4375) implies: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (4376) op(e3, e3) = e1 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236), % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (238), (4068), (4349), (4376), (function-axioms) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #667. % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | (4377) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4377) gives: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (4378) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (133), (168), (203), (271), (4068), (4340), % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (4358), (4378), (function-axioms) are inconsistent % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #217. % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (4379) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4379) implies: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | (4380) op(e2, e2) = e3 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (4073), (4380), (function-axioms) are % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228. % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (4381) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.05 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4381) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (4382) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4346), (4359), (4382), (function-axioms) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #348. % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (4383) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4383) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4384) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4384) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4385) op(e2, e0) = e2 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4360), (4385), (function-axioms) are % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4386) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4386) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4387) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4387) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4388) op(e1, e1) = e2 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (4388), (function-axioms) are % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4389) op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4389) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4390) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4390) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | (4391) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4391) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4392) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4392) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4393) ~ (all_56_17 = e1) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4394) op(e3, e1) = all_56_17 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4346), (4393), (4394), (function-axioms) are % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349. % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4395) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4395) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4396) ~ (all_56_11 = e2) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4397) op(e0, e2) = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4398) op(e2, e2) = all_56_11 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (158), (199), (267), (354), (373), (4073), % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4396), (4397), (4398), (function-axioms) are % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #227. % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | (4399) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4399) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4400) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4400) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4401) op(e1, e1) = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4313), (4401), (function-axioms) are % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4402) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4402) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4403) op(e0, e1) = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4370), (4403), (function-axioms) are % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660. % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.06 | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | End of split % 133.26/19.06 | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | End of split % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | (4404) all_54_5 = e1 | all_54_5 = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (373), (4351), (4404) are inconsistent by % 133.26/19.06 | | | | | | | | | | | | | | | | | sub-proof #624. % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | End of split % 133.26/19.06 | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | End of split % 133.26/19.06 | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | (4405) all_30_2 = e0 % 133.26/19.06 | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | COMBINE_EQS: (309), (4405) imply: % 133.26/19.06 | | | | | | | | | | | | | | | (4406) all_8_2 = e0 % 133.26/19.06 | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | SIMP: (4406) implies: % 133.26/19.06 | | | | | | | | | | | | | | | (4407) all_8_2 = e0 % 133.26/19.06 | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | REDUCE: (356), (4407) imply: % 133.26/19.06 | | | | | | | | | | | | | | | (4408) ~ (all_52_9 = e0) % 133.26/19.06 | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | REDUCE: (358), (4407) imply: % 133.26/19.06 | | | | | | | | | | | | | | | (4409) ~ (all_52_13 = e0) % 133.26/19.06 | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | REDUCE: (4073), (4407) imply: % 133.26/19.06 | | | | | | | | | | | | | | | (4410) ~ (e3 = e0) % 133.26/19.06 | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | REDUCE: (373), (4407) imply: % 133.26/19.06 | | | | | | | | | | | | | | | (4411) ~ (e1 = e0) % 133.26/19.06 | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | REDUCE: (42), (4407) imply: % 133.26/19.06 | | | | | | | | | | | | | | | (4412) op(e2, e2) = e0 % 133.26/19.06 | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 133.26/19.06 | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | (4413) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 133.26/19.06 | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | BETA: splitting (4413) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | (4414) all_57_4 = e0 & op(e3, e1) = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | ALPHA: (4414) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | (4415) op(e3, e1) = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4346), (4415), (function-axioms) are % 133.26/19.06 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #343. % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | (4416) all_57_5 = e0 & op(e2, e1) = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4408), (4416), (function-axioms) are % 133.26/19.06 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #455. % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | End of split % 133.26/19.06 | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | (4417) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 133.26/19.06 | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 133.26/19.06 | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | BETA: splitting (4417) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | (4418) all_57_8 = e0 & op(e1, e1) = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | ALPHA: (4418) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | (4419) op(e1, e1) = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4313), (4419), (function-axioms) are % 133.26/19.06 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | (4420) all_57_14 = e0 & op(e0, e1) = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | ALPHA: (4420) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | (4421) all_57_14 = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | (4422) all_54_6 = e3 % 133.26/19.06 | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (4422) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | (4423) all_52_9 = e3 % 133.26/19.06 | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | REDUCE: (4311), (4423) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | (4424) $false % 133.26/19.06 | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | CLOSE: (4424) is inconsistent. % 133.26/19.06 | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | (4425) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | BETA: splitting (4425) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | (4426) all_54_6 = e2 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (4426) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | (4427) all_52_9 = e2 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | REDUCE: (118), (4427) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | (4428) ~ (all_52_11 = e2) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | SIMP: (4428) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | (4429) ~ (all_52_11 = e2) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | (4430) all_54_14 = e3 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4430) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | (4431) all_52_11 = e3 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | REDUCE: (4312), (4431) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | (4432) $false % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | CLOSE: (4432) is inconsistent. % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | (4433) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4433) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (4434) all_54_14 = e2 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4434) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (4435) all_52_11 = e2 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4429), (4435) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (4436) $false % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | CLOSE: (4436) is inconsistent. % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | (4437) all_54_14 = e1 | all_54_14 = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4437) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4438) all_54_14 = e1 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4438) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4439) all_52_11 = e1 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4342), (4439) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4440) $false % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4440) is inconsistent. % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4441) all_54_14 = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4441) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4442) all_52_11 = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (4442) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4443) ~ (all_52_7 = e0) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (4442) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4444) ~ (all_4_2 = e0) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4444) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4445) ~ (all_4_2 = e0) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (4442) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | (4446) op(e0, e1) = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4447) all_54_15 = e3 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (4447) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4448) all_4_2 = e3 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (4448) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4449) all_34_2 = e3 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (4448) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4450) ~ (all_52_12 = e3) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (4448) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4451) ~ (all_52_13 = e3) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (4448) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | (4452) op(e0, e0) = e3 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | (4453) all_54_3 = e3 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (4450), (4453) are inconsistent by % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #216. % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | (4454) ~ (all_54_3 = e3) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | (4455) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4455) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4456) all_54_3 = e2 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4456) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4457) all_52_12 = e2 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4457) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4458) all_52_12 = e2 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (4458) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4459) ~ (all_52_4 = e2) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (4458) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4460) ~ (all_52_13 = e2) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4460) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4461) ~ (all_52_13 = e2) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4450), (4458) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4462) ~ (e3 = e2) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (4458) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | (4463) op(e3, e0) = e2 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (4464) ~ (all_34_2 = e3) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4449), (4464) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (4465) $false % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4465) is inconsistent. % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (4466) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_34_1 & $i(all_34_1)) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4466) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4467) ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_0) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4467) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4468) ~ (all_34_0 = e2) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4469) op(e3, e0) = all_34_0 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4463), (4468), (4469), (function-axioms) are % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #551. % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4470) ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 & % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_1) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4470) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4471) ~ (all_34_1 = e1) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4472) op(e3, e3) = all_34_1 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4473) all_54_7 = e3 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (4451), (4473) are inconsistent by % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #338. % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4474) ~ (all_54_7 = e3) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4475) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4475) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4476) all_54_7 = e2 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (4461), (4476) are inconsistent by % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #337. % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4477) ~ (all_54_7 = e2) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4478) all_54_7 = e1 | all_54_7 = e0 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4478) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4479) all_54_7 = e1 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (4479) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4480) all_52_13 = e1 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4480) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4481) all_52_13 = e1 % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (4481) imply: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4482) ~ (all_52_14 = e1) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4482) implies: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4483) ~ (all_52_14 = e1) % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4484) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4484) gives: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4485) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4485) gives: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4486) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (168), (170), % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (221), (222), (232), (372), (4068), (4070), % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4421), (4446), (4486), (function-axioms) are % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #222. % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4487) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4487) implies: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4488) op(e3, e3) = e1 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4471), (4472), (4488), (function-axioms) are % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #626. % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4489) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (133), (168), (203), (271), (4068), (4340), % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4412), (4459), (4489), (function-axioms) are % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #215. % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4490) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4490) gives: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4491) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4491) gives: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4492) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4492) implies: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4493) ~ (all_56_17 = e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4494) op(e3, e1) = all_56_17 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4346), (4493), (4494), (function-axioms) are % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349. % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4495) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4495) implies: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4496) op(e2, e2) = e1 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4412), (4496), (function-axioms) are % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4497) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4497) gives: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4498) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4498) implies: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4499) op(e2, e0) = e2 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4461), (4499), (function-axioms) are % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4500) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4500) gives: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4501) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4501) implies: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4502) op(e1, e1) = e2 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (4502), (function-axioms) are % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4503) op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4503) implies: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4504) op(e0, e0) = all_56_31 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4505) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4505) gives: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4506) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4506) gives: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4507) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4507) implies: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4508) ~ (all_56_17 = e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4509) op(e3, e1) = all_56_17 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4346), (4508), (4509), (function-axioms) are % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349. % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4510) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4510) implies: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4511) op(e0, e2) = e0 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (4443), (4511), (function-axioms) are % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4512) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4512) gives: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4513) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4513) implies: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4514) op(e1, e0) = e1 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4483), (4514), (function-axioms) are % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #327. % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4515) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4515) implies: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4516) all_56_31 = e1 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4504), (4516) imply: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4517) op(e0, e0) = e1 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4452), (4517), (function-axioms) are % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606. % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4518) all_54_7 = e0 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (4409), (4518) are inconsistent by % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #326. % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | (4519) all_54_3 = e1 | all_54_3 = e0 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (4070), (4343), (4519) are inconsistent by % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #321. % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | (4520) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (4075), (4445), (4520) are % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #746. % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | (4521) all_54_6 = e1 | all_54_6 = e0 % 133.26/19.07 | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (4341), (4408), (4521) are inconsistent by % 133.26/19.07 | | | | | | | | | | | | | | | | | | | sub-proof #479. % 133.26/19.07 | | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | (4522) all_57_5 = e1 & op(e2, e1) = e1 % 133.26/19.07 | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | ALPHA: (4522) implies: % 133.26/19.07 | | | | | | | | | | | | | | (4523) all_57_5 = e1 % 133.26/19.07 | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (219), (221), (372), % 133.26/19.07 | | | | | | | | | | | | | | (4313), (4315), (4316), (4346), (4523), % 133.26/19.07 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.07 | | | | | | | | | | | | | | #214. % 133.26/19.07 | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | (4524) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 133.26/19.07 | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 133.26/19.07 | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | BETA: splitting (4524) gives: % 133.26/19.07 | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | Case 1: % 133.26/19.07 | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | (4525) all_57_8 = e1 & op(e1, e1) = e1 % 133.26/19.07 | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | ALPHA: (4525) implies: % 133.26/19.07 | | | | | | | | | | | | | | (4526) op(e1, e1) = e1 % 133.26/19.07 | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (4313), (4526), (function-axioms) are % 133.26/19.07 | | | | | | | | | | | | | | inconsistent by sub-proof #662. % 133.26/19.07 | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | (4527) all_57_14 = e1 & op(e0, e1) = e1 % 133.26/19.07 | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | ALPHA: (4527) implies: % 133.26/19.07 | | | | | | | | | | | | | | (4528) all_57_14 = e1 % 133.26/19.07 | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (219), (221), (372), % 133.26/19.07 | | | | | | | | | | | | | | (4313), (4315), (4316), (4346), (4528), % 133.26/19.07 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.07 | | | | | | | | | | | | | | #212. % 133.26/19.07 | | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | (4529) all_54_2 = e0 % 133.26/19.07 | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | COMBINE_EQS: (4318), (4529) imply: % 133.26/19.07 | | | | | | | | | | | | (4530) all_28_0 = e0 % 133.26/19.07 | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | REDUCE: (4327), (4530) imply: % 133.26/19.07 | | | | | | | | | | | | (4531) $false % 133.26/19.07 | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | | CLOSE: (4531) is inconsistent. % 133.26/19.07 | | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | | % 133.26/19.07 | | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | | % 133.26/19.07 | | | | | | | | | End of split % 133.26/19.07 | | | | | | | | | % 133.26/19.07 | | | | | | | | Case 2: % 133.26/19.07 | | | | | | | | | % 133.26/19.07 | | | | | | | | | (4532) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 & % 133.26/19.07 | | | | | | | | | $i(all_28_1) % 133.26/19.07 | | | | | | | | | % 133.26/19.07 | | | | | | | | | REF_CLOSE: (4071), (4532), (function-axioms) are inconsistent % 133.26/19.07 | | | | | | | | | by sub-proof #211. % 133.26/19.07 | | | | | | | | | % 133.26/19.07 | | | | | | | | End of split % 133.26/19.07 | | | | | | | | % 133.26/19.07 | | | | | | | End of split % 133.26/19.07 | | | | | | | % 133.26/19.07 | | | | | | Case 2: % 133.26/19.07 | | | | | | | % 133.26/19.07 | | | | | | | (4533) all_20_2 = e2 % 133.26/19.07 | | | | | | | % 133.26/19.07 | | | | | | | COMBINE_EQS: (318), (4533) imply: % 133.26/19.08 | | | | | | | (4534) all_4_2 = e2 % 133.26/19.08 | | | | | | | % 133.26/19.08 | | | | | | | SIMP: (4534) implies: % 133.26/19.08 | | | | | | | (4535) all_4_2 = e2 % 133.26/19.08 | | | | | | | % 133.26/19.08 | | | | | | | REDUCE: (349), (4535) imply: % 133.26/19.08 | | | | | | | (4536) ~ (all_52_3 = e2) % 133.26/19.08 | | | | | | | % 133.26/19.08 | | | | | | | REDUCE: (368), (4535) imply: % 133.26/19.08 | | | | | | | (4537) ~ (all_52_12 = e2) % 133.26/19.08 | | | | | | | % 133.26/19.08 | | | | | | | REDUCE: (369), (4535) imply: % 133.26/19.08 | | | | | | | (4538) ~ (all_52_13 = e2) % 133.26/19.08 | | | | | | | % 133.26/19.08 | | | | | | | REDUCE: (36), (4535) imply: % 133.26/19.08 | | | | | | | (4539) op(e0, e0) = e2 % 133.26/19.08 | | | | | | | % 133.26/19.08 | | | | | | | BETA: splitting (67) gives: % 133.26/19.08 | | | | | | | % 133.26/19.08 | | | | | | | Case 1: % 133.26/19.08 | | | | | | | | % 133.26/19.08 | | | | | | | | (4540) ~ (all_24_2 = e0) % 133.26/19.08 | | | | | | | | % 133.26/19.08 | | | | | | | | REDUCE: (4065), (4540) imply: % 133.26/19.08 | | | | | | | | (4541) $false % 133.26/19.08 | | | | | | | | % 133.26/19.08 | | | | | | | | CLOSE: (4541) is inconsistent. % 133.26/19.08 | | | | | | | | % 133.26/19.08 | | | | | | | Case 2: % 133.26/19.08 | | | | | | | | % 133.26/19.08 | | | | | | | | (4542) ( ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 & % 133.26/19.08 | | | | | | | | $i(all_24_0)) | ( ~ (all_24_1 = e2) & op(e0, e0) = % 133.26/19.08 | | | | | | | | all_24_1 & $i(all_24_1)) % 133.26/19.08 | | | | | | | | % 133.26/19.08 | | | | | | | | BETA: splitting (4542) gives: % 133.26/19.08 | | | | | | | | % 133.26/19.08 | | | | | | | | Case 1: % 133.26/19.08 | | | | | | | | | % 133.26/19.08 | | | | | | | | | (4543) ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 & % 133.26/19.08 | | | | | | | | | $i(all_24_0) % 133.26/19.08 | | | | | | | | | % 133.26/19.08 | | | | | | | | | ALPHA: (4543) implies: % 133.26/19.08 | | | | | | | | | (4544) ~ (all_24_0 = e1) % 133.26/19.08 | | | | | | | | | (4545) op(e0, e3) = all_24_0 % 133.26/19.08 | | | | | | | | | % 133.26/19.08 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, % 133.26/19.08 | | | | | | | | | all_24_0, e3, e0, simplifying with (159), (4545) % 133.26/19.08 | | | | | | | | | gives: % 133.26/19.08 | | | | | | | | | (4546) all_52_3 = all_24_0 % 133.26/19.08 | | | | | | | | | % 133.26/19.08 | | | | | | | | | COMBINE_EQS: (248), (4546) imply: % 133.26/19.08 | | | | | | | | | (4547) all_54_12 = all_24_0 % 133.26/19.08 | | | | | | | | | % 133.26/19.08 | | | | | | | | | REDUCE: (148), (4546) imply: % 133.26/19.08 | | | | | | | | | (4548) ~ (all_52_1 = all_24_0) % 133.26/19.08 | | | | | | | | | % 133.26/19.08 | | | | | | | | | REDUCE: (144), (4546) imply: % 133.26/19.08 | | | | | | | | | (4549) ~ (all_52_2 = all_24_0) % 133.26/19.08 | | | | | | | | | % 133.26/19.08 | | | | | | | | | REDUCE: (140), (4546) imply: % 133.26/19.08 | | | | | | | | | (4550) ~ (all_52_7 = all_24_0) % 133.26/19.08 | | | | | | | | | % 133.26/19.08 | | | | | | | | | SIMP: (4550) implies: % 133.26/19.08 | | | | | | | | | (4551) ~ (all_52_7 = all_24_0) % 133.26/19.08 | | | | | | | | | % 133.26/19.08 | | | | | | | | | REDUCE: (139), (4546) imply: % 133.26/19.08 | | | | | | | | | (4552) ~ (all_52_11 = all_24_0) % 133.26/19.08 | | | | | | | | | % 133.26/19.08 | | | | | | | | | SIMP: (4552) implies: % 133.26/19.08 | | | | | | | | | (4553) ~ (all_52_11 = all_24_0) % 133.26/19.08 | | | | | | | | | % 133.26/19.08 | | | | | | | | | REDUCE: (4536), (4546) imply: % 133.26/19.08 | | | | | | | | | (4554) ~ (all_24_0 = e2) % 133.26/19.08 | | | | | | | | | % 133.26/19.08 | | | | | | | | | REDUCE: (4067), (4546) imply: % 133.26/19.08 | | | | | | | | | (4555) ~ (all_24_0 = e0) % 133.26/19.08 | | | | | | | | | % 133.26/19.08 | | | | | | | | | BETA: splitting (192) gives: % 133.26/19.08 | | | | | | | | | % 133.26/19.08 | | | | | | | | | Case 1: % 133.26/19.08 | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | (4556) all_54_12 = e3 % 133.26/19.08 | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | COMBINE_EQS: (4547), (4556) imply: % 133.26/19.08 | | | | | | | | | | (4557) all_24_0 = e3 % 133.26/19.08 | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | REDUCE: (4548), (4557) imply: % 133.26/19.08 | | | | | | | | | | (4558) ~ (all_52_1 = e3) % 133.26/19.08 | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | REDUCE: (4549), (4557) imply: % 133.26/19.08 | | | | | | | | | | (4559) ~ (all_52_2 = e3) % 133.26/19.08 | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | REDUCE: (4551), (4557) imply: % 133.26/19.08 | | | | | | | | | | (4560) ~ (all_52_7 = e3) % 133.26/19.08 | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | REDUCE: (4553), (4557) imply: % 133.26/19.08 | | | | | | | | | | (4561) ~ (all_52_11 = e3) % 133.26/19.08 | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | BETA: splitting (237) gives: % 133.26/19.08 | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | Case 1: % 133.26/19.08 | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | (4562) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 133.26/19.08 | | | | | | | | | | | & op(e2, e3) = e3) % 133.26/19.08 | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | REF_CLOSE: (7), (167), (4071), (4558), (4562), % 133.26/19.08 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.08 | | | | | | | | | | | #210. % 133.26/19.08 | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | Case 2: % 133.26/19.08 | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | (4563) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 133.26/19.08 | | | | | | | | | | | e3 & op(e0, e3) = e3) % 133.26/19.08 | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | BETA: splitting (4563) gives: % 133.26/19.08 | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | Case 1: % 133.26/19.08 | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | (4564) all_57_6 = e3 & op(e1, e3) = e3 % 133.26/19.08 | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | REF_CLOSE: (163), (4559), (4564), (function-axioms) are % 133.26/19.08 | | | | | | | | | | | | inconsistent by sub-proof #761. % 133.26/19.08 | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | Case 2: % 133.26/19.08 | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | (4565) all_57_12 = e3 & op(e0, e3) = e3 % 133.26/19.08 | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | ALPHA: (4565) implies: % 133.26/19.08 | | | | | | | | | | | | (4566) all_57_12 = e3 % 133.26/19.08 | | | | | | | | | | | | (4567) op(e0, e3) = e3 % 133.26/19.08 | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | BETA: splitting (73) gives: % 133.26/19.08 | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | Case 1: % 133.26/19.08 | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | (4568) ~ (all_28_2 = e3) % 133.26/19.08 | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | REDUCE: (316), (4568) imply: % 133.26/19.08 | | | | | | | | | | | | | (4569) ~ (all_6_2 = e3) % 133.26/19.08 | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.26/19.08 | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | Case 1: % 133.26/19.08 | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | (4570) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.26/19.08 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.08 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.26/19.08 | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.26/19.08 | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.08 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.08 | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.08 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.08 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.26/19.08 | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.26/19.08 | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.08 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.26/19.08 | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.08 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.08 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.26/19.08 | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.08 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.08 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.08 | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.08 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.08 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.08 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.08 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.26/19.08 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.26/19.08 | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | BETA: splitting (4570) gives: % 133.26/19.08 | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | Case 1: % 133.26/19.08 | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | (4571) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.26/19.08 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.08 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.26/19.08 | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.26/19.08 | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.08 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.08 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.08 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.08 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.26/19.08 | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.26/19.08 | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.08 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.26/19.08 | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (4071), (4571), (function-axioms) are % 133.26/19.08 | | | | | | | | | | | | | | | inconsistent by sub-proof #229. % 133.26/19.08 | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | Case 2: % 133.26/19.08 | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | (4572) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.08 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.08 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.26/19.08 | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.08 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.08 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.08 | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.08 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.08 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.08 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.08 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.26/19.08 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.26/19.08 | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | BETA: splitting (4572) gives: % 133.26/19.08 | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | Case 1: % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | (4573) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.08 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.26/19.08 | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 133.26/19.08 | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.08 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.26/19.08 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | ALPHA: (4573) implies: % 133.26/19.08 | | | | | | | | | | | | | | | | (4574) ~ (all_56_7 = e3) % 133.26/19.08 | | | | | | | | | | | | | | | | (4575) op(e0, e3) = all_56_7 % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_7, % 133.26/19.08 | | | | | | | | | | | | | | | | e3, e0, simplifying with (4567), (4575) gives: % 133.26/19.08 | | | | | | | | | | | | | | | | (4576) all_56_7 = e3 % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | REDUCE: (4574), (4576) imply: % 133.26/19.08 | | | | | | | | | | | | | | | | (4577) $false % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | CLOSE: (4577) is inconsistent. % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | Case 2: % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | (4578) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.08 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.26/19.08 | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.08 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.08 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 133.26/19.08 | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | ALPHA: (4578) implies: % 133.26/19.08 | | | | | | | | | | | | | | | | (4579) op(e2, e2) = e3 % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | REF_CLOSE: (42), (4073), (4579), (function-axioms) are % 133.26/19.08 | | | | | | | | | | | | | | | | inconsistent by sub-proof #228. % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | End of split % 133.26/19.08 | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | End of split % 133.26/19.08 | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | Case 2: % 133.26/19.08 | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | (4580) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.08 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.08 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.08 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.08 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.08 | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.08 | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.08 | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.08 | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.08 | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.08 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.08 | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.26/19.08 | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.26/19.08 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.08 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.26/19.08 | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.08 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.26/19.08 | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.26/19.08 | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.26/19.08 | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.08 | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.08 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.26/19.08 | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.26/19.08 | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.26/19.08 | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.26/19.08 | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.26/19.08 | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.26/19.08 | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.08 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.26/19.08 | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.26/19.08 | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.26/19.08 | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.26/19.08 | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.26/19.08 | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.08 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.08 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.26/19.08 | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.26/19.08 | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.26/19.08 | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.26/19.08 | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.26/19.08 | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.26/19.08 | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.26/19.08 | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.08 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.08 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.08 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.08 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.08 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.08 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.08 | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.08 | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | BETA: splitting (4580) gives: % 133.26/19.08 | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | Case 1: % 133.26/19.08 | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | (4581) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.08 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.08 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.08 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.08 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.08 | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.08 | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.08 | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.08 | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.08 | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.08 | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.08 | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.26/19.08 | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | BETA: splitting (4581) gives: % 133.26/19.08 | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | Case 1: % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | (4582) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.08 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.26/19.08 | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.08 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.08 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 133.26/19.08 | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | ALPHA: (4582) implies: % 133.26/19.08 | | | | | | | | | | | | | | | | (4583) op(e1, e1) = e3 % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | REF_CLOSE: (39), (4569), (4583), (function-axioms) are % 133.26/19.08 | | | | | | | | | | | | | | | | inconsistent by sub-proof #771. % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | Case 2: % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | (4584) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 133.26/19.08 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.26/19.08 | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 133.26/19.08 | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.08 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.26/19.08 | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | ALPHA: (4584) implies: % 133.26/19.08 | | | | | | | | | | | | | | | | (4585) op(e2, e2) = e1 % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e1, % 133.26/19.08 | | | | | | | | | | | | | | | | e2, e2, simplifying with (42), (4585) gives: % 133.26/19.08 | | | | | | | | | | | | | | | | (4586) all_8_2 = e1 % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | REDUCE: (373), (4586) imply: % 133.26/19.08 | | | | | | | | | | | | | | | | (4587) $false % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | CLOSE: (4587) is inconsistent. % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | End of split % 133.26/19.08 | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | Case 2: % 133.26/19.08 | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | (4588) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.26/19.08 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.08 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.26/19.08 | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.08 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.08 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.08 | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.08 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.08 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.26/19.08 | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.08 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.26/19.08 | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.08 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.08 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.26/19.08 | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.26/19.08 | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.08 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.26/19.08 | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.26/19.08 | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.26/19.08 | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.26/19.08 | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.26/19.08 | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.26/19.08 | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.08 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.26/19.08 | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.26/19.08 | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.08 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.08 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.08 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.08 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.08 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.08 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.08 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.08 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.08 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.08 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.08 | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.08 | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | BETA: splitting (4588) gives: % 133.26/19.08 | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | Case 1: % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | (4589) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.26/19.08 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.26/19.08 | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.26/19.08 | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.08 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.26/19.08 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | ALPHA: (4589) implies: % 133.26/19.08 | | | | | | | | | | | | | | | | (4590) op(e2, e0) = e2 % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4538), (4590), (function-axioms) are % 133.26/19.08 | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | Case 2: % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | (4591) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.08 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.08 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.26/19.08 | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.08 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.26/19.08 | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.08 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.08 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.26/19.08 | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.26/19.08 | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.08 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.26/19.08 | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.26/19.08 | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.26/19.08 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.26/19.08 | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.26/19.08 | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.26/19.08 | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.08 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.26/19.08 | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.26/19.08 | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.08 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.08 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.08 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.08 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.08 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.08 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.08 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.08 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.08 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.08 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.08 | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | BETA: splitting (4591) gives: % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | Case 1: % 133.26/19.08 | | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | | (4592) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.08 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.26/19.08 | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.08 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.08 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 133.26/19.08 | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.26/19.08 | | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | | ALPHA: (4592) implies: % 133.26/19.08 | | | | | | | | | | | | | | | | | (4593) op(e1, e1) = e2 % 133.26/19.08 | | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (4593), (function-axioms) are % 133.26/19.08 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 133.26/19.08 | | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | Case 2: % 133.26/19.08 | | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | | (4594) op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.08 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.26/19.08 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 133.26/19.08 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.08 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 133.26/19.08 | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.26/19.08 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 133.26/19.08 | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.08 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.08 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.26/19.08 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.26/19.08 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.08 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.08 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 133.26/19.08 | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 133.26/19.08 | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 133.26/19.08 | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.26/19.08 | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_29))) % 133.26/19.08 | | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | | ALPHA: (4594) implies: % 133.26/19.08 | | | | | | | | | | | | | | | | | (4595) op(e0, e0) = all_56_31 % 133.26/19.08 | | | | | | | | | | | | | | | | | (4596) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.26/19.08 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.08 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.08 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.08 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.26/19.08 | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.26/19.08 | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.26/19.08 | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.26/19.08 | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.26/19.08 | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.26/19.08 | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.26/19.08 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 133.26/19.08 | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.08 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.26/19.08 | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.26/19.08 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.08 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.26/19.08 | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.26/19.08 | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.26/19.08 | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.08 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.26/19.08 | | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (157), (158), % 133.26/19.08 | | | | | | | | | | | | | | | | | (199), (208), (209), (211), (267), (354), (373), % 133.26/19.08 | | | | | | | | | | | | | | | | | (4073), (4539), (4561), (4566), (4567), (4595), % 133.26/19.08 | | | | | | | | | | | | | | | | | (4596), (function-axioms) are inconsistent by % 133.26/19.08 | | | | | | | | | | | | | | | | | sub-proof #208. % 133.26/19.08 | | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | | End of split % 133.26/19.08 | | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | | End of split % 133.26/19.08 | | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | | End of split % 133.26/19.08 | | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | End of split % 133.26/19.08 | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | Case 2: % 133.26/19.08 | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | (4597) all_28_2 = e3 % 133.26/19.08 | | | | | | | | | | | | | (4598) ( ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 & % 133.26/19.08 | | | | | | | | | | | | | $i(all_28_0)) | ( ~ (all_28_1 = e0) & op(e3, e3) % 133.26/19.08 | | | | | | | | | | | | | = all_28_1 & $i(all_28_1)) % 133.26/19.08 | | | | | | | | | | | | | % 133.26/19.08 | | | | | | | | | | | | | COMBINE_EQS: (316), (4597) imply: % 133.26/19.09 | | | | | | | | | | | | | (4599) all_6_2 = e3 % 133.26/19.09 | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | SIMP: (4599) implies: % 133.26/19.09 | | | | | | | | | | | | | (4600) all_6_2 = e3 % 133.26/19.09 | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | REDUCE: (359), (4600) imply: % 133.26/19.09 | | | | | | | | | | | | | (4601) ~ (all_52_6 = e3) % 133.26/19.09 | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | BETA: splitting (4598) gives: % 133.26/19.09 | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | (4602) ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 & % 133.26/19.09 | | | | | | | | | | | | | | $i(all_28_0) % 133.26/19.09 | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | ALPHA: (4602) implies: % 133.26/19.09 | | | | | | | | | | | | | | (4603) ~ (all_28_0 = e2) % 133.26/19.09 | | | | | | | | | | | | | | (4604) op(e3, e1) = all_28_0 % 133.26/19.09 | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | BETA: splitting (230) gives: % 133.26/19.09 | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | (4605) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 133.26/19.09 | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 133.26/19.09 | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | BETA: splitting (4605) gives: % 133.26/19.09 | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | (4606) all_57_1 = e3 & op(e3, e2) = e3 % 133.26/19.09 | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | ALPHA: (4606) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | (4607) all_57_1 = e3 % 133.26/19.09 | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (168), (208), % 133.26/19.09 | | | | | | | | | | | | | | | | (209), (211), (236), (4071), (4537), (4539), % 133.26/19.09 | | | | | | | | | | | | | | | | (4561), (4566), (4603), (4604), (4607), % 133.26/19.09 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.09 | | | | | | | | | | | | | | | | #206. % 133.26/19.09 | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | (4608) all_57_3 = e3 & op(e2, e2) = e3 % 133.26/19.09 | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | ALPHA: (4608) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | (4609) op(e2, e2) = e3 % 133.26/19.09 | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | REF_CLOSE: (42), (4073), (4609), (function-axioms) are % 133.26/19.09 | | | | | | | | | | | | | | | | inconsistent by sub-proof #228. % 133.26/19.09 | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | End of split % 133.26/19.09 | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | (4610) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 133.26/19.09 | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 133.26/19.09 | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (4560), (4601), (4610), % 133.26/19.09 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.09 | | | | | | | | | | | | | | | #555. % 133.26/19.09 | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | End of split % 133.26/19.09 | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | (4611) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 & % 133.26/19.09 | | | | | | | | | | | | | | $i(all_28_1) % 133.26/19.09 | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | REF_CLOSE: (4071), (4611), (function-axioms) are inconsistent % 133.26/19.09 | | | | | | | | | | | | | | by sub-proof #211. % 133.26/19.09 | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | End of split % 133.26/19.09 | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | End of split % 133.26/19.09 | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | End of split % 133.26/19.09 | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | End of split % 133.26/19.09 | | | | | | | | | | % 133.26/19.09 | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | (4612) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 133.26/19.09 | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | REF_CLOSE: (4544), (4547), (4554), (4555), (4612) are % 133.26/19.09 | | | | | | | | | | inconsistent by sub-proof #205. % 133.26/19.09 | | | | | | | | | | % 133.26/19.09 | | | | | | | | | End of split % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | (4613) ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 & % 133.26/19.09 | | | | | | | | | $i(all_24_1) % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | REF_CLOSE: (4539), (4613), (function-axioms) are inconsistent % 133.26/19.09 | | | | | | | | | by sub-proof #204. % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | End of split % 133.26/19.09 | | | | | | | | % 133.26/19.09 | | | | | | | End of split % 133.26/19.09 | | | | | | | % 133.26/19.09 | | | | | | End of split % 133.26/19.09 | | | | | | % 133.26/19.09 | | | | | Case 2: % 133.26/19.09 | | | | | | % 133.26/19.09 | | | | | | (4614) all_14_2 = e3 % 133.26/19.09 | | | | | | (4615) ( ~ (all_14_0 = e1) & op(e3, e2) = all_14_0 & % 133.26/19.09 | | | | | | $i(all_14_0)) | ( ~ (all_14_1 = e0) & op(e3, e3) = % 133.26/19.09 | | | | | | all_14_1 & $i(all_14_1)) % 133.26/19.09 | | | | | | % 133.26/19.09 | | | | | | COMBINE_EQS: (329), (4614) imply: % 133.26/19.09 | | | | | | (4616) all_8_2 = e3 % 133.26/19.09 | | | | | | % 133.26/19.09 | | | | | | REDUCE: (347), (4616) imply: % 133.26/19.09 | | | | | | (4617) ~ (all_52_1 = e3) % 133.26/19.09 | | | | | | % 133.26/19.09 | | | | | | REDUCE: (350), (4616) imply: % 133.26/19.09 | | | | | | (4618) ~ (all_52_4 = e3) % 133.26/19.09 | | | | | | % 133.26/19.09 | | | | | | REDUCE: (352), (4616) imply: % 133.26/19.09 | | | | | | (4619) ~ (all_52_6 = e3) % 133.26/19.09 | | | | | | % 133.26/19.09 | | | | | | REDUCE: (354), (4616) imply: % 133.26/19.09 | | | | | | (4620) ~ (all_52_7 = e3) % 133.26/19.09 | | | | | | % 133.26/19.09 | | | | | | REDUCE: (356), (4616) imply: % 133.26/19.09 | | | | | | (4621) ~ (all_52_9 = e3) % 133.26/19.09 | | | | | | % 133.26/19.09 | | | | | | REDUCE: (358), (4616) imply: % 133.26/19.09 | | | | | | (4622) ~ (all_52_13 = e3) % 133.26/19.09 | | | | | | % 133.26/19.09 | | | | | | BETA: splitting (4615) gives: % 133.26/19.09 | | | | | | % 133.26/19.09 | | | | | | Case 1: % 133.26/19.09 | | | | | | | % 133.26/19.09 | | | | | | | (4623) ~ (all_14_0 = e1) & op(e3, e2) = all_14_0 & % 133.26/19.09 | | | | | | | $i(all_14_0) % 133.26/19.09 | | | | | | | % 133.26/19.09 | | | | | | | ALPHA: (4623) implies: % 133.26/19.09 | | | | | | | (4624) ~ (all_14_0 = e1) % 133.26/19.09 | | | | | | | (4625) op(e3, e2) = all_14_0 % 133.26/19.09 | | | | | | | % 133.26/19.09 | | | | | | | BETA: splitting (230) gives: % 133.26/19.09 | | | | | | | % 133.26/19.09 | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | % 133.26/19.09 | | | | | | | | (4626) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & % 133.26/19.09 | | | | | | | | op(e2, e2) = e3) % 133.26/19.09 | | | | | | | | % 133.26/19.09 | | | | | | | | BETA: splitting (4626) gives: % 133.26/19.09 | | | | | | | | % 133.26/19.09 | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | (4627) all_57_1 = e3 & op(e3, e2) = e3 % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | ALPHA: (4627) implies: % 133.26/19.09 | | | | | | | | | (4628) op(e3, e2) = e3 % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | REF_CLOSE: (170), (4618), (4628), (function-axioms) are % 133.26/19.09 | | | | | | | | | inconsistent by sub-proof #738. % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | (4629) all_57_3 = e3 & op(e2, e2) = e3 % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | ALPHA: (4629) implies: % 133.26/19.09 | | | | | | | | | (4630) all_57_3 = e3 % 133.26/19.09 | | | | | | | | | (4631) op(e2, e2) = e3 % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 133.26/19.09 | | | | | | | | | all_14_0, e2, e3, simplifying with (170), (4625) % 133.26/19.09 | | | | | | | | | gives: % 133.26/19.09 | | | | | | | | | (4632) all_52_4 = all_14_0 % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | COMBINE_EQS: (271), (4632) imply: % 133.26/19.09 | | | | | | | | | (4633) all_54_1 = all_14_0 % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | REDUCE: (136), (4632) imply: % 133.26/19.09 | | | | | | | | | (4634) ~ (all_52_6 = all_14_0) % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | SIMP: (4634) implies: % 133.26/19.09 | | | | | | | | | (4635) ~ (all_52_6 = all_14_0) % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | REDUCE: (134), (4632) imply: % 133.26/19.09 | | | | | | | | | (4636) ~ (all_52_8 = all_14_0) % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | SIMP: (4636) implies: % 133.26/19.09 | | | | | | | | | (4637) ~ (all_52_8 = all_14_0) % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | REDUCE: (133), (4632) imply: % 133.26/19.09 | | | | | | | | | (4638) ~ (all_52_12 = all_14_0) % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | SIMP: (4638) implies: % 133.26/19.09 | | | | | | | | | (4639) ~ (all_52_12 = all_14_0) % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | REDUCE: (4618), (4632) imply: % 133.26/19.09 | | | | | | | | | (4640) ~ (all_14_0 = e3) % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | REDUCE: (4068), (4632) imply: % 133.26/19.09 | | | | | | | | | (4641) ~ (all_14_0 = e0) % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | BETA: splitting (203) gives: % 133.26/19.09 | | | | | | | | | % 133.26/19.09 | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | (4642) all_54_1 = e3 % 133.26/19.09 | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | COMBINE_EQS: (4633), (4642) imply: % 133.26/19.09 | | | | | | | | | | (4643) all_14_0 = e3 % 133.26/19.09 | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | SIMP: (4643) implies: % 133.26/19.09 | | | | | | | | | | (4644) all_14_0 = e3 % 133.26/19.09 | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | REDUCE: (4640), (4644) imply: % 133.26/19.09 | | | | | | | | | | (4645) $false % 133.26/19.09 | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | CLOSE: (4645) is inconsistent. % 133.26/19.09 | | | | | | | | | | % 133.26/19.09 | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | (4646) ~ (all_54_1 = e3) % 133.26/19.09 | | | | | | | | | | (4647) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 133.26/19.09 | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | BETA: splitting (4647) gives: % 133.26/19.09 | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | (4648) all_54_1 = e2 % 133.26/19.09 | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | COMBINE_EQS: (4633), (4648) imply: % 133.26/19.09 | | | | | | | | | | | (4649) all_14_0 = e2 % 133.26/19.09 | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | SIMP: (4649) implies: % 133.26/19.09 | | | | | | | | | | | (4650) all_14_0 = e2 % 133.26/19.09 | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | REDUCE: (4635), (4650) imply: % 133.26/19.09 | | | | | | | | | | | (4651) ~ (all_52_6 = e2) % 133.26/19.09 | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | REDUCE: (4637), (4650) imply: % 133.26/19.09 | | | | | | | | | | | (4652) ~ (all_52_8 = e2) % 133.26/19.09 | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | REDUCE: (4639), (4650) imply: % 133.26/19.09 | | | | | | | | | | | (4653) ~ (all_52_12 = e2) % 133.26/19.09 | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | REDUCE: (4640), (4650) imply: % 133.26/19.09 | | | | | | | | | | | (4654) ~ (e3 = e2) % 133.26/19.09 | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | BETA: splitting (229) gives: % 133.26/19.09 | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | (4655) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 133.26/19.09 | | | | | | | | | | | | & op(e2, e2) = e2) % 133.26/19.09 | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | BETA: splitting (4655) gives: % 133.26/19.09 | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | (4656) all_57_1 = e2 & op(e3, e2) = e2 % 133.26/19.09 | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | ALPHA: (4656) implies: % 133.26/19.09 | | | | | | | | | | | | | (4657) all_57_1 = e2 % 133.26/19.09 | | | | | | | | | | | | | (4658) op(e3, e2) = e2 % 133.26/19.09 | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | BETA: splitting (61) gives: % 133.26/19.09 | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | (4659) ~ (all_20_2 = e2) % 133.26/19.09 | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | REDUCE: (318), (4659) imply: % 133.26/19.09 | | | | | | | | | | | | | | (4660) ~ (all_4_2 = e2) % 133.26/19.09 | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | BETA: splitting (73) gives: % 133.26/19.09 | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | (4661) ~ (all_28_2 = e3) % 133.26/19.09 | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | REDUCE: (316), (4661) imply: % 133.26/19.09 | | | | | | | | | | | | | | | (4662) ~ (all_6_2 = e3) % 133.26/19.09 | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 133.26/19.09 | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | (4663) ~ (all_34_2 = e3) % 133.26/19.09 | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | REDUCE: (307), (4663) imply: % 133.26/19.09 | | | | | | | | | | | | | | | | (4664) ~ (all_4_2 = e3) % 133.26/19.09 | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | (4665) all_54_15 = e3 % 133.26/19.09 | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (4664), (4665) are inconsistent by % 133.26/19.09 | | | | | | | | | | | | | | | | | sub-proof #601. % 133.26/19.09 | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | (4666) ~ (all_54_15 = e3) % 133.26/19.09 | | | | | | | | | | | | | | | | | (4667) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 133.26/19.09 | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | BETA: splitting (4667) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | (4668) all_54_15 = e2 % 133.26/19.09 | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (4660), (4668) are inconsistent by % 133.26/19.09 | | | | | | | | | | | | | | | | | | sub-proof #748. % 133.26/19.09 | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | (4669) ~ (all_54_15 = e2) % 133.26/19.09 | | | | | | | | | | | | | | | | | | (4670) all_54_15 = e1 | all_54_15 = e0 % 133.26/19.09 | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | BETA: splitting (4670) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | (4671) all_54_15 = e1 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (4671) are inconsistent by sub-proof % 133.26/19.09 | | | | | | | | | | | | | | | | | | | #747. % 133.26/19.09 | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | (4672) all_54_15 = e0 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (4672) imply: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | (4673) all_4_2 = e0 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | SIMP: (4673) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | (4674) all_4_2 = e0 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | REDUCE: (4664), (4674) imply: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | (4675) ~ (e3 = e0) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | REDUCE: (4660), (4674) imply: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | (4676) ~ (e2 = e0) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | REDUCE: (371), (4674) imply: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | (4677) ~ (e1 = e0) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | REDUCE: (36), (4674) imply: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | (4678) op(e0, e0) = e0 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | (4679) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4679) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | (4680) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (4071), (4680), (function-axioms) are % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #229. % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | (4681) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4681) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | (4682) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4682) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | (4683) ~ (all_56_31 = e0) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | (4684) op(e0, e0) = all_56_31 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4678), (4683), (4684), (function-axioms) are % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #712. % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | (4685) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4685) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | (4686) ~ (all_56_17 = e1) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | (4687) op(e2, e3) = e2 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | (4688) op(e3, e1) = all_56_17 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | (4689) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (167), (4066), (4631), (4689), % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | #203. % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | (4690) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4690) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | (4691) all_57_5 = e0 & op(e2, e1) = e0 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4691) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | (4692) all_57_5 = e0 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | (4693) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4693) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (4694) all_57_4 = e2 & op(e3, e1) = e2 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4652), (4694), (function-axioms) are % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442. % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (4695) all_57_5 = e2 & op(e2, e1) = e2 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4695) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (4696) all_57_5 = e2 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4692), (4696) are inconsistent by sub-proof % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | #372. % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | (4697) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4697) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (4698) all_57_8 = e2 & op(e1, e1) = e2 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4698) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (4699) op(e1, e1) = e2 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (4699), (function-axioms) are % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (4700) all_57_14 = e2 & op(e0, e1) = e2 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4700) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (4701) all_57_14 = e2 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4702) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4702) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4703) all_57_4 = e3 & op(e3, e1) = e3 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4703) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4704) op(e3, e1) = e3 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4705) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (168), (169), (170), (232), (4068), % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4070), (4657), (4704), (4705), (function-axioms) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #202. % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4706) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4706) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4707) all_57_4 = e1 & op(e3, e1) = e1 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4707) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4708) op(e3, e1) = e1 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4686), (4688), (4708), (function-axioms) are % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349. % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4709) all_57_9 = e1 & op(e3, e0) = e1 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4709) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4710) all_57_9 = e1 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4711) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4711) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4712) all_57_12 = e3 & op(e0, e3) = e3 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4712) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4713) all_57_12 = e3 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4714) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (4622), (4710), (4714), % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #331. % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4715) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4715) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4716) all_57_11 = e3 & op(e1, e0) = e3 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4716) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4717) all_57_11 = e3 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4718) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4718) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4719) all_57_9 = e2 & op(e3, e0) = e2 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4653), (4719), (function-axioms) are % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4720) all_57_10 = e2 & op(e2, e0) = e2 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4720) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4721) all_57_10 = e2 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4722) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (4631), (4687), (4722), % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #292. % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4723) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (4692), (4721), (4723) are inconsistent % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #364. % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4724) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4724) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4725) all_57_11 = e2 & op(e1, e0) = e2 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4725) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4726) all_57_11 = e2 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228), % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (4619), (4630), (4657), (4717), (4726), % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #201. % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4727) all_57_15 = e2 & op(e0, e0) = e2 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4727) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4728) all_57_15 = e2 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (208), (209), (4701), % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4713), (4728) are inconsistent by sub-proof #434. % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4729) all_57_15 = e3 & op(e0, e0) = e3 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4729) implies: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4730) all_57_15 = e3 % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4731) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4731) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4732) all_57_12 = e1 & op(e0, e3) = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4713), (4732) are inconsistent by sub-proof % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #490. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4733) all_57_13 = e1 & op(e0, e2) = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4733) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4734) all_57_13 = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4735) all_57_15 = e0 & op(e0, e0) = e0 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4730), (4735) are inconsistent by sub-proof % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #406. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4736) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4736) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4737) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4737) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4738) all_57_12 = e0 & op(e0, e3) = e0 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4713), (4738) are inconsistent by sub-proof % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #436. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4739) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (4701), (4734), (4739) are inconsistent % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #579. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4740) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4740) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4741) all_57_14 = e1 & op(e0, e1) = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4741) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4742) all_57_14 = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4701), (4742) are inconsistent by sub-proof % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #560. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4743) all_57_15 = e1 & op(e0, e0) = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4743) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4744) all_57_15 = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4730), (4744) imply: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4745) e3 = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4745) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4746) e3 = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (4746) imply: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4747) $false % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4747) is inconsistent. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4748) all_57_13 = e3 & op(e0, e2) = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (4620), (4748), (function-axioms) are % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #556. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4749) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4749) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4750) all_57_14 = e3 & op(e0, e1) = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4750) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4751) all_57_14 = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4701), (4751) imply: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4752) e3 = e2 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4630), (4752) imply: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4753) all_57_3 = e2 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228), % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (4619), (4657), (4753), (function-axioms) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #463. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4754) all_57_15 = e3 & op(e0, e0) = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4754) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4755) op(e0, e0) = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4678), (4755), (function-axioms) are % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #715. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4756) all_57_5 = e3 & op(e2, e1) = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4621), (4756), (function-axioms) are % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4757) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4757) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4758) all_57_8 = e3 & op(e1, e1) = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4758) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4759) op(e1, e1) = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (4662), (4759), (function-axioms) are % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4760) all_57_14 = e3 & op(e0, e1) = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4760) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4761) all_57_14 = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4701), (4761) imply: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4762) e3 = e2 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4762) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4763) e3 = e2 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4630), (4763) imply: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4764) all_57_3 = e2 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228), % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (4619), (4657), (4764), (function-axioms) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #463. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | (4765) all_57_10 = e0 & op(e2, e0) = e0 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4765) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | (4766) op(e2, e0) = e0 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | (4767) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (4653), (4766), (4767), % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | #200. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | (4768) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4768) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (4769) all_57_11 = e2 & op(e1, e0) = e2 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4769) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (4770) all_57_11 = e2 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (4771) op(e1, e0) = e2 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4772) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4772) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4773) all_57_9 = e1 & op(e3, e0) = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4773) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4774) all_57_9 = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4775) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4775) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4776) all_57_9 = e3 & op(e3, e0) = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4774), (4776) are inconsistent by sub-proof % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #345. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4777) all_57_10 = e3 & op(e2, e0) = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4622), (4777), (function-axioms) are % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4778) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4778) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4779) all_57_11 = e3 & op(e1, e0) = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4779) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4780) all_57_11 = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228), % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (4619), (4630), (4657), (4770), (4780), % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #201. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4781) all_57_15 = e3 & op(e0, e0) = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4781) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4782) op(e0, e0) = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4678), (4782), (function-axioms) are % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #715. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4783) all_57_10 = e1 & op(e2, e0) = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4783) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4784) op(e2, e0) = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4766), (4784), (function-axioms) are % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #695. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4785) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4785) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4786) all_57_11 = e1 & op(e1, e0) = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4786) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4787) op(e1, e0) = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4771), (4787), (function-axioms) are % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #720. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4788) all_57_15 = e1 & op(e0, e0) = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4788) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4789) op(e0, e0) = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4678), (4789), (function-axioms) are % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #220. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (4790) all_57_15 = e2 & op(e0, e0) = e2 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4790) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (4791) op(e0, e0) = e2 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4678), (4791), (function-axioms) are % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #714. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (4792) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4792) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (4793) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (4631), (4662), (4793), % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | #324. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (4794) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4794) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4795) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4795) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4796) op(e2, e2) = e0 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4631), (4796), (function-axioms) are % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4797) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (372), (4678), (4797), % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | #709. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | (4798) all_34_2 = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (4798) imply: % 133.26/19.10 | | | | | | | | | | | | | | | | (4799) all_4_2 = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | SIMP: (4799) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | (4800) all_4_2 = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | REDUCE: (368), (4800) imply: % 133.26/19.10 | | | | | | | | | | | | | | | | (4801) ~ (all_52_12 = e3) % 133.26/19.10 | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | REDUCE: (370), (4800) imply: % 133.26/19.10 | | | | | | | | | | | | | | | | (4802) ~ (all_52_14 = e3) % 133.26/19.10 | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | (4803) all_54_3 = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4803) imply: % 133.26/19.10 | | | | | | | | | | | | | | | | | (4804) all_52_12 = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | REDUCE: (4801), (4804) imply: % 133.26/19.10 | | | | | | | | | | | | | | | | | (4805) $false % 133.26/19.10 | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | CLOSE: (4805) is inconsistent. % 133.26/19.10 | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | (4806) ~ (all_54_3 = e3) % 133.26/19.10 | | | | | | | | | | | | | | | | | (4807) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 133.26/19.10 | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | (4808) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 133.26/19.10 | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | BETA: splitting (4808) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | (4809) all_57_6 = e3 & op(e1, e3) = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | ALPHA: (4809) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | (4810) all_57_6 = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | (4811) op(e1, e3) = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (4812) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4812) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (4813) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4813) gives: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4814) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4814) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4815) op(e3, e3) = e2 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4071), (4815), (function-axioms) are % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4816) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4816) implies: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4817) op(e3, e1) = e3 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4818) op(e3, e3) = e1 % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (168), (169), (170), (232), (4068), % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | (4070), (4817), (4818), (function-axioms) are % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #599. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (4819) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4658), (4801), (4819), (function-axioms) % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #198. % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.10 | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (4820) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4820) gives: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | (4821) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4821) gives: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (4822) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4822) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (4823) op(e1, e1) = e3 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (4662), (4823), (function-axioms) are % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771. % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (4824) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4824) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (4825) ~ (all_56_5 = e3) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (4826) op(e1, e3) = all_56_5 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4811), (4825), (4826), (function-axioms) are % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #724. % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | (4827) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4827) gives: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (4828) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4828) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (4829) op(e2, e2) = e0 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4631), (4829), (function-axioms) are % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (4830) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4830) gives: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (4831) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4831) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (4832) op(e1, e1) = e2 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (4832), (function-axioms) are % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (4833) op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4833) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (4834) op(e0, e0) = all_56_31 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (4835) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4807) gives: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | (4836) all_54_3 = e2 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4836) imply: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | (4837) all_52_12 = e2 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4653), (4837) imply: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | (4838) $false % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4838) is inconsistent. % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | (4839) all_54_3 = e1 | all_54_3 = e0 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | (4840) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4840) gives: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4841) all_57_6 = e2 & op(e1, e3) = e2 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4841) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4842) all_57_6 = e2 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4810), (4842) imply: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4843) e3 = e2 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4630), (4843) imply: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4844) all_57_3 = e2 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228), % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (4619), (4657), (4844), (function-axioms) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #463. % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4845) all_57_7 = e2 & op(e1, e2) = e2 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4651), (4845), (function-axioms) are % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515. % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | (4846) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4846) gives: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4847) all_57_8 = e2 & op(e1, e1) = e2 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4847) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4848) op(e1, e1) = e2 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (4848), (function-axioms) are % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4849) all_57_11 = e2 & op(e1, e0) = e2 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4849) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4850) all_57_11 = e2 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (4851) op(e1, e0) = e2 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4852) all_57_15 = e0 & op(e0, e0) = e0 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4852) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4853) op(e0, e0) = e0 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (4834), (4835), (4853), % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | #710. % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4854) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4854) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4855) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4855) gives: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4856) all_57_9 = e0 & op(e3, e0) = e0 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4856) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4857) op(e3, e0) = e0 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (208), (212), % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214), (4622), (4811), (4834), (4835), (4850), % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4851), (4857), (function-axioms) are inconsistent % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #632. % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4858) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4858) gives: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4859) all_57_10 = e0 & op(e2, e0) = e0 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4859) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4860) op(e2, e0) = e0 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4839) gives: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4861) all_54_3 = e1 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4861) imply: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4862) all_52_12 = e1 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (4862) imply: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4863) ~ (all_52_14 = e1) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4863) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4864) ~ (all_52_14 = e1) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (4811) gives: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4865) all_52_2 = e3 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e0, e2, simplifying with (164), (4860) gives: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4866) all_52_13 = e0 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4835) gives: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4867) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4867) gives: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4868) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4868) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4869) ~ (all_56_9 = e2) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4870) op(e3, e2) = all_56_9 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4658), (4869), (4870), (function-axioms) are % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4871) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4871) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4872) ~ (all_56_27 = e0) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4873) op(e2, e0) = all_56_27 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4860), (4872), (4873), (function-axioms) are % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #275. % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4874) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4874) gives: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4875) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4875) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4876) op(e1, e0) = e1 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4864), (4876), (function-axioms) are % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #327. % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4877) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4877) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4878) ~ (all_56_5 = e3) % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4879) op(e1, e3) = all_56_5 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4811), (4878), (4879), (function-axioms) are % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #724. % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4880) all_54_3 = e0 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4880) imply: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4881) all_52_12 = e0 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4070), (4881) imply: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4882) $false % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4882) is inconsistent. % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4883) all_57_11 = e0 & op(e1, e0) = e0 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4883) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4884) all_57_11 = e0 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4850), (4884) are inconsistent by sub-proof % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #638. % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | (4885) all_57_7 = e3 & op(e1, e2) = e3 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | ALPHA: (4885) implies: % 133.26/19.11 | | | | | | | | | | | | | | | | | | | (4886) op(e1, e2) = e3 % 133.26/19.11 | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4619), (4886), (function-axioms) are % 133.26/19.11 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654. % 133.26/19.11 | | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | (4887) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 133.26/19.11 | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 133.26/19.11 | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (4662), (4802), (4887), % 133.26/19.11 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.11 | | | | | | | | | | | | | | | | | | #653. % 133.26/19.11 | | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | End of split % 133.26/19.11 | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | Case 2: % 133.26/19.11 | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | (4888) all_28_2 = e3 % 133.26/19.11 | | | | | | | | | | | | | | | (4889) ( ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 & % 133.26/19.11 | | | | | | | | | | | | | | | $i(all_28_0)) | ( ~ (all_28_1 = e0) & op(e3, e3) % 133.26/19.11 | | | | | | | | | | | | | | | = all_28_1 & $i(all_28_1)) % 133.26/19.11 | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | COMBINE_EQS: (316), (4888) imply: % 133.26/19.11 | | | | | | | | | | | | | | | (4890) all_6_2 = e3 % 133.26/19.11 | | | | | | | | | | | | | | | % 133.26/19.11 | | | | | | | | | | | | | | | SIMP: (4890) implies: % 133.26/19.12 | | | | | | | | | | | | | | | (4891) all_6_2 = e3 % 133.26/19.12 | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | REDUCE: (348), (4891) imply: % 133.26/19.12 | | | | | | | | | | | | | | | (4892) ~ (all_52_2 = e3) % 133.26/19.12 | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | REDUCE: (361), (4891) imply: % 133.26/19.12 | | | | | | | | | | | | | | | (4893) ~ (all_52_8 = e3) % 133.26/19.12 | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | REDUCE: (364), (4891) imply: % 133.26/19.12 | | | | | | | | | | | | | | | (4894) ~ (all_52_11 = e3) % 133.26/19.12 | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | REDUCE: (366), (4891) imply: % 133.26/19.12 | | | | | | | | | | | | | | | (4895) ~ (all_52_14 = e3) % 133.26/19.12 | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | REDUCE: (39), (4891) imply: % 133.26/19.12 | | | | | | | | | | | | | | | (4896) op(e1, e1) = e3 % 133.26/19.12 | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 133.26/19.12 | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | (4897) all_54_2 = e3 % 133.26/19.12 | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (4897) imply: % 133.26/19.12 | | | | | | | | | | | | | | | | (4898) all_52_8 = e3 % 133.26/19.12 | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | REDUCE: (4893), (4898) imply: % 133.26/19.12 | | | | | | | | | | | | | | | | (4899) $false % 133.26/19.12 | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | CLOSE: (4899) is inconsistent. % 133.26/19.12 | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | Case 2: % 133.26/19.12 | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | (4900) ~ (all_54_2 = e3) % 133.26/19.12 | | | | | | | | | | | | | | | | (4901) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 133.26/19.12 | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | BETA: splitting (4889) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | (4902) ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 & % 133.26/19.12 | | | | | | | | | | | | | | | | | $i(all_28_0) % 133.26/19.12 | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | ALPHA: (4902) implies: % 133.26/19.12 | | | | | | | | | | | | | | | | | (4903) ~ (all_28_0 = e2) % 133.26/19.12 | | | | | | | | | | | | | | | | | (4904) op(e3, e1) = all_28_0 % 133.26/19.12 | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | BETA: splitting (4901) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | (4905) all_54_2 = e2 % 133.26/19.12 | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (4905) imply: % 133.26/19.12 | | | | | | | | | | | | | | | | | | (4906) all_52_8 = e2 % 133.26/19.12 | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | REDUCE: (4652), (4906) imply: % 133.26/19.12 | | | | | | | | | | | | | | | | | | (4907) $false % 133.26/19.12 | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | CLOSE: (4907) is inconsistent. % 133.26/19.12 | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.12 | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | (4908) ~ (all_54_2 = e2) % 133.26/19.12 | | | | | | | | | | | | | | | | | | (4909) all_54_2 = e1 | all_54_2 = e0 % 133.26/19.12 | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | BETA: splitting (4909) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4910) all_54_2 = e1 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (4910) imply: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4911) all_52_8 = e1 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | REDUCE: (121), (4911) imply: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4912) ~ (all_52_11 = e1) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | SIMP: (4912) implies: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4913) ~ (all_52_11 = e1) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | REDUCE: (120), (4911) imply: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4914) ~ (all_52_12 = e1) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | SIMP: (4914) implies: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4915) ~ (all_52_12 = e1) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | REDUCE: (4893), (4911) imply: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4916) ~ (e3 = e1) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | REDUCE: (4652), (4911) imply: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4917) ~ (e2 = e1) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | REDUCE: (169), (4911) imply: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | (4918) op(e3, e1) = e1 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | (4919) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4919) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | (4920) all_57_4 = e1 & op(e3, e1) = e1 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4920) implies: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | (4921) all_57_4 = e1 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | (4922) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (167), (4071), (4617), (4922), % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | #210. % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | (4923) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4923) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | (4924) all_57_6 = e3 & op(e1, e3) = e3 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4892), (4924), (function-axioms) are % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #761. % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | (4925) all_57_12 = e3 & op(e0, e3) = e3 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4925) implies: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | (4926) all_57_12 = e3 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | (4927) op(e0, e3) = e3 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (4928) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4928) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4929) all_57_12 = e2 & op(e0, e3) = e2 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4929) implies: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4930) all_57_12 = e2 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4926), (4930) imply: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4931) e3 = e2 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4630), (4931) imply: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4932) all_57_3 = e2 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228), % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (230), (4619), (4657), (4932), (function-axioms) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #463. % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4933) all_57_13 = e2 & op(e0, e2) = e2 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4933) implies: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4934) all_57_13 = e2 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (227), (228), (4630), % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4657), (4934) are inconsistent by sub-proof #301. % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (4935) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4935) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4936) all_57_14 = e2 & op(e0, e1) = e2 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4936) implies: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (4937) all_57_14 = e2 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (4938) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (4071), (4618), (4938), % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | #197. % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (4939) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4939) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4940) all_57_4 = e3 & op(e3, e1) = e3 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4940) implies: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4941) op(e3, e1) = e3 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (169), (201), (269), (4070), (4653), % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4915), (4941), (function-axioms) are inconsistent % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #319. % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4942) all_57_9 = e3 & op(e3, e0) = e3 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4942) implies: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4943) all_57_9 = e3 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4944) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4944) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4945) all_57_12 = e1 & op(e0, e3) = e1 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4926), (4945) are inconsistent by sub-proof % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #490. % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4946) all_57_13 = e1 & op(e0, e2) = e1 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4946) implies: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4947) all_57_13 = e1 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4948) all_57_15 = e0 & op(e0, e0) = e0 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4948) implies: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4949) op(e0, e0) = e0 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4950) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4950) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4951) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4951) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4952) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4952) implies: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4953) op(e3, e3) = e2 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234), % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (4618), (4657), (4943), (4953), % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #237. % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4954) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4954) implies: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4955) op(e3, e3) = e1 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236), % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (4068), (4921), (4955), (function-axioms) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #667. % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4956) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4956) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4957) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4957) implies: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4958) ~ (all_56_7 = e3) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4959) op(e0, e3) = all_56_7 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4927), (4958), (4959), (function-axioms) are % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #209. % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4960) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4960) implies: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4961) ~ (all_56_17 = e1) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4962) op(e3, e1) = all_56_17 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4918), (4961), (4962), (function-axioms) are % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349. % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4963) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4963) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4964) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4964) gives: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4965) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4965) implies: % 133.26/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4966) ~ (all_56_17 = e1) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4967) op(e3, e1) = all_56_17 % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4918), (4966), (4967), (function-axioms) are % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349. % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4968) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4968) implies: % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4969) op(e2, e2) = e1 % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4631), (4969), (function-axioms) are % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4970) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4970) gives: % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4971) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4971) implies: % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4972) op(e2, e2) = e0 % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4631), (4972), (function-axioms) are % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4973) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4973) gives: % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4974) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4974) implies: % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4975) op(e1, e1) = e2 % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (4975), (function-axioms) are % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4976) op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4976) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4977) op(e0, e0) = all_56_31 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4978) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (210), (227), (228), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4630), (4657), (4896), (4926), (4949), (4977), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4978), (function-axioms) are inconsistent by % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #300. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4979) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4979) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4980) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (4926), (4937), (4947), (4980) are % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #285. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4981) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4981) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4982) all_57_14 = e1 & op(e0, e1) = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4982) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4983) all_57_14 = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (219), (221), (372), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4896), (4903), (4904), (4918), (4983), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #212. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4984) all_57_15 = e1 & op(e0, e0) = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4984) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4985) op(e0, e0) = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (4985), (function-axioms) are % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | (4986) all_57_15 = e2 & op(e0, e0) = e2 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4986) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | (4987) op(e0, e0) = e2 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (4988) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4988) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4989) all_57_0 = e3 & op(e3, e3) = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4989) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4990) op(e3, e3) = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4071), (4990), (function-axioms) are % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #773. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4991) all_57_1 = e3 & op(e3, e2) = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4991) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4992) all_57_1 = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (168), (208), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (211), (236), (4071), (4653), (4894), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4903), (4904), (4926), (4987), (4992), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | #206. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (4993) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4993) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4994) all_57_4 = e3 & op(e3, e1) = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4994) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4995) op(e3, e1) = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (169), (201), (269), (4070), (4653), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4915), (4995), (function-axioms) are inconsistent % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #319. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4996) all_57_9 = e3 & op(e3, e0) = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4996) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4997) all_57_9 = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4998) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4998) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4999) all_57_12 = e1 & op(e0, e3) = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4999) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5000) all_57_12 = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4926), (5000) imply: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5001) e3 = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4997), (5001) imply: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5002) all_57_9 = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (160), (164), (214), (4622), (4895), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4987), (5002), (function-axioms) are inconsistent % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #329. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5003) all_57_13 = e1 & op(e0, e2) = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5003) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5004) all_57_13 = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5005) all_57_15 = e0 & op(e0, e0) = e0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5005) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5006) op(e0, e0) = e0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4987), (5006), (function-axioms) are % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #714. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5007) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5007) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5008) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5008) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5009) all_57_12 = e0 & op(e0, e3) = e0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5009) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5010) op(e0, e3) = e0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4067), (5010), (function-axioms) are % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5011) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5011) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5012) all_57_13 = e0 & op(e0, e2) = e0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5012) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5013) all_57_13 = e0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5004), (5013) are inconsistent by sub-proof % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #681. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5014) all_57_14 = e0 & op(e0, e1) = e0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5014) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5015) op(e0, e1) = e0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5016) all_54_3 = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (5016) imply: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5017) all_52_12 = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (5017) imply: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5018) ~ (all_4_2 = e3) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5018) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5019) ~ (all_4_2 = e3) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5020) all_54_15 = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (5019), (5020) are inconsistent by % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #601. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5021) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (190), (245), (246), (367), (371), (4660), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4894), (4913), (5015), (5021), (function-axioms) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #232. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5022) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (4070), (4653), (4915), (5022) are % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5023) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5023) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5024) all_57_14 = e1 & op(e0, e1) = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5024) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5025) all_57_14 = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (219), (221), (372), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4896), (4903), (4904), (4918), (5025), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #212. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5026) all_57_15 = e1 & op(e0, e0) = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5026) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5027) op(e0, e0) = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4987), (5027), (function-axioms) are % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (5028) all_57_5 = e1 & op(e2, e1) = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5028) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (5029) all_57_5 = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (219), (221), (372), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (4896), (4903), (4904), (4918), (5029), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | #214. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | (5030) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5030) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (5031) all_57_8 = e1 & op(e1, e1) = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5031) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (5032) op(e1, e1) = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (4896), (5032), (function-axioms) are % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (5033) all_57_14 = e1 & op(e0, e1) = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5033) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (5034) all_57_14 = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (219), (221), (372), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (4896), (4903), (4904), (4918), (5034), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | #212. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | (5035) all_54_2 = e0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (5035) imply: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | (5036) all_52_8 = e0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | REDUCE: (4069), (5036) imply: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | (5037) $false % 133.56/19.13 | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | CLOSE: (5037) is inconsistent. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | (5038) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 & % 133.56/19.13 | | | | | | | | | | | | | | | | | $i(all_28_1) % 133.56/19.13 | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | REF_CLOSE: (4071), (5038), (function-axioms) are inconsistent % 133.56/19.13 | | | | | | | | | | | | | | | | | by sub-proof #211. % 133.56/19.13 | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | (5039) all_20_2 = e2 % 133.56/19.13 | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | COMBINE_EQS: (318), (5039) imply: % 133.56/19.13 | | | | | | | | | | | | | | (5040) all_4_2 = e2 % 133.56/19.13 | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | SIMP: (5040) implies: % 133.56/19.13 | | | | | | | | | | | | | | (5041) all_4_2 = e2 % 133.56/19.13 | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | COMBINE_EQS: (331), (5041) imply: % 133.56/19.13 | | | | | | | | | | | | | | (5042) all_26_2 = e2 % 133.56/19.13 | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | REDUCE: (369), (5041) imply: % 133.56/19.13 | | | | | | | | | | | | | | (5043) ~ (all_52_13 = e2) % 133.56/19.13 | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | REDUCE: (36), (5041) imply: % 133.56/19.13 | | | | | | | | | | | | | | (5044) op(e0, e0) = e2 % 133.56/19.13 | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | BETA: splitting (67) gives: % 133.56/19.13 | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | (5045) ~ (all_24_2 = e0) % 133.56/19.13 | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | REDUCE: (4065), (5045) imply: % 133.56/19.13 | | | | | | | | | | | | | | | (5046) $false % 133.56/19.13 | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | CLOSE: (5046) is inconsistent. % 133.56/19.13 | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | (5047) ( ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 & % 133.56/19.13 | | | | | | | | | | | | | | | $i(all_24_0)) | ( ~ (all_24_1 = e2) & op(e0, e0) % 133.56/19.13 | | | | | | | | | | | | | | | = all_24_1 & $i(all_24_1)) % 133.56/19.13 | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | BETA: splitting (70) gives: % 133.56/19.13 | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | (5048) ~ (all_26_2 = e2) % 133.56/19.13 | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | REDUCE: (5042), (5048) imply: % 133.56/19.13 | | | | | | | | | | | | | | | | (5049) $false % 133.56/19.13 | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | CLOSE: (5049) is inconsistent. % 133.56/19.13 | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | (5050) ( ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 & % 133.56/19.13 | | | | | | | | | | | | | | | | $i(all_26_0)) | ( ~ (all_26_1 = e3) & op(e2, e2) % 133.56/19.13 | | | | | | | | | | | | | | | | = all_26_1 & $i(all_26_1)) % 133.56/19.13 | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | BETA: splitting (5047) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | (5051) ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 & % 133.56/19.13 | | | | | | | | | | | | | | | | | $i(all_24_0) % 133.56/19.13 | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | ALPHA: (5051) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | (5052) ~ (all_24_0 = e1) % 133.56/19.13 | | | | | | | | | | | | | | | | | (5053) op(e0, e3) = all_24_0 % 133.56/19.13 | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | BETA: splitting (5050) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | (5054) ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 & % 133.56/19.13 | | | | | | | | | | | | | | | | | | $i(all_26_0) % 133.56/19.13 | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | ALPHA: (5054) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | (5055) ~ (all_26_0 = e1) % 133.56/19.13 | | | | | | | | | | | | | | | | | | (5056) op(e2, e0) = all_26_0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | (5057) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | BETA: splitting (5057) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | (5058) all_57_6 = e2 & op(e1, e3) = e2 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | ALPHA: (5058) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | (5059) all_57_6 = e2 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | (5060) op(e1, e3) = e2 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | (5061) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5061) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | (5062) all_57_4 = e2 & op(e3, e1) = e2 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4652), (5062), (function-axioms) are % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | (5063) all_57_5 = e2 & op(e2, e1) = e2 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5063) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | (5064) all_57_5 = e2 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | (5065) op(e2, e1) = e2 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | (5066) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (167), (4066), (4631), (5066), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | #203. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | (5067) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5067) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | (5068) all_57_5 = e0 & op(e2, e1) = e0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5064), (5068) are inconsistent by sub-proof % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | #277. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | (5069) all_57_10 = e0 & op(e2, e0) = e0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5069) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | (5070) all_57_10 = e0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | (5071) op(e2, e0) = e0 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | (5072) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5072) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5073) all_57_0 = e3 & op(e3, e3) = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5073) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5074) op(e3, e3) = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4071), (5074), (function-axioms) are % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #773. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5075) all_57_2 = e3 & op(e2, e3) = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5075) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5076) all_57_2 = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (224), (4630), (5064), (5070), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5076) are inconsistent by sub-proof #369. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | (5077) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5077) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5078) all_57_6 = e3 & op(e1, e3) = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5078) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5079) all_57_6 = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5059), (5079) imply: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5080) e3 = e2 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5080) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5081) e3 = e2 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4630), (5081) imply: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5082) all_57_3 = e2 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228), % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (4619), (4657), (5082), (function-axioms) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #463. % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5083) all_57_12 = e3 & op(e0, e3) = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5083) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5084) all_57_12 = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (5085) op(e0, e3) = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5086) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5086) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5087) all_57_2 = e1 & op(e2, e3) = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5087) implies: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5088) all_57_2 = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5089) op(e2, e3) = e1 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3, % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (5085) gives: % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5090) all_52_3 = e3 % 133.56/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_24_0, e3, e0, simplifying with (159), (5053) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5091) all_52_3 = all_24_0 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (5060) gives: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5092) all_52_2 = e2 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e0, e2, simplifying with (164), (5071) gives: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5093) all_52_13 = e0 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_26_0, e0, e2, simplifying with (164), (5056) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5094) all_52_13 = all_26_0 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (5065) gives: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5095) all_52_9 = e2 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e1, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (167), (5089) gives: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5096) all_52_1 = e1 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5090), (5091) imply: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5097) all_24_0 = e3 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5097) implies: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5098) all_24_0 = e3 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5093), (5094) imply: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5099) all_26_0 = e0 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (5095), (5096) imply: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5100) ~ (e2 = e1) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (5095) imply: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5101) ~ (all_52_11 = e2) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5101) implies: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5102) ~ (all_52_11 = e2) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (5095) imply: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5103) ~ (all_6_2 = e2) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4622), (5093) imply: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5104) ~ (e3 = e0) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5043), (5093) imply: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5105) ~ (e2 = e0) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5055), (5099) imply: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5106) ~ (e1 = e0) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5107) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5107) gives: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5108) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5108) gives: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5109) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5109) implies: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5110) op(e3, e3) = e2 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (231), (5059), (5084), (5088), % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5110), (function-axioms) are inconsistent by % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #392. % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5111) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (231), (235), (5084), % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5088), (5089), (5111), (function-axioms) are % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #195. % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5112) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4658), (5085), (5112), (function-axioms) are % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #194. % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5113) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5113) gives: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5114) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5114) gives: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5115) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5115) implies: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5116) op(e1, e3) = e1 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (5060), (5116), (function-axioms) are % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #517. % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5117) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5117) implies: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5118) op(e2, e2) = e1 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4631), (5118), (function-axioms) are % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5119) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (39), (91), (157), (190), (246), % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332), (364), (372), (4631), (5044), (5071), % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5102), (5119), (function-axioms) are inconsistent % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #265. % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5120) all_57_3 = e1 & op(e2, e2) = e1 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5120) implies: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5121) op(e2, e2) = e1 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4631), (5121), (function-axioms) are % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5122) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5122) gives: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5123) all_57_5 = e1 & op(e2, e1) = e1 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5064), (5123) are inconsistent by sub-proof % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #500. % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5124) all_57_10 = e1 & op(e2, e0) = e1 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5124) implies: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5125) op(e2, e0) = e1 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5055), (5056), (5125), (function-axioms) are % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #336. % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | (5126) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (158), (208), % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | (209), (211), (372), (4620), (5044), (5126), % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | #262. % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | (5127) all_57_7 = e2 & op(e1, e2) = e2 % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4651), (5127), (function-axioms) are % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515. % 133.56/19.14 | | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | (5128) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 133.56/19.14 | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 133.56/19.14 | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (164), (208), % 133.56/19.14 | | | | | | | | | | | | | | | | | | | (212), (214), (372), (4622), (5044), (5128), % 133.56/19.14 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.14 | | | | | | | | | | | | | | | | | | | #268. % 133.56/19.14 | | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | (5129) ~ (all_26_1 = e3) & op(e2, e2) = all_26_1 & % 133.56/19.14 | | | | | | | | | | | | | | | | | | $i(all_26_1) % 133.56/19.14 | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | ALPHA: (5129) implies: % 133.56/19.14 | | | | | | | | | | | | | | | | | | (5130) ~ (all_26_1 = e3) % 133.56/19.14 | | | | | | | | | | | | | | | | | | (5131) op(e2, e2) = all_26_1 % 133.56/19.14 | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4631), (5130), (5131), (function-axioms) are % 133.56/19.14 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #334. % 133.56/19.14 | | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | (5132) ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 & % 133.56/19.14 | | | | | | | | | | | | | | | | | $i(all_24_1) % 133.56/19.14 | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | | REF_CLOSE: (5044), (5132), (function-axioms) are inconsistent % 133.56/19.14 | | | | | | | | | | | | | | | | | by sub-proof #204. % 133.56/19.14 | | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | (5133) all_57_3 = e2 & op(e2, e2) = e2 % 133.56/19.14 | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | REF_CLOSE: (9), (4630), (5133) are inconsistent by sub-proof % 133.56/19.14 | | | | | | | | | | | | | #375. % 133.56/19.14 | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | (5134) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 133.56/19.14 | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 133.56/19.14 | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | BETA: splitting (5134) gives: % 133.56/19.14 | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | Case 1: % 133.56/19.14 | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | (5135) all_57_7 = e2 & op(e1, e2) = e2 % 133.56/19.14 | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | REF_CLOSE: (162), (4651), (5135), (function-axioms) are % 133.56/19.14 | | | | | | | | | | | | | inconsistent by sub-proof #515. % 133.56/19.14 | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | (5136) all_57_13 = e2 & op(e0, e2) = e2 % 133.56/19.14 | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (168), (169), (227), % 133.56/19.14 | | | | | | | | | | | | | (228), (236), (4071), (4630), (4652), (4653), % 133.56/19.14 | | | | | | | | | | | | | (5136), (function-axioms) are inconsistent by % 133.56/19.14 | | | | | | | | | | | | | sub-proof #193. % 133.56/19.14 | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | (5137) all_54_1 = e1 | all_54_1 = e0 % 133.56/19.14 | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | REF_CLOSE: (4624), (4633), (4641), (5137) are inconsistent by % 133.56/19.14 | | | | | | | | | | | sub-proof #192. % 133.56/19.14 | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | | % 133.56/19.14 | | | | | | | | | End of split % 133.56/19.14 | | | | | | | | | % 133.56/19.14 | | | | | | | | End of split % 133.56/19.14 | | | | | | | | % 133.56/19.14 | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | % 133.56/19.14 | | | | | | | | (5138) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & % 133.56/19.14 | | | | | | | | op(e0, e2) = e3) % 133.56/19.14 | | | | | | | | % 133.56/19.14 | | | | | | | | REF_CLOSE: (158), (162), (4619), (4620), (5138), % 133.56/19.14 | | | | | | | | (function-axioms) are inconsistent by sub-proof #555. % 133.56/19.14 | | | | | | | | % 133.56/19.14 | | | | | | | End of split % 133.56/19.14 | | | | | | | % 133.56/19.14 | | | | | | Case 2: % 133.56/19.14 | | | | | | | % 133.56/19.14 | | | | | | | (5139) ~ (all_14_1 = e0) & op(e3, e3) = all_14_1 & % 133.56/19.14 | | | | | | | $i(all_14_1) % 133.56/19.14 | | | | | | | % 133.56/19.14 | | | | | | | REF_CLOSE: (4071), (5139), (function-axioms) are inconsistent by % 133.56/19.14 | | | | | | | sub-proof #191. % 133.56/19.14 | | | | | | | % 133.56/19.14 | | | | | | End of split % 133.56/19.14 | | | | | | % 133.56/19.14 | | | | | End of split % 133.56/19.14 | | | | | % 133.56/19.14 | | | | End of split % 133.56/19.14 | | | | % 133.56/19.14 | | | Case 2: % 133.56/19.14 | | | | % 133.56/19.14 | | | | (5140) all_8_2 = e1 % 133.56/19.14 | | | | (5141) ( ~ (all_8_0 = e0) & op(e1, e2) = all_8_0 & $i(all_8_0)) | ( ~ % 133.56/19.14 | | | | (all_8_1 = e3) & op(e1, e1) = all_8_1 & $i(all_8_1)) % 133.56/19.14 | | | | % 133.56/19.14 | | | | COMBINE_EQS: (291), (5140) imply: % 133.56/19.14 | | | | (5142) all_48_2 = e1 % 133.56/19.14 | | | | % 133.56/19.14 | | | | REDUCE: (347), (5140) imply: % 133.56/19.14 | | | | (5143) ~ (all_52_1 = e1) % 133.56/19.14 | | | | % 133.56/19.14 | | | | REDUCE: (350), (5140) imply: % 133.56/19.14 | | | | (5144) ~ (all_52_4 = e1) % 133.56/19.14 | | | | % 133.56/19.14 | | | | REDUCE: (352), (5140) imply: % 133.56/19.14 | | | | (5145) ~ (all_52_6 = e1) % 133.56/19.14 | | | | % 133.56/19.14 | | | | REDUCE: (354), (5140) imply: % 133.56/19.14 | | | | (5146) ~ (all_52_7 = e1) % 133.56/19.14 | | | | % 133.56/19.14 | | | | REDUCE: (356), (5140) imply: % 133.56/19.14 | | | | (5147) ~ (all_52_9 = e1) % 133.56/19.14 | | | | % 133.56/19.14 | | | | REDUCE: (358), (5140) imply: % 133.56/19.14 | | | | (5148) ~ (all_52_13 = e1) % 133.56/19.14 | | | | % 133.56/19.14 | | | | BETA: splitting (224) gives: % 133.56/19.14 | | | | % 133.56/19.14 | | | | Case 1: % 133.56/19.14 | | | | | % 133.56/19.14 | | | | | (5149) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, % 133.56/19.14 | | | | | e2) = e1) % 133.56/19.14 | | | | | % 133.56/19.14 | | | | | BETA: splitting (5149) gives: % 133.56/19.14 | | | | | % 133.56/19.14 | | | | | Case 1: % 133.56/19.14 | | | | | | % 133.56/19.14 | | | | | | (5150) all_57_2 = e1 & op(e2, e3) = e1 % 133.56/19.14 | | | | | | % 133.56/19.14 | | | | | | REF_CLOSE: (167), (5143), (5150), (function-axioms) are inconsistent % 133.56/19.14 | | | | | | by sub-proof #676. % 133.56/19.14 | | | | | | % 133.56/19.14 | | | | | Case 2: % 133.56/19.14 | | | | | | % 133.56/19.14 | | | | | | (5151) all_57_3 = e1 & op(e2, e2) = e1 % 133.56/19.14 | | | | | | % 133.56/19.14 | | | | | | ALPHA: (5151) implies: % 133.56/19.14 | | | | | | (5152) all_57_3 = e1 % 133.56/19.14 | | | | | | (5153) op(e2, e2) = e1 % 133.56/19.14 | | | | | | % 133.56/19.14 | | | | | | BETA: splitting (46) gives: % 133.56/19.14 | | | | | | % 133.56/19.14 | | | | | | Case 1: % 133.56/19.14 | | | | | | | % 133.56/19.14 | | | | | | | (5154) ~ (all_10_2 = e0) % 133.56/19.14 | | | | | | | % 133.56/19.14 | | | | | | | BETA: splitting (55) gives: % 133.56/19.14 | | | | | | | % 133.56/19.14 | | | | | | | Case 1: % 133.56/19.14 | | | | | | | | % 133.56/19.14 | | | | | | | | (5155) ~ (all_16_2 = e2) % 133.56/19.14 | | | | | | | | % 133.56/19.14 | | | | | | | | REDUCE: (327), (5155) imply: % 133.56/19.14 | | | | | | | | (5156) ~ (all_10_2 = e2) % 133.56/19.14 | | | | | | | | % 133.56/19.14 | | | | | | | | BETA: splitting (61) gives: % 133.56/19.14 | | | | | | | | % 133.56/19.14 | | | | | | | | Case 1: % 133.56/19.14 | | | | | | | | | % 133.56/19.14 | | | | | | | | | (5157) ~ (all_20_2 = e2) % 133.56/19.14 | | | | | | | | | % 133.56/19.14 | | | | | | | | | REDUCE: (318), (5157) imply: % 133.56/19.14 | | | | | | | | | (5158) ~ (all_4_2 = e2) % 133.56/19.14 | | | | | | | | | % 133.56/19.14 | | | | | | | | | BETA: splitting (73) gives: % 133.56/19.14 | | | | | | | | | % 133.56/19.14 | | | | | | | | | Case 1: % 133.56/19.14 | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | (5159) ~ (all_28_2 = e3) % 133.56/19.14 | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | REDUCE: (316), (5159) imply: % 133.56/19.14 | | | | | | | | | | (5160) ~ (all_6_2 = e3) % 133.56/19.14 | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | BETA: splitting (79) gives: % 133.56/19.14 | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | Case 1: % 133.56/19.14 | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | (5161) ~ (all_32_2 = e1) % 133.56/19.14 | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | REDUCE: (312), (5161) imply: % 133.56/19.14 | | | | | | | | | | | (5162) ~ (all_10_2 = e1) % 133.56/19.14 | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | BETA: splitting (204) gives: % 133.56/19.14 | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | Case 1: % 133.56/19.14 | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | (5163) all_54_0 = e3 % 133.56/19.14 | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | COMBINE_EQS: (278), (5163) imply: % 133.56/19.14 | | | | | | | | | | | | (5164) all_10_2 = e3 % 133.56/19.14 | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | REDUCE: (342), (5164) imply: % 133.56/19.14 | | | | | | | | | | | | (5165) ~ (all_52_4 = e3) % 133.56/19.14 | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | REDUCE: (344), (5164) imply: % 133.56/19.14 | | | | | | | | | | | | (5166) ~ (all_52_8 = e3) % 133.56/19.14 | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | REDUCE: (346), (5164) imply: % 133.56/19.14 | | | | | | | | | | | | (5167) ~ (all_52_12 = e3) % 133.56/19.14 | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | REDUCE: (45), (5164) imply: % 133.56/19.14 | | | | | | | | | | | | (5168) op(e3, e3) = e3 % 133.56/19.14 | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | BETA: splitting (82) gives: % 133.56/19.14 | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | Case 1: % 133.56/19.14 | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | (5169) ~ (all_34_2 = e3) % 133.56/19.14 | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | REDUCE: (307), (5169) imply: % 133.56/19.14 | | | | | | | | | | | | | (5170) ~ (all_4_2 = e3) % 133.56/19.14 | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | BETA: splitting (189) gives: % 133.56/19.14 | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | Case 1: % 133.56/19.14 | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | (5171) all_54_15 = e3 % 133.56/19.14 | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | COMBINE_EQS: (245), (5171) imply: % 133.56/19.14 | | | | | | | | | | | | | | (5172) all_4_2 = e3 % 133.56/19.14 | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | REDUCE: (5170), (5172) imply: % 133.56/19.14 | | | | | | | | | | | | | | (5173) $false % 133.56/19.14 | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | CLOSE: (5173) is inconsistent. % 133.56/19.14 | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | (5174) ~ (all_54_15 = e3) % 133.56/19.14 | | | | | | | | | | | | | | (5175) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 133.56/19.14 | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | BETA: splitting (5175) gives: % 133.56/19.14 | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | Case 1: % 133.56/19.14 | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | (5176) all_54_15 = e2 % 133.56/19.14 | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5176) imply: % 133.56/19.14 | | | | | | | | | | | | | | | (5177) all_4_2 = e2 % 133.56/19.14 | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | REDUCE: (5158), (5177) imply: % 133.56/19.14 | | | | | | | | | | | | | | | (5178) $false % 133.56/19.14 | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | CLOSE: (5178) is inconsistent. % 133.56/19.14 | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | (5179) ~ (all_54_15 = e2) % 133.56/19.14 | | | | | | | | | | | | | | | (5180) all_54_15 = e1 | all_54_15 = e0 % 133.56/19.14 | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | BETA: splitting (5180) gives: % 133.56/19.14 | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | Case 1: % 133.56/19.14 | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | (5181) all_54_15 = e1 % 133.56/19.14 | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5181) imply: % 133.56/19.14 | | | | | | | | | | | | | | | | (5182) all_4_2 = e1 % 133.56/19.14 | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | REDUCE: (371), (5182) imply: % 133.56/19.14 | | | | | | | | | | | | | | | | (5183) $false % 133.56/19.14 | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | CLOSE: (5183) is inconsistent. % 133.56/19.14 | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | Case 2: % 133.56/19.14 | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | (5184) all_54_15 = e0 % 133.56/19.14 | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5184) imply: % 133.56/19.14 | | | | | | | | | | | | | | | | (5185) all_4_2 = e0 % 133.56/19.14 | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | REDUCE: (369), (5185) imply: % 133.56/19.14 | | | | | | | | | | | | | | | | (5186) ~ (all_52_13 = e0) % 133.56/19.14 | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | REDUCE: (5170), (5185) imply: % 133.56/19.14 | | | | | | | | | | | | | | | | (5187) ~ (e3 = e0) % 133.56/19.14 | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | REDUCE: (5158), (5185) imply: % 133.56/19.14 | | | | | | | | | | | | | | | | (5188) ~ (e2 = e0) % 133.56/19.14 | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | REDUCE: (371), (5185) imply: % 133.56/19.14 | | | | | | | | | | | | | | | | (5189) ~ (e1 = e0) % 133.56/19.14 | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | REDUCE: (36), (5185) imply: % 133.56/19.14 | | | | | | | | | | | | | | | | (5190) op(e0, e0) = e0 % 133.56/19.14 | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.56/19.14 | | | | | | | | | | | | | | | | % 133.56/19.14 | | | | | | | | | | | | | | | | Case 1: % 133.56/19.14 | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | (5191) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.56/19.15 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.15 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.56/19.15 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.56/19.15 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.56/19.15 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.56/19.15 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.56/19.15 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.15 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.15 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.56/19.15 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.56/19.15 | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (45), (168), (204), (278), (5153), (5154), % 133.56/19.15 | | | | | | | | | | | | | | | | | (5156), (5162), (5167), (5168), (5191), % 133.56/19.15 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.15 | | | | | | | | | | | | | | | | | #189. % 133.56/19.15 | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | Case 2: % 133.56/19.15 | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | (5192) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.56/19.15 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.56/19.15 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.15 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.56/19.15 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.56/19.15 | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.56/19.15 | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.56/19.15 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.56/19.15 | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.56/19.15 | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.56/19.15 | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.56/19.15 | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.56/19.15 | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.56/19.15 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.56/19.15 | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.56/19.15 | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.56/19.15 | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.15 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.56/19.15 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.56/19.15 | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.56/19.15 | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.56/19.15 | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.56/19.15 | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.56/19.15 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.56/19.15 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.56/19.15 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.56/19.15 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.15 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.56/19.15 | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.56/19.15 | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | BETA: splitting (5192) gives: % 133.56/19.15 | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.15 | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | (5193) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.56/19.15 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.56/19.15 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.56/19.15 | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | BETA: splitting (5193) gives: % 133.56/19.15 | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5194) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | ALPHA: (5194) implies: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5195) op(e1, e1) = e3 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (5160), (5195), (function-axioms) are % 133.56/19.15 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771. % 133.56/19.15 | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5196) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | ALPHA: (5196) implies: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5197) ~ (all_56_21 = e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5198) ~ (all_56_5 = e3) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5199) op(e1, e0) = all_56_29 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5200) op(e1, e1) = all_56_21 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5201) op(e1, e3) = all_56_5 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5202) op(e2, e1) = e2 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (103), (110), (117), (160), (165), (194), % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (197), (218), (259), (334), (362), (5142), (5148), % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5160), (5186), (5197), (5198), (5199), (5200), % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5201), (5202), (function-axioms) are inconsistent % 133.56/19.15 | | | | | | | | | | | | | | | | | | | by sub-proof #185. % 133.56/19.15 | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | End of split % 133.56/19.15 | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.15 | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | (5203) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.15 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.56/19.15 | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.56/19.15 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.15 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.56/19.15 | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.56/19.15 | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.56/19.15 | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.56/19.15 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.56/19.15 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.56/19.15 | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.56/19.15 | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.56/19.15 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.15 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.56/19.15 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.56/19.15 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.56/19.15 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.56/19.15 | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.56/19.15 | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (372), (5153), (5190), % 133.56/19.15 | | | | | | | | | | | | | | | | | | (5203), (function-axioms) are inconsistent by % 133.56/19.15 | | | | | | | | | | | | | | | | | | sub-proof #184. % 133.56/19.15 | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | End of split % 133.56/19.15 | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | End of split % 133.56/19.15 | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | End of split % 133.56/19.15 | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | End of split % 133.56/19.15 | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | End of split % 133.56/19.15 | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | Case 2: % 133.56/19.15 | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | (5204) all_34_2 = e3 % 133.56/19.15 | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | COMBINE_EQS: (307), (5204) imply: % 133.56/19.15 | | | | | | | | | | | | | (5205) all_4_2 = e3 % 133.56/19.15 | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | SIMP: (5205) implies: % 133.56/19.15 | | | | | | | | | | | | | (5206) all_4_2 = e3 % 133.56/19.15 | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | REDUCE: (360), (5206) imply: % 133.56/19.15 | | | | | | | | | | | | | (5207) ~ (all_52_7 = e3) % 133.56/19.15 | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | REDUCE: (367), (5206) imply: % 133.56/19.15 | | | | | | | | | | | | | (5208) ~ (all_52_11 = e3) % 133.56/19.15 | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | REDUCE: (36), (5206) imply: % 133.56/19.15 | | | | | | | | | | | | | (5209) op(e0, e0) = e3 % 133.56/19.15 | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | BETA: splitting (222) gives: % 133.56/19.15 | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | Case 1: % 133.56/19.15 | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | (5210) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 133.56/19.15 | | | | | | | | | | | | | | & op(e2, e1) = e3) % 133.56/19.15 | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | BETA: splitting (5210) gives: % 133.56/19.15 | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | Case 1: % 133.56/19.15 | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | (5211) all_57_4 = e3 & op(e3, e1) = e3 % 133.56/19.15 | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | ALPHA: (5211) implies: % 133.56/19.15 | | | | | | | | | | | | | | | (5212) op(e3, e1) = e3 % 133.56/19.15 | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | REF_CLOSE: (169), (5166), (5212), (function-axioms) are % 133.56/19.15 | | | | | | | | | | | | | | | inconsistent by sub-proof #705. % 133.56/19.15 | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | Case 2: % 133.56/19.15 | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | (5213) all_57_5 = e3 & op(e2, e1) = e3 % 133.56/19.15 | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | ALPHA: (5213) implies: % 133.56/19.15 | | | | | | | | | | | | | | | (5214) op(e2, e1) = e3 % 133.56/19.15 | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 133.56/19.15 | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | Case 1: % 133.56/19.15 | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | (5215) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 133.56/19.15 | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 133.56/19.15 | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (5153), (5165), (5215), % 133.56/19.15 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.15 | | | | | | | | | | | | | | | | #183. % 133.56/19.15 | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | Case 2: % 133.56/19.15 | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | (5216) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 133.56/19.15 | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 133.56/19.15 | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | BETA: splitting (5216) gives: % 133.56/19.15 | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | Case 1: % 133.56/19.15 | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | (5217) all_57_7 = e3 & op(e1, e2) = e3 % 133.56/19.15 | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | ALPHA: (5217) implies: % 133.56/19.15 | | | | | | | | | | | | | | | | | (5218) op(e1, e2) = e3 % 133.56/19.15 | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e3, % 133.56/19.15 | | | | | | | | | | | | | | | | | e2, e1, simplifying with (162), (5218) gives: % 133.56/19.15 | | | | | | | | | | | | | | | | | (5219) all_52_6 = e3 % 133.56/19.15 | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e3, % 133.56/19.15 | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (5214) gives: % 133.56/19.15 | | | | | | | | | | | | | | | | | (5220) all_52_9 = e3 % 133.56/19.15 | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | REDUCE: (362), (5220) imply: % 133.56/19.15 | | | | | | | | | | | | | | | | | (5221) ~ (all_6_2 = e3) % 133.56/19.15 | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 133.56/19.15 | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.15 | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | (5222) ~ (all_48_2 = e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | REDUCE: (5142), (5222) imply: % 133.56/19.15 | | | | | | | | | | | | | | | | | | (5223) $false % 133.56/19.15 | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | CLOSE: (5223) is inconsistent. % 133.56/19.15 | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.15 | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | (5224) ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | | = all_48_1 & $i(all_48_1)) % 133.56/19.15 | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | BETA: splitting (5224) gives: % 133.56/19.15 | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5225) ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | $i(all_48_0) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | ALPHA: (5225) implies: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5226) ~ (all_48_0 = e3) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5227) op(e1, e2) = all_48_0 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5218), (5226), (5227), (function-axioms) are % 133.56/19.15 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #188. % 133.56/19.15 | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5228) ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | $i(all_48_1) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | ALPHA: (5228) implies: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5229) ~ (all_48_1 = e0) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | (5230) op(e1, e1) = all_48_1 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (5231) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (45), (168), (204), (278), (5153), (5154), % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (5156), (5162), (5167), (5168), (5231), % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | #189. % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (5232) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5232) gives: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | (5233) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5233) gives: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5234) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5234) implies: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5235) op(e1, e1) = e3 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (5160), (5235), (function-axioms) are % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771. % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5236) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5236) implies: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5237) op(e2, e1) = e2 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e2, e1, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e2, simplifying with (5214), (5237) gives: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5238) e3 = e2 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (5238) imply: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5239) $false % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5239) is inconsistent. % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | (5240) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5240) gives: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5241) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5241) implies: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5242) op(e2, e2) = e0 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5153), (5242), (function-axioms) are % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (5243) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5243) gives: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (5244) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5244) implies: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (5245) op(e1, e1) = e2 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (5245), (function-axioms) are % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (5246) op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5246) implies: % 133.56/19.15 | | | | | | | | | | | | | | | | | | | | | | | (5247) op(e0, e0) = all_56_31 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | (5248) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (5209), (5247) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | (5249) all_56_31 = e3 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | all_48_1, e1, e1, simplifying with (39), (5230) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | (5250) all_48_1 = all_6_2 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5229), (5250) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | (5251) ~ (all_6_2 = e0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | (5252) all_54_10 = e3 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (5160), (5252) are inconsistent by % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #742. % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | (5253) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5253) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | (5254) all_54_10 = e2 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (372), (5254) are inconsistent by sub-proof % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | #741. % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | (5255) all_54_10 = e1 | all_54_10 = e0 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5255) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5256) all_54_10 = e1 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (5256) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5257) all_6_2 = e1 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5257) implies: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5258) all_6_2 = e1 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (5258) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5259) ~ (all_52_14 = e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (5258) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5260) op(e1, e1) = e1 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5248) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5261) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5261) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5262) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5262) implies: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5263) ~ (all_56_1 = e3) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5264) op(e3, e3) = all_56_1 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5168), (5263), (5264), (function-axioms) are % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #766. % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5265) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5265) implies: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5266) all_56_31 = e2 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5249), (5266) are inconsistent by sub-proof % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #532. % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5267) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (5259), (5260), (5267), (function-axioms) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #182. % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5268) all_54_10 = e0 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (5251), (5268) are inconsistent by % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #506. % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | (5269) all_57_13 = e3 & op(e0, e2) = e3 % 133.56/19.16 | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5207), (5269), (function-axioms) are % 133.56/19.16 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #556. % 133.56/19.16 | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | (5270) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 133.56/19.16 | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 133.56/19.16 | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (5160), (5208), (5270), % 133.56/19.16 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.16 | | | | | | | | | | | | | | #651. % 133.56/19.16 | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | (5271) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 133.56/19.16 | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | REF_CLOSE: (278), (5154), (5156), (5162), (5271) are % 133.56/19.16 | | | | | | | | | | | | inconsistent by sub-proof #777. % 133.56/19.16 | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | (5272) all_32_2 = e1 % 133.56/19.16 | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | COMBINE_EQS: (312), (5272) imply: % 133.56/19.16 | | | | | | | | | | | (5273) all_10_2 = e1 % 133.56/19.16 | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | COMBINE_EQS: (280), (5273) imply: % 133.56/19.16 | | | | | | | | | | | (5274) all_50_2 = e1 % 133.56/19.16 | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | REDUCE: (346), (5273) imply: % 133.56/19.16 | | | | | | | | | | | (5275) ~ (all_52_12 = e1) % 133.56/19.16 | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | REDUCE: (5156), (5273) imply: % 133.56/19.16 | | | | | | | | | | | (5276) ~ (e2 = e1) % 133.56/19.16 | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | REDUCE: (45), (5273) imply: % 133.56/19.16 | | | | | | | | | | | (5277) op(e3, e3) = e1 % 133.56/19.16 | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | BETA: splitting (212) gives: % 133.56/19.16 | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | (5278) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 133.56/19.16 | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 133.56/19.16 | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | REF_CLOSE: (164), (168), (5148), (5275), (5278), % 133.56/19.16 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.16 | | | | | | | | | | | | #179. % 133.56/19.16 | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | (5279) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 133.56/19.16 | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.56/19.16 | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | BETA: splitting (5279) gives: % 133.56/19.16 | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | (5280) all_57_11 = e1 & op(e1, e0) = e1 % 133.56/19.16 | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | ALPHA: (5280) implies: % 133.56/19.16 | | | | | | | | | | | | | (5281) all_57_11 = e1 % 133.56/19.16 | | | | | | | | | | | | | (5282) op(e1, e0) = e1 % 133.56/19.16 | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | BETA: splitting (209) gives: % 133.56/19.16 | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | (5283) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 133.56/19.16 | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 133.56/19.16 | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (231), (235), % 133.56/19.16 | | | | | | | | | | | | | | (237), (5146), (5277), (5283), (function-axioms) % 133.56/19.16 | | | | | | | | | | | | | | are inconsistent by sub-proof #177. % 133.56/19.16 | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | (5284) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 133.56/19.16 | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.56/19.16 | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | BETA: splitting (5284) gives: % 133.56/19.16 | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | (5285) all_57_14 = e1 & op(e0, e1) = e1 % 133.56/19.16 | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | ALPHA: (5285) implies: % 133.56/19.16 | | | | | | | | | | | | | | | (5286) all_57_14 = e1 % 133.56/19.16 | | | | | | | | | | | | | | | (5287) op(e0, e1) = e1 % 133.56/19.16 | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11, % 133.56/19.16 | | | | | | | | | | | | | | | e1, e1, e0, simplifying with (157), (5287) gives: % 133.56/19.16 | | | | | | | | | | | | | | | (5288) all_52_11 = e1 % 133.56/19.16 | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 133.56/19.16 | | | | | | | | | | | | | | | e1, e0, e1, simplifying with (160), (5282) gives: % 133.56/19.16 | | | | | | | | | | | | | | | (5289) all_52_14 = e1 % 133.56/19.16 | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | REDUCE: (141), (5289) imply: % 133.56/19.16 | | | | | | | | | | | | | | | (5290) ~ (all_52_2 = e1) % 133.56/19.16 | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | REDUCE: (139), (5288) imply: % 133.56/19.16 | | | | | | | | | | | | | | | (5291) ~ (all_52_3 = e1) % 133.56/19.16 | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | REDUCE: (366), (5289) imply: % 133.56/19.16 | | | | | | | | | | | | | | | (5292) ~ (all_6_2 = e1) % 133.56/19.16 | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | SIMP: (5292) implies: % 133.56/19.16 | | | | | | | | | | | | | | | (5293) ~ (all_6_2 = e1) % 133.56/19.16 | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | REDUCE: (370), (5289) imply: % 133.56/19.16 | | | | | | | | | | | | | | | (5294) ~ (all_4_2 = e1) % 133.56/19.16 | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 133.56/19.16 | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | (5295) all_54_10 = e3 % 133.56/19.16 | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (5295) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | (5296) all_6_2 = e3 % 133.56/19.16 | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | REDUCE: (5160), (5296) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | (5297) $false % 133.56/19.16 | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | CLOSE: (5297) is inconsistent. % 133.56/19.16 | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | (5298) ~ (all_54_10 = e3) % 133.56/19.16 | | | | | | | | | | | | | | | | (5299) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 133.56/19.16 | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | BETA: splitting (5299) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | (5300) all_54_10 = e2 % 133.56/19.16 | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (5300) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | (5301) all_6_2 = e2 % 133.56/19.16 | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | REDUCE: (372), (5301) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | (5302) $false % 133.56/19.16 | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | CLOSE: (5302) is inconsistent. % 133.56/19.16 | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | (5303) ~ (all_54_10 = e2) % 133.56/19.16 | | | | | | | | | | | | | | | | | (5304) all_54_10 = e1 | all_54_10 = e0 % 133.56/19.16 | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | BETA: splitting (5304) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | (5305) all_54_10 = e1 % 133.56/19.16 | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (5305) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | (5306) all_6_2 = e1 % 133.56/19.16 | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | REDUCE: (5293), (5306) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | (5307) $false % 133.56/19.16 | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | CLOSE: (5307) is inconsistent. % 133.56/19.16 | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | (5308) all_54_10 = e0 % 133.56/19.16 | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (5308) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | (5309) all_6_2 = e0 % 133.56/19.16 | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (5309) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | (5310) all_46_2 = e0 % 133.56/19.16 | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | REDUCE: (348), (5309) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | (5311) ~ (all_52_2 = e0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | REDUCE: (359), (5309) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | (5312) ~ (all_52_6 = e0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | REDUCE: (5160), (5309) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | (5313) ~ (e3 = e0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | REDUCE: (5293), (5309) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | (5314) ~ (e1 = e0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | REDUCE: (39), (5309) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | (5315) op(e1, e1) = e0 % 133.56/19.16 | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | (5316) ~ (all_48_2 = e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | REDUCE: (5142), (5316) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | (5317) $false % 133.56/19.16 | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | CLOSE: (5317) is inconsistent. % 133.56/19.16 | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | (5318) ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | = all_48_1 & $i(all_48_1)) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | (5319) ~ (all_50_2 = e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | REDUCE: (5274), (5319) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | (5320) $false % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | CLOSE: (5320) is inconsistent. % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | (5321) ( ~ (all_50_0 = e2) & op(e1, e3) = all_50_0 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | $i(all_50_0)) | ( ~ (all_50_1 = e0) & op(e1, e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | = all_50_1 & $i(all_50_1)) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5321) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | (5322) ~ (all_50_0 = e2) & op(e1, e3) = all_50_0 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | $i(all_50_0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5322) implies: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | (5323) ~ (all_50_0 = e2) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | (5324) op(e1, e3) = all_50_0 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5318) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5325) ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | $i(all_48_0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5325) implies: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5326) ~ (all_48_0 = e3) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5327) op(e1, e2) = all_48_0 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | all_48_0, e2, e1, simplifying with (162), (5327) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5328) all_52_6 = all_48_0 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | all_50_0, e3, e1, simplifying with (163), (5324) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5329) all_52_2 = all_50_0 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (5328) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5330) all_54_9 = all_48_0 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (5329) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5331) all_54_8 = all_50_0 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (5329) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5332) ~ (all_52_3 = all_50_0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | SIMP: (5332) implies: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5333) ~ (all_52_3 = all_50_0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (5328), (5329) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5334) ~ (all_50_0 = all_48_0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5290), (5329) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5335) ~ (all_50_0 = e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5311), (5329) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5336) ~ (all_50_0 = e0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (5328) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5337) ~ (all_52_4 = all_48_0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5145), (5328) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5338) ~ (all_48_0 = e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5312), (5328) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | (5339) ~ (all_48_0 = e0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | (5340) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5340) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | (5341) all_57_6 = e3 & op(e1, e3) = e3 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5341) implies: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | (5342) all_57_6 = e3 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | (5343) all_54_9 = e3 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5326), (5330), (5343) are inconsistent by % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #176. % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | (5344) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5345) all_54_8 = e3 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5331), (5345) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5346) all_50_0 = e3 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5346) implies: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5347) all_50_0 = e3 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5333), (5347) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5348) ~ (all_52_3 = e3) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5334), (5347) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5349) ~ (all_48_0 = e3) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5324), (5347) imply: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (5350) op(e1, e3) = e3 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5351) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (5153), (5277), (5350), (5351), % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | #174. % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5352) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5352) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5353) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5353) gives: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5354) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5354) implies: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5355) op(e1, e1) = e3 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5315), (5355), (function-axioms) are % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5356) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5356) implies: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5357) ~ (all_56_5 = e3) % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5358) op(e1, e3) = all_56_5 % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5350), (5357), (5358), (function-axioms) are % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #724. % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5359) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5359) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5360) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5360) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5361) op(e2, e2) = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5153), (5361), (function-axioms) are % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5362) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5362) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5363) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5363) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5364) op(e1, e1) = e2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (5364), (function-axioms) are % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5365) op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5365) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5366) op(e0, e0) = all_56_31 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5367) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5368) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5368) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5369) all_57_6 = e2 & op(e1, e3) = e2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5369) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5370) op(e1, e3) = e2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5323), (5324), (5370), (function-axioms) are % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #735. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5371) all_57_7 = e2 & op(e1, e2) = e2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5371) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5372) all_57_7 = e2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5344) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5373) all_54_9 = e2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5330), (5373) imply: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5374) all_48_0 = e2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5337), (5374) imply: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5375) ~ (all_52_4 = e2) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5326), (5374) imply: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5376) ~ (e3 = e2) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5377) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5377) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5378) all_57_12 = e2 & op(e0, e3) = e2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5378) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5379) all_57_12 = e2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5380) op(e0, e3) = e2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5381) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5381) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5382) all_57_0 = e0 & op(e3, e3) = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5382) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5383) op(e3, e3) = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5277), (5383), (function-axioms) are % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5384) all_57_2 = e0 & op(e2, e3) = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5384) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5385) op(e2, e3) = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (36), (5366) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5386) all_56_31 = all_4_2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e2, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (5380) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5387) all_52_3 = e2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e0, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (167), (5385) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5388) all_52_1 = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (5387), (5388) imply: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5389) ~ (e2 = e0) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (5387) imply: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5390) ~ (all_4_2 = e2) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5367) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5391) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5391) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5392) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5392) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5393) all_56_31 = e3 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5394) ~ (all_56_25 = e0) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5395) op(e0, e3) = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5396) op(e3, e0) = all_56_25 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5397) op(e3, e2) = all_56_9 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5398) op(e3, e3) = all_56_1 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5386), (5393) imply: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5399) all_4_2 = e3 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (5399) imply: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5400) all_34_2 = e3 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (5399) imply: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5401) ~ (all_52_7 = e3) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5402) ~ (all_34_2 = e3) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5400), (5402) imply: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5403) $false % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5403) is inconsistent. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5404) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_34_1 & $i(all_34_1)) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5405) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (159), (168), (170), (232), (236), % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5153), (5277), (5291), (5348), (5375), (5394), % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5395), (5396), (5397), (5398), (5404), (5405), % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #173. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5406) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5406) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5407) all_57_7 = e3 & op(e1, e2) = e3 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (217), (372), (5282), (5323), % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5324), (5407), (function-axioms) are inconsistent % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #171. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5408) all_57_13 = e3 & op(e0, e2) = e3 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5401), (5408), (function-axioms) are % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #556. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5409) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5158), (5386), (5409) are inconsistent by % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #765. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5410) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5410) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5411) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5411) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5412) ~ (all_56_31 = e0) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5413) ~ (all_56_23 = e1) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5414) op(e0, e1) = all_56_23 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5386), (5412) imply: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5415) ~ (all_4_2 = e0) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5416) all_54_15 = e3 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5416) imply: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5417) all_4_2 = e3 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5417) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5418) all_4_2 = e3 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (5418) imply: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5419) op(e0, e0) = e3 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5420) ~ (all_46_2 = e0) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5310), (5420) imply: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5421) $false % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5421) is inconsistent. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5422) ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_46_1 & $i(all_46_1)) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5422) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5423) ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_46_0) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5423) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5424) op(e0, e1) = all_46_0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23, e1, e0, simplifying with (5287), (5414) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5425) all_56_23 = e1 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_46_0, % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23, e1, e0, simplifying with (5414), (5424) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5426) all_56_23 = all_46_0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5425), (5426) imply: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5427) all_46_0 = e1 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5413), (5425) imply: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5428) $false % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5428) is inconsistent. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5429) ~ (all_46_1 = e3) & op(e0, e0) = all_46_1 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_46_1) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5419), (5429), (function-axioms) are inconsistent % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #758. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5430) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (5158), (5415), (5430) are % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #746. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5431) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5431) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5432) ~ (all_56_5 = e3) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5433) op(e1, e3) = all_56_5 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5350), (5432), (5433), (function-axioms) are % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #724. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5434) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5434) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5435) all_57_6 = e0 & op(e1, e3) = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5435) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5436) all_57_6 = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5342), (5436) are inconsistent by sub-proof % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #588. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5437) all_57_12 = e0 & op(e0, e3) = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5437) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5438) all_57_12 = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5379), (5438) are inconsistent by sub-proof % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #682. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5439) all_57_13 = e2 & op(e0, e2) = e2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5439) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5440) all_57_13 = e2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5441) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5441) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5442) all_57_1 = e0 & op(e3, e2) = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5442) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5443) all_57_1 = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5444) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5444) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5445) all_57_1 = e3 & op(e3, e2) = e3 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5443), (5445) are inconsistent by sub-proof % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #376. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5446) all_57_3 = e3 & op(e2, e2) = e3 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5446) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5447) all_57_3 = e3 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (227), (228), (5372), % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5440), (5447) are inconsistent by sub-proof #287. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5448) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5448) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5449) all_57_7 = e3 & op(e1, e2) = e3 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (217), (372), (5282), (5323), % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5324), (5449), (function-axioms) are inconsistent % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #171. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5450) all_57_13 = e3 & op(e0, e2) = e3 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5450) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5451) all_57_13 = e3 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5440), (5451) are inconsistent by sub-proof % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #408. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5452) all_57_3 = e0 & op(e2, e2) = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5452) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5453) op(e2, e2) = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5153), (5453), (function-axioms) are % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5454) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (162), (5312), (5440), (5454), % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #170. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5455) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5455) gives: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5456) all_57_14 = e2 & op(e0, e1) = e2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5286), (5456) are inconsistent by sub-proof % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #213. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5457) all_57_15 = e2 & op(e0, e0) = e2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5457) implies: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5458) op(e0, e0) = e2 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (5158), (5366), (5458), (function-axioms) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #427. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5459) all_54_9 = e1 | all_54_9 = e0 % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (5145), (5312), (5459) are inconsistent by % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #168. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5460) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (372), (5282), (5460), % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #172. % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (5461) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (5290), (5311), (5323), (5331), (5461) are % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #473. % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5462) all_57_7 = e3 & op(e1, e2) = e3 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (217), (372), (5282), (5323), % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5324), (5462), (function-axioms) are inconsistent % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #171. % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5463) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5463) gives: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5464) all_57_8 = e3 & op(e1, e1) = e3 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5464) implies: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5465) op(e1, e1) = e3 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5315), (5465), (function-axioms) are % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5466) all_57_11 = e3 & op(e1, e0) = e3 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5466) implies: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5467) all_57_11 = e3 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5281), (5467) are inconsistent by sub-proof % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | #167. % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (5468) ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_48_1) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5468) implies: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (5469) ~ (all_48_1 = e0) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (5470) op(e1, e1) = all_48_1 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_48_1, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (5315), (5470) gives: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (5471) all_48_1 = e0 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5469), (5471) imply: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (5472) $false % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5472) is inconsistent. % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (5473) ~ (all_50_1 = e0) & op(e1, e1) = all_50_1 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_50_1) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5315), (5473), (function-axioms) are inconsistent % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | by sub-proof #719. % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | (5474) all_57_15 = e1 & op(e0, e0) = e1 % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | ALPHA: (5474) implies: % 133.56/19.18 | | | | | | | | | | | | | | | (5475) op(e0, e0) = e1 % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (5475), (function-axioms) are % 133.56/19.18 | | | | | | | | | | | | | | | inconsistent by sub-proof #354. % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | (5476) all_57_15 = e1 & op(e0, e0) = e1 % 133.56/19.18 | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | ALPHA: (5476) implies: % 133.56/19.18 | | | | | | | | | | | | | (5477) op(e0, e0) = e1 % 133.56/19.18 | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | REF_CLOSE: (36), (371), (5477), (function-axioms) are % 133.56/19.18 | | | | | | | | | | | | | inconsistent by sub-proof #354. % 133.56/19.18 | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | % 133.56/19.18 | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | (5478) all_28_2 = e3 % 133.56/19.18 | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | COMBINE_EQS: (316), (5478) imply: % 133.56/19.18 | | | | | | | | | | (5479) all_6_2 = e3 % 133.56/19.18 | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | REDUCE: (359), (5479) imply: % 133.56/19.18 | | | | | | | | | | (5480) ~ (all_52_6 = e3) % 133.56/19.18 | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | REDUCE: (361), (5479) imply: % 133.56/19.18 | | | | | | | | | | (5481) ~ (all_52_8 = e3) % 133.56/19.18 | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | REDUCE: (362), (5479) imply: % 133.56/19.18 | | | | | | | | | | (5482) ~ (all_52_9 = e3) % 133.56/19.18 | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | REDUCE: (39), (5479) imply: % 133.56/19.18 | | | | | | | | | | (5483) op(e1, e1) = e3 % 133.56/19.18 | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | BETA: splitting (5141) gives: % 133.56/19.18 | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | (5484) ~ (all_8_0 = e0) & op(e1, e2) = all_8_0 & % 133.56/19.18 | | | | | | | | | | | $i(all_8_0) % 133.56/19.18 | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | ALPHA: (5484) implies: % 133.56/19.18 | | | | | | | | | | | (5485) ~ (all_8_0 = e0) % 133.56/19.18 | | | | | | | | | | | (5486) op(e1, e2) = all_8_0 % 133.56/19.18 | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, % 133.56/19.18 | | | | | | | | | | | all_8_0, e2, e1, simplifying with (162), (5486) % 133.56/19.18 | | | | | | | | | | | gives: % 133.56/19.18 | | | | | | | | | | | (5487) all_52_6 = all_8_0 % 133.56/19.18 | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | COMBINE_EQS: (257), (5487) imply: % 133.56/19.18 | | | | | | | | | | | (5488) all_54_9 = all_8_0 % 133.56/19.18 | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | REDUCE: (136), (5487) imply: % 133.56/19.18 | | | | | | | | | | | (5489) ~ (all_52_4 = all_8_0) % 133.56/19.18 | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | REDUCE: (5480), (5487) imply: % 133.56/19.18 | | | | | | | | | | | (5490) ~ (all_8_0 = e3) % 133.56/19.18 | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | REDUCE: (5145), (5487) imply: % 133.56/19.18 | | | | | | | | | | | (5491) ~ (all_8_0 = e1) % 133.56/19.18 | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | BETA: splitting (195) gives: % 133.56/19.18 | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | (5492) all_54_9 = e3 % 133.56/19.18 | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | COMBINE_EQS: (5488), (5492) imply: % 133.56/19.18 | | | | | | | | | | | | (5493) all_8_0 = e3 % 133.56/19.18 | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | REDUCE: (5490), (5493) imply: % 133.56/19.18 | | | | | | | | | | | | (5494) $false % 133.56/19.18 | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | CLOSE: (5494) is inconsistent. % 133.56/19.18 | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | (5495) ~ (all_54_9 = e3) % 133.56/19.18 | | | | | | | | | | | | (5496) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 133.56/19.18 | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | BETA: splitting (5496) gives: % 133.56/19.18 | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | (5497) all_54_9 = e2 % 133.56/19.18 | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | COMBINE_EQS: (5488), (5497) imply: % 133.56/19.18 | | | | | | | | | | | | | (5498) all_8_0 = e2 % 133.56/19.18 | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | REDUCE: (5489), (5498) imply: % 133.56/19.18 | | | | | | | | | | | | | (5499) ~ (all_52_4 = e2) % 133.56/19.18 | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | REDUCE: (5490), (5498) imply: % 133.56/19.18 | | | | | | | | | | | | | (5500) ~ (e3 = e2) % 133.56/19.18 | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | REDUCE: (5486), (5498) imply: % 133.56/19.18 | | | | | | | | | | | | | (5501) op(e1, e2) = e2 % 133.56/19.18 | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | BETA: splitting (79) gives: % 133.56/19.18 | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | (5502) ~ (all_32_2 = e1) % 133.56/19.18 | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | REDUCE: (312), (5502) imply: % 133.56/19.18 | | | | | | | | | | | | | | (5503) ~ (all_10_2 = e1) % 133.56/19.18 | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | BETA: splitting (204) gives: % 133.56/19.18 | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | (5504) all_54_0 = e3 % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | COMBINE_EQS: (278), (5504) imply: % 133.56/19.18 | | | | | | | | | | | | | | | (5505) all_10_2 = e3 % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | REDUCE: (336), (5505) imply: % 133.56/19.18 | | | | | | | | | | | | | | | (5506) ~ (all_52_1 = e3) % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | REDUCE: (342), (5505) imply: % 133.56/19.18 | | | | | | | | | | | | | | | (5507) ~ (all_52_4 = e3) % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | REDUCE: (346), (5505) imply: % 133.56/19.18 | | | | | | | | | | | | | | | (5508) ~ (all_52_12 = e3) % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | REDUCE: (45), (5505) imply: % 133.56/19.18 | | | | | | | | | | | | | | | (5509) op(e3, e3) = e3 % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | (5510) all_54_1 = e3 % 133.56/19.18 | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (5510) imply: % 133.56/19.18 | | | | | | | | | | | | | | | | (5511) all_52_4 = e3 % 133.56/19.18 | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | REDUCE: (5507), (5511) imply: % 133.56/19.18 | | | | | | | | | | | | | | | | (5512) $false % 133.56/19.18 | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | CLOSE: (5512) is inconsistent. % 133.56/19.18 | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | (5513) ~ (all_54_1 = e3) % 133.56/19.18 | | | | | | | | | | | | | | | | (5514) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 133.56/19.18 | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | BETA: splitting (5514) gives: % 133.56/19.18 | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | (5515) all_54_1 = e2 % 133.56/19.18 | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (5515) imply: % 133.56/19.18 | | | | | | | | | | | | | | | | | (5516) all_52_4 = e2 % 133.56/19.18 | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | REDUCE: (5499), (5516) imply: % 133.56/19.18 | | | | | | | | | | | | | | | | | (5517) $false % 133.56/19.18 | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | CLOSE: (5517) is inconsistent. % 133.56/19.18 | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | (5518) all_54_1 = e1 | all_54_1 = e0 % 133.56/19.18 | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | BETA: splitting (5518) gives: % 133.56/19.18 | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | (5519) all_54_1 = e1 % 133.56/19.18 | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (5519) imply: % 133.56/19.18 | | | | | | | | | | | | | | | | | | (5520) all_52_4 = e1 % 133.56/19.18 | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | REDUCE: (5144), (5520) imply: % 133.56/19.18 | | | | | | | | | | | | | | | | | | (5521) $false % 133.56/19.18 | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | CLOSE: (5521) is inconsistent. % 133.56/19.18 | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | (5522) all_54_1 = e0 % 133.56/19.18 | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (5522) imply: % 133.56/19.18 | | | | | | | | | | | | | | | | | | (5523) all_52_4 = e0 % 133.56/19.18 | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | REDUCE: (135), (5523) imply: % 133.56/19.18 | | | | | | | | | | | | | | | | | | (5524) ~ (all_52_7 = e0) % 133.56/19.18 | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | SIMP: (5524) implies: % 133.56/19.18 | | | | | | | | | | | | | | | | | | (5525) ~ (all_52_7 = e0) % 133.56/19.18 | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | REDUCE: (5507), (5523) imply: % 133.56/19.18 | | | | | | | | | | | | | | | | | | (5526) ~ (e3 = e0) % 133.56/19.18 | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | REDUCE: (5144), (5523) imply: % 133.56/19.18 | | | | | | | | | | | | | | | | | | (5527) ~ (e1 = e0) % 133.56/19.18 | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 133.56/19.18 | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | (5528) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (5153), (5506), (5528), % 133.56/19.18 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.18 | | | | | | | | | | | | | | | | | | | #166. % 133.56/19.18 | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | (5529) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | BETA: splitting (5529) gives: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | (5530) all_57_5 = e3 & op(e2, e1) = e3 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5482), (5530), (function-axioms) are % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | (5531) all_57_10 = e3 & op(e2, e0) = e3 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | ALPHA: (5531) implies: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | (5532) op(e2, e0) = e3 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (5533) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (45), (168), (204), (278), (5153), (5154), % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (5156), (5503), (5508), (5509), (5533), % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | #189. % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (5534) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5534) gives: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (5535) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5535) gives: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5536) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5536) implies: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5537) ~ (all_56_1 = e3) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5538) op(e3, e3) = all_56_1 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5509), (5537), (5538), (function-axioms) are % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #766. % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5539) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5539) implies: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5540) ~ (all_56_13 = e2) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5541) op(e1, e2) = all_56_13 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5501), (5540), (5541), (function-axioms) are % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #165. % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (5542) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5542) gives: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5543) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5543) implies: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5544) op(e2, e2) = e0 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (36), (39), (158), (164), % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (168), (206), (371), (372), (5483), (5508), % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5509), (5525), (5532), (5544), (function-axioms) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #542. % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (5545) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5545) gives: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5546) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5546) implies: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5547) op(e1, e1) = e2 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (5547), (function-axioms) are % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5548) op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5548) implies: % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5549) op(e0, e0) = all_56_31 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5550) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (158), (371), (5483), (5509), (5525), % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (5549), (5550), (function-axioms) are inconsistent % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #543. % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | (5551) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | REF_CLOSE: (278), (5154), (5156), (5503), (5551) are % 133.56/19.18 | | | | | | | | | | | | | | | inconsistent by sub-proof #777. % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | End of split % 133.56/19.18 | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | Case 2: % 133.56/19.18 | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | (5552) all_32_2 = e1 % 133.56/19.18 | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | COMBINE_EQS: (312), (5552) imply: % 133.56/19.18 | | | | | | | | | | | | | | (5553) all_10_2 = e1 % 133.56/19.18 | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | SIMP: (5553) implies: % 133.56/19.18 | | | | | | | | | | | | | | (5554) all_10_2 = e1 % 133.56/19.18 | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | REDUCE: (338), (5554) imply: % 133.56/19.18 | | | | | | | | | | | | | | (5555) ~ (all_52_2 = e1) % 133.56/19.18 | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | REDUCE: (340), (5554) imply: % 133.56/19.18 | | | | | | | | | | | | | | (5556) ~ (all_52_3 = e1) % 133.56/19.18 | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | REDUCE: (5156), (5554) imply: % 133.56/19.18 | | | | | | | | | | | | | | (5557) ~ (e2 = e1) % 133.56/19.18 | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | REDUCE: (45), (5554) imply: % 133.56/19.18 | | | | | | | | | | | | | | (5558) op(e3, e3) = e1 % 133.56/19.18 | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | BETA: splitting (220) gives: % 133.56/19.18 | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | (5559) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 133.56/19.18 | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | BETA: splitting (5559) gives: % 133.56/19.18 | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | Case 1: % 133.56/19.18 | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | (5560) all_57_4 = e1 & op(e3, e1) = e1 % 133.56/19.18 | | | | | | | | | | | | | | | | % 133.56/19.18 | | | | | | | | | | | | | | | | ALPHA: (5560) implies: % 133.56/19.18 | | | | | | | | | | | | | | | | (5561) all_57_4 = e1 % 133.56/19.18 | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (170), (232), % 133.56/19.19 | | | | | | | | | | | | | | | | (236), (238), (5481), (5499), (5558), (5561), % 133.56/19.19 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.19 | | | | | | | | | | | | | | | | #162. % 133.56/19.19 | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | Case 2: % 133.56/19.19 | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | (5562) all_57_5 = e1 & op(e2, e1) = e1 % 133.56/19.19 | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5147), (5562), (function-axioms) are % 133.56/19.19 | | | | | | | | | | | | | | | | inconsistent by sub-proof #161. % 133.56/19.19 | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | End of split % 133.56/19.19 | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | Case 2: % 133.56/19.19 | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | (5563) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 133.56/19.19 | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 133.56/19.19 | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | BETA: splitting (5563) gives: % 133.56/19.19 | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | Case 1: % 133.56/19.19 | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | (5564) all_57_8 = e1 & op(e1, e1) = e1 % 133.56/19.19 | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | ALPHA: (5564) implies: % 133.56/19.19 | | | | | | | | | | | | | | | | (5565) op(e1, e1) = e1 % 133.56/19.19 | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (5483), (5565), (function-axioms) are % 133.56/19.19 | | | | | | | | | | | | | | | | inconsistent by sub-proof #662. % 133.56/19.19 | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | Case 2: % 133.56/19.19 | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | (5566) all_57_14 = e1 & op(e0, e1) = e1 % 133.56/19.19 | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | ALPHA: (5566) implies: % 133.56/19.19 | | | | | | | | | | | | | | | | (5567) all_57_14 = e1 % 133.56/19.19 | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 133.56/19.19 | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | Case 1: % 133.56/19.19 | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | (5568) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 133.56/19.19 | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 133.56/19.19 | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | BETA: splitting (5568) gives: % 133.56/19.19 | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.19 | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | (5569) all_57_12 = e2 & op(e0, e3) = e2 % 133.56/19.19 | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | ALPHA: (5569) implies: % 133.56/19.19 | | | | | | | | | | | | | | | | | | (5570) all_57_12 = e2 % 133.56/19.19 | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.56/19.19 | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.19 | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (5571) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | BETA: splitting (5571) gives: % 133.56/19.19 | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (5572) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5572) gives: % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | (5573) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5573) implies: % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | (5574) op(e3, e3) = e2 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237), % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | (5570), (5574), (function-axioms) are inconsistent % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | by sub-proof #290. % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | (5575) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5575) implies: % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | (5576) ~ (all_56_13 = e2) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | (5577) op(e1, e2) = all_56_13 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5501), (5576), (5577), (function-axioms) are % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #165. % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (5578) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (5153), (5558), (5578), % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | #175. % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.19 | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.19 | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (5579) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (39), (82), (159), % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (163), (168), (169), (170), (232), (236), (238), % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (307), (349), (368), (371), (372), (5153), (5158), % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (5481), (5483), (5499), (5501), (5555), (5556), % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (5558), (5579), (function-axioms) are inconsistent % 133.56/19.19 | | | | | | | | | | | | | | | | | | | by sub-proof #159. % 133.56/19.19 | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | End of split % 133.56/19.19 | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.19 | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | (5580) all_57_13 = e2 & op(e0, e2) = e2 % 133.56/19.19 | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | ALPHA: (5580) implies: % 133.56/19.19 | | | | | | | | | | | | | | | | | | (5581) op(e0, e2) = e2 % 133.56/19.19 | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.56/19.19 | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.19 | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (5582) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | BETA: splitting (5582) gives: % 133.56/19.19 | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (5583) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5501), (5558), (5583), (function-axioms) are % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #158. % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (5584) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5153), (5581), (5584), (function-axioms) are % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #157. % 133.56/19.19 | | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | End of split % 133.56/19.19 | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.19 | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (5585) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.56/19.19 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.56/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.56/19.19 | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (36), (39), (82), (159), % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (163), (168), (169), (170), (232), (236), (238), % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (307), (349), (368), (371), (372), (5153), (5158), % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (5481), (5483), (5499), (5501), (5555), (5556), % 133.56/19.19 | | | | | | | | | | | | | | | | | | | (5558), (5585), (function-axioms) are inconsistent % 133.56/19.19 | | | | | | | | | | | | | | | | | | | by sub-proof #159. % 133.56/19.19 | | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | End of split % 133.56/19.19 | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | End of split % 133.56/19.19 | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | Case 2: % 133.56/19.19 | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | (5586) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 133.56/19.19 | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 133.56/19.19 | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | BETA: splitting (5586) gives: % 133.56/19.19 | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | Case 1: % 133.56/19.19 | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | (5587) all_57_14 = e2 & op(e0, e1) = e2 % 133.56/19.19 | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | ALPHA: (5587) implies: % 133.56/19.19 | | | | | | | | | | | | | | | | | | (5588) all_57_14 = e2 % 133.56/19.19 | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5567), (5588) are inconsistent by sub-proof % 133.56/19.19 | | | | | | | | | | | | | | | | | | #560. % 133.56/19.19 | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | Case 2: % 133.56/19.19 | | | | | | | | | | | | | | | | | | % 133.56/19.19 | | | | | | | | | | | | | | | | | | (5589) all_57_15 = e2 & op(e0, e0) = e2 % 133.67/19.19 | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | ALPHA: (5589) implies: % 133.67/19.19 | | | | | | | | | | | | | | | | | | (5590) op(e0, e0) = e2 % 133.67/19.19 | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.67/19.19 | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.19 | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | (5591) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.19 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | BETA: splitting (5591) gives: % 133.67/19.19 | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (5592) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5501), (5558), (5592), (function-axioms) are % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #158. % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (5593) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (5153), (5558), (5593), % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | #175. % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.19 | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.19 | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | (5594) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.67/19.19 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.67/19.19 | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.67/19.19 | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.67/19.19 | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.67/19.19 | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.67/19.19 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.67/19.19 | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.67/19.19 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.67/19.19 | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.67/19.19 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.67/19.19 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | BETA: splitting (5594) gives: % 133.67/19.19 | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (5595) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5501), (5555), (5595), (function-axioms) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #160. % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (5596) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (39), (372), (5153), (5158), (5590), % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | (5596), (function-axioms) are inconsistent by % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | sub-proof #156. % 133.67/19.19 | | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.19 | | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | | End of split % 133.67/19.19 | | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | | End of split % 133.67/19.19 | | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | | End of split % 133.67/19.19 | | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | | End of split % 133.67/19.19 | | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | | End of split % 133.67/19.19 | | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | End of split % 133.67/19.19 | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | Case 2: % 133.67/19.19 | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | (5597) all_54_9 = e1 | all_54_9 = e0 % 133.67/19.19 | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | | REF_CLOSE: (5485), (5488), (5491), (5597) are inconsistent by % 133.67/19.19 | | | | | | | | | | | | | sub-proof #155. % 133.67/19.19 | | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | | End of split % 133.67/19.19 | | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | End of split % 133.67/19.19 | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | Case 2: % 133.67/19.19 | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | (5598) ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 & % 133.67/19.19 | | | | | | | | | | | $i(all_8_1) % 133.67/19.19 | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | ALPHA: (5598) implies: % 133.67/19.19 | | | | | | | | | | | (5599) ~ (all_8_1 = e3) % 133.67/19.19 | | | | | | | | | | | (5600) op(e1, e1) = all_8_1 % 133.67/19.19 | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_8_1, % 133.67/19.19 | | | | | | | | | | | e1, e1, simplifying with (5483), (5600) gives: % 133.67/19.19 | | | | | | | | | | | (5601) all_8_1 = e3 % 133.67/19.19 | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | REDUCE: (5599), (5601) imply: % 133.67/19.19 | | | | | | | | | | | (5602) $false % 133.67/19.19 | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | | CLOSE: (5602) is inconsistent. % 133.67/19.19 | | | | | | | | | | | % 133.67/19.19 | | | | | | | | | | End of split % 133.67/19.19 | | | | | | | | | | % 133.67/19.19 | | | | | | | | | End of split % 133.67/19.19 | | | | | | | | | % 133.67/19.19 | | | | | | | | Case 2: % 133.67/19.19 | | | | | | | | | % 133.67/19.19 | | | | | | | | | (5603) all_20_2 = e2 % 133.67/19.19 | | | | | | | | | (5604) ( ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 & % 133.67/19.19 | | | | | | | | | $i(all_20_0)) | ( ~ (all_20_1 = e1) & op(e2, e2) = % 133.67/19.19 | | | | | | | | | all_20_1 & $i(all_20_1)) % 133.67/19.19 | | | | | | | | | % 133.67/19.19 | | | | | | | | | COMBINE_EQS: (318), (5603) imply: % 133.67/19.19 | | | | | | | | | (5605) all_4_2 = e2 % 133.67/19.19 | | | | | | | | | % 133.67/19.19 | | | | | | | | | SIMP: (5605) implies: % 133.67/19.19 | | | | | | | | | (5606) all_4_2 = e2 % 133.67/19.19 | | | | | | | | | % 133.67/19.19 | | | | | | | | | REDUCE: (367), (5606) imply: % 133.67/19.19 | | | | | | | | | (5607) ~ (all_52_11 = e2) % 133.67/19.19 | | | | | | | | | % 133.67/19.19 | | | | | | | | | REDUCE: (368), (5606) imply: % 133.67/19.19 | | | | | | | | | (5608) ~ (all_52_12 = e2) % 133.67/19.19 | | | | | | | | | % 133.67/19.19 | | | | | | | | | REDUCE: (369), (5606) imply: % 133.67/19.19 | | | | | | | | | (5609) ~ (all_52_13 = e2) % 133.67/19.19 | | | | | | | | | % 133.67/19.19 | | | | | | | | | REDUCE: (370), (5606) imply: % 133.67/19.19 | | | | | | | | | (5610) ~ (all_52_14 = e2) % 133.67/19.19 | | | | | | | | | % 133.67/19.19 | | | | | | | | | REDUCE: (36), (5606) imply: % 133.67/19.20 | | | | | | | | | (5611) op(e0, e0) = e2 % 133.67/19.20 | | | | | | | | | % 133.67/19.20 | | | | | | | | | BETA: splitting (5604) gives: % 133.67/19.20 | | | | | | | | | % 133.67/19.20 | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | (5612) ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 & % 133.67/19.20 | | | | | | | | | | $i(all_20_0) % 133.67/19.20 | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | ALPHA: (5612) implies: % 133.67/19.20 | | | | | | | | | | (5613) ~ (all_20_0 = e3) % 133.67/19.20 | | | | | | | | | | (5614) op(e2, e0) = all_20_0 % 133.67/19.20 | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 133.67/19.20 | | | | | | | | | | all_20_0, e0, e2, simplifying with (164), (5614) % 133.67/19.20 | | | | | | | | | | gives: % 133.67/19.20 | | | | | | | | | | (5615) all_52_13 = all_20_0 % 133.67/19.20 | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | COMBINE_EQS: (259), (5615) imply: % 133.67/19.20 | | | | | | | | | | (5616) all_54_7 = all_20_0 % 133.67/19.20 | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | REDUCE: (145), (5615) imply: % 133.67/19.20 | | | | | | | | | | (5617) ~ (all_52_1 = all_20_0) % 133.67/19.20 | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | REDUCE: (117), (5615) imply: % 133.67/19.20 | | | | | | | | | | (5618) ~ (all_52_9 = all_20_0) % 133.67/19.20 | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | REDUCE: (113), (5615) imply: % 133.67/19.20 | | | | | | | | | | (5619) ~ (all_52_12 = all_20_0) % 133.67/19.20 | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | REDUCE: (110), (5615) imply: % 133.67/19.20 | | | | | | | | | | (5620) ~ (all_52_14 = all_20_0) % 133.67/19.20 | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | SIMP: (5620) implies: % 133.67/19.20 | | | | | | | | | | (5621) ~ (all_52_14 = all_20_0) % 133.67/19.20 | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | REDUCE: (5609), (5615) imply: % 133.67/19.20 | | | | | | | | | | (5622) ~ (all_20_0 = e2) % 133.67/19.20 | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | REDUCE: (5148), (5615) imply: % 133.67/19.20 | | | | | | | | | | (5623) ~ (all_20_0 = e1) % 133.67/19.20 | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | BETA: splitting (197) gives: % 133.67/19.20 | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | (5624) all_54_7 = e3 % 133.67/19.20 | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | COMBINE_EQS: (5616), (5624) imply: % 133.67/19.20 | | | | | | | | | | | (5625) all_20_0 = e3 % 133.67/19.20 | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | REDUCE: (5613), (5625) imply: % 133.67/19.20 | | | | | | | | | | | (5626) $false % 133.67/19.20 | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | CLOSE: (5626) is inconsistent. % 133.67/19.20 | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | (5627) ~ (all_54_7 = e3) % 133.67/19.20 | | | | | | | | | | | (5628) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 133.67/19.20 | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | BETA: splitting (5628) gives: % 133.67/19.20 | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | (5629) all_54_7 = e2 % 133.67/19.20 | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | COMBINE_EQS: (5616), (5629) imply: % 133.67/19.20 | | | | | | | | | | | | (5630) all_20_0 = e2 % 133.67/19.20 | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | REDUCE: (5622), (5630) imply: % 133.67/19.20 | | | | | | | | | | | | (5631) $false % 133.67/19.20 | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | CLOSE: (5631) is inconsistent. % 133.67/19.20 | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | (5632) ~ (all_54_7 = e2) % 133.67/19.20 | | | | | | | | | | | | (5633) all_54_7 = e1 | all_54_7 = e0 % 133.67/19.20 | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | BETA: splitting (5633) gives: % 133.67/19.20 | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | (5634) all_54_7 = e1 % 133.67/19.20 | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | COMBINE_EQS: (5616), (5634) imply: % 133.67/19.20 | | | | | | | | | | | | | (5635) all_20_0 = e1 % 133.67/19.20 | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5623), (5635) imply: % 133.67/19.20 | | | | | | | | | | | | | (5636) $false % 133.67/19.20 | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | CLOSE: (5636) is inconsistent. % 133.67/19.20 | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | (5637) all_54_7 = e0 % 133.67/19.20 | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | COMBINE_EQS: (5616), (5637) imply: % 133.67/19.20 | | | | | | | | | | | | | (5638) all_20_0 = e0 % 133.67/19.20 | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5617), (5638) imply: % 133.67/19.20 | | | | | | | | | | | | | (5639) ~ (all_52_1 = e0) % 133.67/19.20 | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5618), (5638) imply: % 133.67/19.20 | | | | | | | | | | | | | (5640) ~ (all_52_9 = e0) % 133.67/19.20 | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5619), (5638) imply: % 133.67/19.20 | | | | | | | | | | | | | (5641) ~ (all_52_12 = e0) % 133.67/19.20 | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5621), (5638) imply: % 133.67/19.20 | | | | | | | | | | | | | (5642) ~ (all_52_14 = e0) % 133.67/19.20 | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5613), (5638) imply: % 133.67/19.20 | | | | | | | | | | | | | (5643) ~ (e3 = e0) % 133.67/19.20 | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5622), (5638) imply: % 133.67/19.20 | | | | | | | | | | | | | (5644) ~ (e2 = e0) % 133.67/19.20 | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5623), (5638) imply: % 133.67/19.20 | | | | | | | | | | | | | (5645) ~ (e1 = e0) % 133.67/19.20 | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | REDUCE: (5614), (5638) imply: % 133.67/19.20 | | | | | | | | | | | | | (5646) op(e2, e0) = e0 % 133.67/19.20 | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | BETA: splitting (208) gives: % 133.67/19.20 | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | (5647) all_57_15 = e0 & op(e0, e0) = e0 % 133.67/19.20 | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | ALPHA: (5647) implies: % 133.67/19.20 | | | | | | | | | | | | | | (5648) op(e0, e0) = e0 % 133.67/19.20 | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | REF_CLOSE: (5), (5611), (5648), (function-axioms) are % 133.67/19.20 | | | | | | | | | | | | | | inconsistent by sub-proof #714. % 133.67/19.20 | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | (5649) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 133.67/19.20 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 133.67/19.20 | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 133.67/19.20 | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 133.67/19.20 | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 133.67/19.20 | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | ALPHA: (5649) implies: % 133.67/19.20 | | | | | | | | | | | | | | (5650) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 133.67/19.20 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, % 133.67/19.20 | | | | | | | | | | | | | | e0) = e0) % 133.67/19.20 | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | BETA: splitting (5650) gives: % 133.67/19.20 | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | (5651) all_57_9 = e0 & op(e3, e0) = e0 % 133.67/19.20 | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | REF_CLOSE: (168), (5641), (5651), (function-axioms) are % 133.67/19.20 | | | | | | | | | | | | | | | inconsistent by sub-proof #618. % 133.67/19.20 | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | (5652) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = % 133.67/19.20 | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 133.67/19.20 | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | BETA: splitting (5652) gives: % 133.67/19.20 | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | (5653) all_57_10 = e0 & op(e2, e0) = e0 % 133.67/19.20 | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | ALPHA: (5653) implies: % 133.67/19.20 | | | | | | | | | | | | | | | | (5654) all_57_10 = e0 % 133.67/19.20 | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | (5655) ~ (all_28_2 = e3) % 133.67/19.20 | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | REDUCE: (316), (5655) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | (5656) ~ (all_6_2 = e3) % 133.67/19.20 | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | (5657) ~ (all_32_2 = e1) % 133.67/19.20 | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | REDUCE: (312), (5657) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | (5658) ~ (all_10_2 = e1) % 133.67/19.20 | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | (5659) all_54_0 = e3 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (5659) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | (5660) all_10_2 = e3 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | REDUCE: (336), (5660) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | (5661) ~ (all_52_1 = e3) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | REDUCE: (342), (5660) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | (5662) ~ (all_52_4 = e3) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | REDUCE: (346), (5660) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | (5663) ~ (all_52_12 = e3) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5664) all_54_4 = e3 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (5664) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5665) all_52_1 = e3 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | REDUCE: (5661), (5665) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5666) $false % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | CLOSE: (5666) is inconsistent. % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5667) ~ (all_54_4 = e3) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5668) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5668) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5669) all_54_4 = e2 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (5669) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5670) all_52_1 = e2 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (5670) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5671) ~ (all_52_9 = e2) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | SIMP: (5671) implies: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5672) ~ (all_52_9 = e2) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5661), (5670) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5673) ~ (e3 = e2) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | (5674) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5674) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | (5675) all_57_4 = e2 & op(e3, e1) = e2 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5675) implies: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | (5676) all_57_4 = e2 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (5677) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5677) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (5678) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5678) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (5679) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5679) implies: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (5680) op(e3, e3) = e2 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (204), (278), (5154), (5156), (5658), % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (5680), (function-axioms) are inconsistent by % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #776. % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (5681) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5681) implies: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (5682) op(e3, e3) = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (168), (170), (238), (5662), (5663), % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (5676), (5682), (function-axioms) are inconsistent % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #732. % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (5683) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (5153), (5663), (5683), % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | #190. % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (5684) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5684) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (5685) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (165), (5656), (5672), (5685), % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | #769. % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (5686) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (39), (91), (157), (190), (246), % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (332), (364), (372), (5153), (5607), (5611), % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (5646), (5686), (function-axioms) are inconsistent % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #154. % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | (5687) all_57_5 = e2 & op(e2, e1) = e2 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5687) implies: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | (5688) op(e2, e1) = e2 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5672), (5688), (function-axioms) are % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770. % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | (5689) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (372), (5607), (5689), % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | #511. % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5690) all_54_4 = e1 | all_54_4 = e0 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (5143), (5639), (5690) are inconsistent by % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | sub-proof #153. % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | (5691) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (5154), (5156), (5658), (5691) are % 133.67/19.20 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #777. % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | End of split % 133.67/19.20 | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | (5692) all_32_2 = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (312), (5692) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | (5693) all_10_2 = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | SIMP: (5693) implies: % 133.67/19.20 | | | | | | | | | | | | | | | | | | (5694) all_10_2 = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | REDUCE: (344), (5694) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | (5695) ~ (all_52_8 = e1) % 133.67/19.20 | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | REDUCE: (346), (5694) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | (5696) ~ (all_52_12 = e1) % 133.67/19.20 | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | REDUCE: (5156), (5694) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | (5697) ~ (e2 = e1) % 133.67/19.20 | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | REDUCE: (45), (5694) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | (5698) op(e3, e3) = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | (5699) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (5699) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5700) all_57_9 = e1 & op(e3, e0) = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | ALPHA: (5700) implies: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5701) all_57_9 = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5702) all_54_3 = e3 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (5702) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5703) all_52_12 = e3 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (5703) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5704) ~ (all_52_14 = e3) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | SIMP: (5704) implies: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5705) ~ (all_52_14 = e3) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (160), (165), (167), (214), % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (223), (5153), (5611), (5639), (5640), (5701), % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5705), (function-axioms) are inconsistent by % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | sub-proof #150. % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5706) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (5608), (5641), (5696), (5706) are % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320. % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5707) all_57_10 = e1 & op(e2, e0) = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | ALPHA: (5707) implies: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5708) op(e2, e0) = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5646), (5708), (function-axioms) are % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #695. % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | (5709) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (5709) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5710) all_57_11 = e1 & op(e1, e0) = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | ALPHA: (5710) implies: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | (5711) all_57_11 = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5712) all_54_3 = e3 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (5712) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5713) all_52_12 = e3 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (5713) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5714) ~ (all_52_4 = e3) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (5713) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5715) ~ (all_52_8 = e3) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (5713) imply: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5716) ~ (all_52_14 = e3) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | SIMP: (5716) implies: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | (5717) ~ (all_52_14 = e3) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | (5718) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5718) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | (5719) all_57_9 = e3 & op(e3, e0) = e3 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5719) implies: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | (5720) all_57_9 = e3 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (5721) all_54_11 = e3 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5717), (5721) are inconsistent by % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #260. % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (5722) ~ (all_54_11 = e3) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | (5723) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5723) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (5724) all_54_11 = e2 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5610), (5724) are inconsistent by % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #259. % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (5725) ~ (all_54_11 = e2) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | (5726) all_54_11 = e1 | all_54_11 = e0 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (5727) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5727) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5728) all_57_12 = e1 & op(e0, e3) = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5728) implies: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5729) all_57_12 = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (235), (237), % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5698), (5729), (function-axioms) are inconsistent % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #583. % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5730) all_57_13 = e1 & op(e0, e2) = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5730) implies: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5731) all_57_13 = e1 % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5732) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (5153), (5714), (5732), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #183. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5733) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5733) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5734) all_57_7 = e3 & op(e1, e2) = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5734) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5735) all_57_7 = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5736) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5736) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5737) all_57_6 = e2 & op(e1, e3) = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5737) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5738) op(e1, e3) = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5739) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5739) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5740) all_57_1 = e0 & op(e3, e2) = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5740) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5741) all_57_1 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5742) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (5698), (5741), (5742), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #148. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5743) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5743) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5744) all_57_4 = e2 & op(e3, e1) = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5744) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5745) op(e3, e1) = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5746) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5746) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5747) all_57_1 = e2 & op(e3, e2) = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5741), (5747) are inconsistent by sub-proof % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #149. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5748) all_57_3 = e2 & op(e2, e2) = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5748) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5749) op(e2, e2) = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (45), (91), (121), (123), (149), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (163), (164), (165), (167), (169), (190), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (246), (332), (344), (361), (364), (5154), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5609), (5611), (5656), (5738), (5745), (5749), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #522. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5750) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5750) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5751) all_57_7 = e2 & op(e1, e2) = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5751) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5752) all_57_7 = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5735), (5752) are inconsistent by sub-proof % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #486. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5753) all_57_13 = e2 & op(e0, e2) = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5753) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5754) all_57_13 = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5731), (5754) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5755) e2 = e1 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (5755) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5756) $false % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5756) is inconsistent. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5757) all_57_9 = e2 & op(e3, e0) = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5608), (5757), (function-axioms) are % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5758) all_57_3 = e0 & op(e2, e2) = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5758) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5759) all_57_3 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5760) op(e2, e2) = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (226), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5646), (5654), (5759), (5760), (function-axioms) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #446. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5761) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5761) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5762) all_57_7 = e0 & op(e1, e2) = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5735), (5762) are inconsistent by sub-proof % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #147. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5763) all_57_13 = e0 & op(e0, e2) = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5763) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5764) all_57_13 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5731), (5764) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5765) e1 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5711), (5765) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5766) all_57_11 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (212), (5611), (5646), (5720), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5766), (function-axioms) are inconsistent by % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #257. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5767) all_57_7 = e2 & op(e1, e2) = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5735), (5767) are inconsistent by sub-proof % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #385. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5768) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (39), (208), (212), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (5611), (5720), (5768), (function-axioms) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #146. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5769) all_57_13 = e3 & op(e0, e2) = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5769) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5770) all_57_13 = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5731), (5770) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5771) e3 = e1 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (160), (165), (167), (214), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (5153), (5611), (5639), (5640), (5717), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5720), (5771), (function-axioms) are inconsistent % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #145. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (5772) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5772) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5773) all_57_14 = e1 & op(e0, e1) = e1 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5773) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5774) all_57_14 = e1 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5726) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5775) all_54_11 = e1 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (5775) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5776) all_52_14 = e1 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5776) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5777) all_52_14 = e1 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (5777) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5778) ~ (all_6_2 = e1) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5778) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5779) ~ (all_6_2 = e1) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5717), (5777) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5780) ~ (e3 = e1) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5781) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5781) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5782) all_57_4 = e3 & op(e3, e1) = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5782) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5783) op(e3, e1) = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (169), (201), (269), (5608), (5641), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5696), (5783), (function-axioms) are inconsistent % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #319. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5784) all_57_5 = e3 & op(e2, e1) = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5784) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5785) all_57_5 = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5786) all_54_10 = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (5656), (5786) are inconsistent by % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #742. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5787) ~ (all_54_10 = e3) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5788) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5788) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5789) all_54_10 = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (372), (5789) are inconsistent by sub-proof % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #741. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5790) ~ (all_54_10 = e2) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5791) all_54_10 = e1 | all_54_10 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5791) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5792) all_54_10 = e1 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (5779), (5792) are inconsistent by % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #736. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5793) all_54_10 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (5793) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5794) all_6_2 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5794) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5795) all_6_2 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (5795) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5796) op(e1, e1) = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5797) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5797) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5798) all_57_2 = e2 & op(e2, e3) = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5798) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5799) all_57_2 = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5800) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5800) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5801) all_57_4 = e2 & op(e3, e1) = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5801) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5802) all_57_4 = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5803) all_54_2 = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (5803) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5804) all_52_8 = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5804) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5805) all_52_8 = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5715), (5805) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5806) $false % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5806) is inconsistent. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5807) ~ (all_54_2 = e3) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5808) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5809) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5809) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5810) all_57_0 = e0 & op(e3, e3) = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5810) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5811) op(e3, e3) = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5698), (5811), (function-axioms) are % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5812) all_57_1 = e0 & op(e3, e2) = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5812) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5813) all_57_1 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5814) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5814) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5815) all_57_0 = e0 & op(e3, e3) = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5815) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5816) op(e3, e3) = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5698), (5816), (function-axioms) are % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5817) all_57_2 = e0 & op(e2, e3) = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5639), (5817), (function-axioms) are % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #225. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5818) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5818) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5819) all_57_6 = e0 & op(e1, e3) = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5819) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5820) all_57_6 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5821) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5821) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5822) all_57_6 = e3 & op(e1, e3) = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5822) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5823) all_57_6 = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5820), (5823) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5824) e3 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5720), (5824) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5825) all_57_9 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (170), (238), (5698), (5714), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5802), (5825), (function-axioms) are inconsistent % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #613. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5826) all_57_7 = e3 & op(e1, e2) = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5826) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5827) all_57_7 = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5828) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5828) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5829) all_57_6 = e2 & op(e1, e3) = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5829) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5830) all_57_6 = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5820), (5830) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5831) e2 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5802), (5831) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5832) all_57_4 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (221), (222), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (5656), (5774), (5832), (function-axioms) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #558. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5833) all_57_7 = e2 & op(e1, e2) = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5827), (5833) are inconsistent by sub-proof % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #385. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5834) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (39), (208), (212), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (5611), (5720), (5834), (function-axioms) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #146. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5835) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5835) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5836) all_57_8 = e3 & op(e1, e1) = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5836) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5837) op(e1, e1) = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5796), (5837), (function-axioms) are % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5838) all_57_11 = e3 & op(e1, e0) = e3 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (5717), (5838), (function-axioms) are % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5839) all_57_12 = e0 & op(e0, e3) = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5839) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5840) all_57_12 = e0 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5808) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5841) all_54_2 = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (5841) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5842) all_52_8 = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (5842) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5843) ~ (all_52_9 = e2) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5843) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5844) ~ (all_52_9 = e2) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (5842) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5845) ~ (all_52_11 = e2) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5715), (5842) imply: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5846) ~ (e3 = e2) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5847) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5847) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5848) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5848) gives: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5849) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5849) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5850) op(e3, e3) = e2 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (234), (5720), (5802), (5813), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5850), (function-axioms) are inconsistent by % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #280. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5851) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5851) implies: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5852) ~ (all_56_5 = e3) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5853) op(e1, e3) = all_56_5 % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (237), (5698), (5799), (5840), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5852), (5853), (function-axioms) are inconsistent % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #144. % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5854) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (5153), (5698), (5854), % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #175. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5855) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5855) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5856) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (165), (5796), (5844), (5856), % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #143. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5857) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (39), (91), (157), (190), (246), % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332), (364), (372), (5153), (5607), (5611), % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5646), (5857), (function-axioms) are inconsistent % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #154. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5858) all_54_2 = e1 | all_54_2 = e0 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (194), (270), (334), (361), (372), (5656), % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5695), (5796), (5858), (function-axioms) are % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #477. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5859) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5859) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5860) all_57_4 = e0 & op(e3, e1) = e0 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5860) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5861) all_57_4 = e0 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (221), (222), % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (5656), (5774), (5861), (function-axioms) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #558. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5862) all_57_9 = e0 & op(e3, e0) = e0 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5862) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5863) all_57_9 = e0 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (170), (238), (5698), (5714), % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5802), (5863), (function-axioms) are inconsistent % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #613. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5864) all_57_5 = e2 & op(e2, e1) = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5785), (5864) are inconsistent by sub-proof % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #677. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5865) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (372), (5607), (5865), % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #511. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5866) all_57_3 = e2 & op(e2, e2) = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5866) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5867) all_57_3 = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5152), (5867) are inconsistent by sub-proof % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #728. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5868) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5868) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5869) all_57_5 = e2 & op(e2, e1) = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5869) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5870) all_57_5 = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5785), (5870) are inconsistent by sub-proof % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #501. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5871) all_57_10 = e2 & op(e2, e0) = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5871) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5872) op(e2, e0) = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5609), (5872), (function-axioms) are % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5873) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5873) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5874) all_57_8 = e3 & op(e1, e1) = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5874) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5875) op(e1, e1) = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (5656), (5875), (function-axioms) are % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5876) all_57_14 = e3 & op(e0, e1) = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5876) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5877) all_57_14 = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5774), (5877) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5878) e3 = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (160), (165), (167), (214), % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (5153), (5611), (5639), (5640), (5717), % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5720), (5878), (function-axioms) are inconsistent % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #145. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5879) all_54_11 = e0 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5642), (5879) are inconsistent by % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #258. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5880) all_57_15 = e1 & op(e0, e0) = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5880) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5881) op(e0, e0) = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5611), (5881), (function-axioms) are % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | (5882) all_57_10 = e3 & op(e2, e0) = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5882) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | (5883) all_57_10 = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (165), (167), (223), (5153), (5639), % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | (5640), (5883), (function-axioms) are inconsistent % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #151. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | (5884) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (5611), (5717), (5884), % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | #330. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | (5885) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (5608), (5641), (5696), (5885) are % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | (5886) all_57_15 = e1 & op(e0, e0) = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | ALPHA: (5886) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | (5887) op(e0, e0) = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5611), (5887), (function-axioms) are % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | End of split % 133.67/19.22 | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | (5888) all_28_2 = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (5888) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | (5889) all_6_2 = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | REDUCE: (362), (5889) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | (5890) ~ (all_52_9 = e3) % 133.67/19.22 | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | REDUCE: (364), (5889) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | (5891) ~ (all_52_11 = e3) % 133.67/19.22 | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | REDUCE: (366), (5889) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | (5892) ~ (all_52_14 = e3) % 133.67/19.22 | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | REDUCE: (39), (5889) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | (5893) op(e1, e1) = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | (5894) all_54_6 = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (5894) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | | (5895) all_52_9 = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | REDUCE: (5890), (5895) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | | (5896) $false % 133.67/19.22 | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | CLOSE: (5896) is inconsistent. % 133.67/19.22 | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | (5897) ~ (all_54_6 = e3) % 133.67/19.22 | | | | | | | | | | | | | | | | | | (5898) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 133.67/19.22 | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | (5899) all_54_11 = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5892), (5899) are inconsistent by % 133.67/19.22 | | | | | | | | | | | | | | | | | | | sub-proof #260. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | (5900) ~ (all_54_11 = e3) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | (5901) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | BETA: splitting (5901) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | (5902) all_54_11 = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5610), (5902) are inconsistent by % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | sub-proof #259. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | (5903) ~ (all_54_11 = e2) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | (5904) all_54_11 = e1 | all_54_11 = e0 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | (5905) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5905) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | (5906) all_57_2 = e3 & op(e2, e3) = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5906) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | (5907) all_57_2 = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | (5908) op(e2, e3) = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5898) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | (5909) all_54_6 = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (5909) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | (5910) all_52_9 = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (5910) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | (5911) ~ (all_52_1 = e2) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (5910) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | (5912) ~ (all_52_8 = e2) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (5910) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | (5913) ~ (all_52_11 = e2) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | (5914) all_54_4 = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (5914) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | (5915) all_52_1 = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (5915) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | (5916) ~ (all_52_3 = e3) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5916) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | (5917) ~ (all_52_3 = e3) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | (5918) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (167), (5156), (5911), (5918), % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | #535. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | (5919) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5919) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (5920) all_57_6 = e2 & op(e1, e3) = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5920) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (5921) all_57_6 = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5922) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (167), (5154), (5639), (5922), % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | #142. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5923) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5923) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5924) all_57_6 = e0 & op(e1, e3) = e0 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5921), (5924) are inconsistent by sub-proof % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #520. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5925) all_57_12 = e0 & op(e0, e3) = e0 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5925) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5926) all_57_12 = e0 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5927) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5927) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5928) all_57_12 = e1 & op(e0, e3) = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5928) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5929) all_57_12 = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5926), (5929) are inconsistent by sub-proof % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #581. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5930) all_57_13 = e1 & op(e0, e2) = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5930) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5931) all_57_13 = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5904) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5932) all_54_11 = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (5932) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5933) all_52_14 = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5933) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5934) all_52_14 = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (5934) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5935) ~ (all_52_2 = e1) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (5934) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5936) ~ (all_52_12 = e1) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5892), (5934) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5937) ~ (e3 = e1) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5610), (5934) imply: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5938) ~ (e2 = e1) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5939) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5939) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5940) all_57_0 = e1 & op(e3, e3) = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5940) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5941) op(e3, e3) = e1 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5942) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (5152), (5911), (5942), % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #141. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5943) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5943) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5944) all_57_5 = e2 & op(e2, e1) = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5944) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5945) all_57_5 = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5946) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5946) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5947) all_57_9 = e3 & op(e3, e0) = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5947) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5948) all_57_9 = e3 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5949) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5949) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5950) all_57_0 = e2 & op(e3, e3) = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5950) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5951) op(e3, e3) = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5941), (5951), (function-axioms) are % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5952) all_57_1 = e2 & op(e3, e2) = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5952) implies: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5953) all_57_1 = e2 % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5954) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5954) gives: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5955) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (120), (169), (201), (269), (5608), (5641), % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5936), (5941), (5955), (function-axioms) are % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #318. % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5956) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (5153), (5941), (5956), % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #175. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5957) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5957) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5958) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5958) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5959) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5959) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5960) op(e1, e3) = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5935), (5960), (function-axioms) are % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #725. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5961) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5961) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5962) ~ (all_56_5 = e3) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5963) op(e1, e3) = all_56_5 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5964) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5964) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5965) all_57_0 = e0 & op(e3, e3) = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5965) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5966) op(e3, e3) = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5941), (5966), (function-axioms) are % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5967) all_57_1 = e0 & op(e3, e2) = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5967) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5968) all_57_1 = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5953), (5968) imply: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5969) e2 = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5921), (5969) imply: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5970) all_57_6 = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (235), (237), (5926), % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5941), (5962), (5963), (5970), (function-axioms) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #139. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5971) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5971) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5972) all_57_4 = e0 & op(e3, e1) = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5972) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5973) all_57_4 = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5974) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5974) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5975) all_57_12 = e3 & op(e0, e3) = e3 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (5917), (5975), (function-axioms) are % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #628. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5976) all_57_13 = e3 & op(e0, e2) = e3 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5976) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5977) all_57_13 = e3 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5931), (5977) imply: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5978) e3 = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5948), (5978) imply: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5979) all_57_9 = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (236), (238), (5941), % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5973), (5979), (function-axioms) are inconsistent % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #688. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5980) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5980) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5981) all_57_14 = e3 & op(e0, e1) = e3 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5981) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5982) all_57_14 = e3 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5983) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5983) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5984) all_57_4 = e1 & op(e3, e1) = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5973), (5984) are inconsistent by sub-proof % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #419. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5985) all_57_5 = e1 & op(e2, e1) = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5945), (5985) are inconsistent by sub-proof % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #500. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5986) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5986) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5987) all_57_8 = e1 & op(e1, e1) = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5987) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5988) op(e1, e1) = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (5893), (5988), (function-axioms) are % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5989) all_57_14 = e1 & op(e0, e1) = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5982), (5989) are inconsistent by sub-proof % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #247. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5990) all_57_15 = e3 & op(e0, e0) = e3 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5990) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5991) op(e0, e0) = e3 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5611), (5991), (function-axioms) are % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5992) all_57_9 = e0 & op(e3, e0) = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5641), (5992), (function-axioms) are % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #618. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5993) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (39), (91), (157), (190), % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (246), (332), (364), (372), (5607), (5611), % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5646), (5907), (5945), (5993), (function-axioms) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #138. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5994) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5994) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5995) all_57_4 = e2 & op(e3, e1) = e2 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (5912), (5995), (function-axioms) are % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5996) all_57_9 = e2 & op(e3, e0) = e2 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5608), (5996), (function-axioms) are % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5997) all_57_10 = e3 & op(e2, e0) = e3 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5997) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5998) all_57_10 = e3 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (165), (167), (223), (5153), (5639), % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5640), (5998), (function-axioms) are inconsistent % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #151. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5999) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (5611), (5892), (5999), % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #330. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6000) all_57_10 = e2 & op(e2, e0) = e2 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6000) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6001) op(e2, e0) = e2 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5609), (6001), (function-axioms) are % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6002) all_57_2 = e1 & op(e2, e3) = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5143), (6002), (function-axioms) are % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #676. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6003) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (163), (5926), (5935), (6003), % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #137. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6004) all_54_11 = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5642), (6004) are inconsistent by % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #258. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6005) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6005) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6006) all_57_14 = e1 & op(e0, e1) = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6006) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6007) all_57_14 = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5904) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6008) all_54_11 = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (6008) imply: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6009) all_52_14 = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6009) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6010) all_52_14 = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (6010) imply: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6011) ~ (all_52_2 = e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5892), (6010) imply: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6012) ~ (e3 = e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5610), (6010) imply: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6013) ~ (e2 = e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6014) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6014) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6015) all_57_0 = e1 & op(e3, e3) = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6015) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6016) op(e3, e3) = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6017) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (5152), (5911), (6017), % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #141. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6018) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6018) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6019) all_57_5 = e2 & op(e2, e1) = e2 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6019) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6020) all_57_5 = e2 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6021) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6021) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6022) all_57_9 = e3 & op(e3, e0) = e3 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6022) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6023) all_57_9 = e3 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6024) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6024) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6025) all_57_0 = e2 & op(e3, e3) = e2 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6025) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6026) op(e3, e3) = e2 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6016), (6026), (function-axioms) are % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6027) all_57_1 = e2 & op(e3, e2) = e2 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6027) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6028) all_57_1 = e2 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6029) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6029) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6030) all_57_9 = e1 & op(e3, e0) = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6030) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6031) all_57_9 = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (160), (165), (167), (214), % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (5153), (5611), (5639), (5640), (5892), % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6031), (function-axioms) are inconsistent by % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #150. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6032) all_57_10 = e1 & op(e2, e0) = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6032) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6033) op(e2, e0) = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5646), (6033), (function-axioms) are % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #695. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6034) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6034) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6035) all_57_11 = e1 & op(e1, e0) = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6035) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6036) all_57_11 = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6037) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6037) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6038) all_57_4 = e0 & op(e3, e1) = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6038) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6039) all_57_4 = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6040) op(e3, e1) = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6041) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6041) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6042) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6042) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6043) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6043) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6044) op(e3, e3) = e2 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6045) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6028), (6044), (6045), (function-axioms) are % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #239. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6046) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6046) gives: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6047) all_57_4 = e1 & op(e3, e1) = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6047) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6048) all_57_4 = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6039), (6048) imply: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6049) e1 = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6049) implies: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6050) e1 = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6007), (6050) imply: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6051) all_57_14 = e0 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (39), (220), (5893), (6020), % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6039), (6051), (function-axioms) are inconsistent % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #230. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6052) all_57_9 = e1 & op(e3, e0) = e1 % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6023), (6052) are inconsistent by sub-proof % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #640. % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6053) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6053) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6054) op(e3, e1) = e3 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (6040), (6054), (function-axioms) are % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #600. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6055) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (5153), (6016), (6055), % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #175. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6056) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6056) gives: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6057) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6057) gives: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6058) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6058) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6059) op(e1, e3) = e1 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6011), (6059), (function-axioms) are % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #725. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6060) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6060) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6061) ~ (all_56_5 = e3) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6062) op(e1, e1) = all_56_21 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6063) op(e1, e2) = all_56_13 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6064) op(e1, e3) = all_56_5 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5141) gives: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6065) ~ (all_8_0 = e0) & op(e1, e2) = all_8_0 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_0) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6065) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6066) ~ (all_8_0 = e0) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6067) op(e1, e2) = all_8_0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6068) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6068) gives: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6069) all_57_6 = e0 & op(e1, e3) = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6069) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6070) all_57_6 = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (235), (237), (5926), % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6016), (6061), (6064), (6070), (function-axioms) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #139. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6071) all_57_7 = e0 & op(e1, e2) = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6071) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6072) op(e1, e2) = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_0, % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e2, e1, simplifying with (6063), (6067) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6073) all_56_13 = all_8_0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e2, e1, simplifying with (6063), (6072) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6074) all_56_13 = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6073), (6074) imply: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6075) all_8_0 = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6075) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6076) all_8_0 = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6066), (6076) imply: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6077) $false % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6077) is inconsistent. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6078) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6078) gives: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6079) all_57_8 = e0 & op(e1, e1) = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6079) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6080) op(e1, e1) = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (169), (361), (6040), (6080), % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #619. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6081) all_57_11 = e0 & op(e1, e0) = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6081) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6082) all_57_11 = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (212), (5611), (5646), (6023), % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6082), (function-axioms) are inconsistent by % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #257. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6083) ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_1) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6083) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6084) ~ (all_8_1 = e3) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6085) op(e1, e1) = all_8_1 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21, e1, e1, simplifying with (6062), (6085) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6086) all_56_21 = all_8_1 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21, e1, e1, simplifying with (5893), (6062) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6087) all_56_21 = e3 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6086), (6087) imply: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6088) all_8_1 = e3 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6088) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6089) all_8_1 = e3 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6084), (6089) imply: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6090) $false % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6090) is inconsistent. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6091) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (39), (91), (157), (190), % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (246), (332), (364), (372), (5607), (5611), % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5646), (5907), (6020), (6091), (function-axioms) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #138. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6092) all_57_5 = e0 & op(e2, e1) = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5640), (6092), (function-axioms) are % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #455. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6093) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6093) gives: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6094) all_57_8 = e0 & op(e1, e1) = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6094) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6095) op(e1, e1) = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5893), (6095), (function-axioms) are % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6096) all_57_14 = e0 & op(e0, e1) = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6096) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6097) all_57_14 = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6007), (6097) imply: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6098) e1 = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6098) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6099) e1 = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6036), (6099) imply: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6100) all_57_11 = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (212), (5611), (5646), (6023), % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6100), (function-axioms) are inconsistent by % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #257. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6101) all_57_15 = e1 & op(e0, e0) = e1 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6101) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6102) op(e0, e0) = e1 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5611), (6102), (function-axioms) are % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6103) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6103) gives: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6104) all_57_4 = e2 & op(e3, e1) = e2 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (5912), (6104), (function-axioms) are % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6105) all_57_9 = e2 & op(e3, e0) = e2 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5608), (6105), (function-axioms) are % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6106) all_57_10 = e3 & op(e2, e0) = e3 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6106) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6107) all_57_10 = e3 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (165), (167), (223), (5153), (5639), % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5640), (6107), (function-axioms) are inconsistent % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #151. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6108) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (5611), (5892), (6108), % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #330. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6109) all_57_10 = e2 & op(e2, e0) = e2 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6109) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6110) op(e2, e0) = e2 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5609), (6110), (function-axioms) are % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6111) all_57_2 = e1 & op(e2, e3) = e1 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5143), (6111), (function-axioms) are % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #676. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6112) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (163), (5926), (6011), (6112), % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #137. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6113) all_54_11 = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5642), (6113) are inconsistent by % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #258. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6114) all_57_15 = e1 & op(e0, e0) = e1 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6114) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6115) op(e0, e0) = e1 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5611), (6115), (function-axioms) are % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (6116) all_57_12 = e2 & op(e0, e3) = e2 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6116) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (6117) all_57_12 = e2 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (208), (209), % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (5611), (5891), (6117), (function-axioms) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #458. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (6118) ~ (all_54_4 = e3) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (268), (6118) imply: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (6119) ~ (all_52_1 = e3) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5908), (6119), (function-axioms) are % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #763. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | (6120) all_54_6 = e1 | all_54_6 = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (5147), (5640), (6120) are inconsistent by % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #479. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | (6121) all_57_3 = e3 & op(e2, e2) = e3 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6121) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | (6122) op(e2, e2) = e3 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5153), (6122), (function-axioms) are % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | (6123) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6123) gives: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | (6124) all_57_5 = e3 & op(e2, e1) = e3 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5890), (6124), (function-axioms) are % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | (6125) all_57_10 = e3 & op(e2, e0) = e3 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6125) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | (6126) all_57_10 = e3 % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (165), (167), (223), (5153), (5639), % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | (5640), (6126), (function-axioms) are inconsistent % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #151. % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | (6127) all_57_11 = e0 & op(e1, e0) = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | ALPHA: (6127) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | (6128) all_57_11 = e0 % 133.67/19.24 | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 133.67/19.24 | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | Case 1: % 133.67/19.24 | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | (6129) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 133.67/19.24 | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 133.67/19.24 | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | BETA: splitting (6129) gives: % 133.67/19.24 | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.24 | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | (6130) all_57_9 = e3 & op(e3, e0) = e3 % 133.67/19.24 | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | ALPHA: (6130) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | (6131) all_57_9 = e3 % 133.67/19.24 | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (212), (5611), (5646), (6128), % 133.67/19.24 | | | | | | | | | | | | | | | | | | (6131), (function-axioms) are inconsistent by % 133.67/19.24 | | | | | | | | | | | | | | | | | | sub-proof #257. % 133.67/19.24 | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | (6132) all_57_10 = e3 & op(e2, e0) = e3 % 133.67/19.24 | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | ALPHA: (6132) implies: % 133.67/19.24 | | | | | | | | | | | | | | | | | | (6133) all_57_10 = e3 % 133.67/19.24 | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (165), (167), (223), (5153), (5639), % 133.67/19.24 | | | | | | | | | | | | | | | | | | (5640), (6133), (function-axioms) are inconsistent % 133.67/19.24 | | | | | | | | | | | | | | | | | | by sub-proof #151. % 133.67/19.24 | | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | (6134) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 133.67/19.24 | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 133.67/19.24 | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (5611), (6128), (6134), % 133.67/19.24 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.24 | | | | | | | | | | | | | | | | | #255. % 133.67/19.24 | | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | | % 133.67/19.24 | | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | (6135) ~ (all_20_1 = e1) & op(e2, e2) = all_20_1 & % 133.67/19.24 | | | | | | | | | | $i(all_20_1) % 133.67/19.24 | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | ALPHA: (6135) implies: % 133.67/19.24 | | | | | | | | | | (6136) ~ (all_20_1 = e1) % 133.67/19.24 | | | | | | | | | | (6137) op(e2, e2) = all_20_1 % 133.67/19.24 | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_20_1, % 133.67/19.24 | | | | | | | | | | e2, e2, simplifying with (5153), (6137) gives: % 133.67/19.24 | | | | | | | | | | (6138) all_20_1 = e1 % 133.67/19.24 | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | REDUCE: (6136), (6138) imply: % 133.67/19.24 | | | | | | | | | | (6139) $false % 133.67/19.24 | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | CLOSE: (6139) is inconsistent. % 133.67/19.24 | | | | | | | | | | % 133.67/19.24 | | | | | | | | | End of split % 133.67/19.24 | | | | | | | | | % 133.67/19.24 | | | | | | | | End of split % 133.67/19.24 | | | | | | | | % 133.67/19.24 | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | % 133.67/19.24 | | | | | | | | (6140) all_16_2 = e2 % 133.67/19.24 | | | | | | | | % 133.67/19.24 | | | | | | | | COMBINE_EQS: (327), (6140) imply: % 133.67/19.24 | | | | | | | | (6141) all_10_2 = e2 % 133.67/19.24 | | | | | | | | % 133.67/19.24 | | | | | | | | COMBINE_EQS: (299), (6141) imply: % 133.67/19.24 | | | | | | | | (6142) all_38_2 = e2 % 133.67/19.24 | | | | | | | | % 133.67/19.24 | | | | | | | | REDUCE: (336), (6141) imply: % 133.67/19.24 | | | | | | | | (6143) ~ (all_52_1 = e2) % 133.67/19.24 | | | | | | | | % 133.67/19.24 | | | | | | | | REDUCE: (338), (6141) imply: % 133.67/19.24 | | | | | | | | (6144) ~ (all_52_2 = e2) % 133.67/19.24 | | | | | | | | % 133.67/19.24 | | | | | | | | REDUCE: (344), (6141) imply: % 133.67/19.24 | | | | | | | | (6145) ~ (all_52_8 = e2) % 133.67/19.24 | | | | | | | | % 133.67/19.24 | | | | | | | | REDUCE: (45), (6141) imply: % 133.67/19.24 | | | | | | | | (6146) op(e3, e3) = e2 % 133.67/19.24 | | | | | | | | % 133.67/19.24 | | | | | | | | BETA: splitting (88) gives: % 133.67/19.24 | | | | | | | | % 133.67/19.24 | | | | | | | | Case 1: % 133.67/19.24 | | | | | | | | | % 133.67/19.24 | | | | | | | | | (6147) ~ (all_38_2 = e2) % 133.67/19.24 | | | | | | | | | % 133.67/19.24 | | | | | | | | | REDUCE: (6142), (6147) imply: % 133.67/19.24 | | | | | | | | | (6148) $false % 133.67/19.24 | | | | | | | | | % 133.67/19.24 | | | | | | | | | CLOSE: (6148) is inconsistent. % 133.67/19.24 | | | | | | | | | % 133.67/19.24 | | | | | | | | Case 2: % 133.67/19.24 | | | | | | | | | % 133.67/19.24 | | | | | | | | | (6149) ( ~ (all_38_0 = e0) & op(e2, e3) = all_38_0 & % 133.67/19.24 | | | | | | | | | $i(all_38_0)) | ( ~ (all_38_1 = e1) & op(e2, e2) = % 133.67/19.24 | | | | | | | | | all_38_1 & $i(all_38_1)) % 133.67/19.24 | | | | | | | | | % 133.67/19.24 | | | | | | | | | BETA: splitting (6149) gives: % 133.67/19.24 | | | | | | | | | % 133.67/19.24 | | | | | | | | | Case 1: % 133.67/19.24 | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | (6150) ~ (all_38_0 = e0) & op(e2, e3) = all_38_0 & % 133.67/19.24 | | | | | | | | | | $i(all_38_0) % 133.67/19.24 | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | ALPHA: (6150) implies: % 133.67/19.24 | | | | | | | | | | (6151) ~ (all_38_0 = e0) % 133.67/19.24 | | | | | | | | | | (6152) op(e2, e3) = all_38_0 % 133.67/19.24 | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | BETA: splitting (235) gives: % 133.67/19.24 | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | Case 1: % 133.67/19.24 | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | (6153) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 133.67/19.24 | | | | | | | | | | | & op(e2, e3) = e2) % 133.67/19.24 | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | BETA: splitting (6153) gives: % 133.67/19.24 | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | Case 1: % 133.67/19.24 | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | (6154) all_57_0 = e2 & op(e3, e3) = e2 % 133.67/19.24 | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | ALPHA: (6154) implies: % 133.67/19.24 | | | | | | | | | | | | (6155) all_57_0 = e2 % 133.67/19.24 | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, % 133.67/19.24 | | | | | | | | | | | | all_38_0, e3, e2, simplifying with (167), (6152) % 133.67/19.24 | | | | | | | | | | | | gives: % 133.67/19.24 | | | | | | | | | | | | (6156) all_52_1 = all_38_0 % 133.67/19.24 | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | COMBINE_EQS: (268), (6156) imply: % 133.67/19.24 | | | | | | | | | | | | (6157) all_54_4 = all_38_0 % 133.67/19.24 | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | REDUCE: (146), (6156) imply: % 133.67/19.24 | | | | | | | | | | | | (6158) ~ (all_52_9 = all_38_0) % 133.67/19.24 | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | SIMP: (6158) implies: % 133.67/19.24 | | | | | | | | | | | | (6159) ~ (all_52_9 = all_38_0) % 133.67/19.24 | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | REDUCE: (145), (6156) imply: % 133.67/19.24 | | | | | | | | | | | | (6160) ~ (all_52_13 = all_38_0) % 133.67/19.24 | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | SIMP: (6160) implies: % 133.67/19.24 | | | | | | | | | | | | (6161) ~ (all_52_13 = all_38_0) % 133.67/19.24 | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | REDUCE: (6143), (6156) imply: % 133.67/19.24 | | | | | | | | | | | | (6162) ~ (all_38_0 = e2) % 133.67/19.24 | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | REDUCE: (5143), (6156) imply: % 133.67/19.24 | | | | | | | | | | | | (6163) ~ (all_38_0 = e1) % 133.67/19.24 | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | BETA: splitting (200) gives: % 133.67/19.24 | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | Case 1: % 133.67/19.24 | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | (6164) all_54_4 = e3 % 133.67/19.24 | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | COMBINE_EQS: (6157), (6164) imply: % 133.67/19.24 | | | | | | | | | | | | | (6165) all_38_0 = e3 % 133.67/19.24 | | | | | | | | | | | | | % 133.67/19.24 | | | | | | | | | | | | | SIMP: (6165) implies: % 133.67/19.25 | | | | | | | | | | | | | (6166) all_38_0 = e3 % 133.67/19.25 | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | REDUCE: (6159), (6166) imply: % 133.67/19.25 | | | | | | | | | | | | | (6167) ~ (all_52_9 = e3) % 133.67/19.25 | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | REDUCE: (6161), (6166) imply: % 133.67/19.25 | | | | | | | | | | | | | (6168) ~ (all_52_13 = e3) % 133.67/19.25 | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | BETA: splitting (226) gives: % 133.67/19.25 | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | (6169) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 133.67/19.25 | | | | | | | | | | | | | | & op(e2, e2) = e3) % 133.67/19.25 | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | BETA: splitting (6169) gives: % 133.67/19.25 | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | (6170) all_57_2 = e3 & op(e2, e3) = e3 % 133.67/19.25 | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | ALPHA: (6170) implies: % 133.67/19.25 | | | | | | | | | | | | | | | (6171) all_57_2 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | (6172) op(e2, e3) = e3 % 133.67/19.25 | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | BETA: splitting (61) gives: % 133.67/19.25 | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | (6173) ~ (all_20_2 = e2) % 133.67/19.25 | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | REDUCE: (318), (6173) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | (6174) ~ (all_4_2 = e2) % 133.67/19.25 | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | (6175) ~ (all_28_2 = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | REDUCE: (316), (6175) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | (6176) ~ (all_6_2 = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | (6177) ~ (all_34_2 = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | REDUCE: (307), (6177) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | (6178) ~ (all_4_2 = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6179) all_54_15 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (6179) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6180) all_4_2 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | REDUCE: (6178), (6180) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6181) $false % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | CLOSE: (6181) is inconsistent. % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6182) ~ (all_54_15 = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6183) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (6183) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6184) all_54_15 = e2 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (6184) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6185) all_4_2 = e2 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | REDUCE: (6174), (6185) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6186) $false % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | CLOSE: (6186) is inconsistent. % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6187) ~ (all_54_15 = e2) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6188) all_54_15 = e1 | all_54_15 = e0 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6188) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6189) all_54_15 = e1 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (6189) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6190) all_4_2 = e1 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (6190) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6191) $false % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | CLOSE: (6191) is inconsistent. % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6192) all_54_15 = e0 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (6192) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6193) all_4_2 = e0 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (6193) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6194) ~ (all_52_13 = e0) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6178), (6193) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6195) ~ (e3 = e0) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6174), (6193) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6196) ~ (e2 = e0) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (6193) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6197) ~ (e1 = e0) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (6193) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6198) op(e0, e0) = e0 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6199) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6199) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (6200) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6146), (6172), (6200), (function-axioms) are % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #335. % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (6201) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (5153), (6146), (6201), % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | #136. % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6202) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (103), (110), (117), (160), % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (165), (194), (197), (218), (259), (334), (362), % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (372), (5142), (5148), (5153), (6176), (6194), % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6198), (6202), (function-axioms) are inconsistent % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #135. % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | End of split % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | (6203) all_34_2 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (6203) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | (6204) all_4_2 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | SIMP: (6204) implies: % 133.67/19.25 | | | | | | | | | | | | | | | | | | (6205) all_4_2 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (6205) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | (6206) all_44_2 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | REDUCE: (367), (6205) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | (6207) ~ (all_52_11 = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6208) ~ (all_44_2 = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | REDUCE: (6206), (6208) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6209) $false % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | CLOSE: (6209) is inconsistent. % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6210) ( ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | $i(all_44_0)) | ( ~ (all_44_1 = e2) & op(e3, e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | = all_44_1 & $i(all_44_1)) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6211) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6211) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6212) all_57_4 = e3 & op(e3, e1) = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | ALPHA: (6212) implies: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6213) all_57_4 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (170), (234), (5144), (6146), (6210), % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6213), (function-axioms) are inconsistent by % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | sub-proof #134. % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6214) all_57_5 = e3 & op(e2, e1) = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6167), (6214), (function-axioms) are % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6215) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (157), (6176), (6207), (6215), % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | #651. % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | End of split % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | End of split % 133.67/19.25 | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | (6216) all_28_2 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (6216) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | (6217) all_6_2 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (6217) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | (6218) all_36_2 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | REDUCE: (359), (6217) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | (6219) ~ (all_52_6 = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | REDUCE: (361), (6217) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | (6220) ~ (all_52_8 = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | REDUCE: (364), (6217) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | (6221) ~ (all_52_11 = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | BETA: splitting (85) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | (6222) ~ (all_36_2 = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | REDUCE: (6218), (6222) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | (6223) $false % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | CLOSE: (6223) is inconsistent. % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | (6224) ( ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | $i(all_36_0)) | ( ~ (all_36_1 = e2) & op(e3, e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | | = all_36_1 & $i(all_36_1)) % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6225) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (6167), (6220), (6225), % 133.67/19.25 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.25 | | | | | | | | | | | | | | | | | | | #310. % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | (6226) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (6226) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6227) all_57_8 = e3 & op(e1, e1) = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | ALPHA: (6227) implies: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6228) all_57_8 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | (6229) op(e1, e1) = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6224) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6230) ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | $i(all_36_0) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | ALPHA: (6230) implies: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6231) ~ (all_36_0 = e0) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | (6232) op(e3, e1) = all_36_0 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5141) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6233) ~ (all_8_0 = e0) & op(e1, e2) = all_8_0 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_8_0) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6233) implies: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6234) ~ (all_8_0 = e0) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6235) op(e1, e2) = all_8_0 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_8_0, e2, e1, simplifying with (162), (6235) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6236) all_52_6 = all_8_0 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | all_36_0, e1, e3, simplifying with (169), (6232) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6237) all_52_8 = all_36_0 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (6236) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6238) all_54_9 = all_8_0 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (6237) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6239) all_54_2 = all_36_0 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (6236) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6240) ~ (all_52_2 = all_8_0) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (6236) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6241) ~ (all_52_4 = all_8_0) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (6236) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6242) ~ (all_52_14 = all_8_0) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | SIMP: (6242) implies: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6243) ~ (all_52_14 = all_8_0) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6219), (6236) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6244) ~ (all_8_0 = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5145), (6236) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6245) ~ (all_8_0 = e1) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6220), (6237) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6246) ~ (all_36_0 = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6145), (6237) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | (6247) ~ (all_36_0 = e2) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (6248) all_54_2 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6239), (6248) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (6249) all_36_0 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6246), (6249) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (6250) $false % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6250) is inconsistent. % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (6251) ~ (all_54_2 = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | (6252) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6252) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | (6253) all_54_2 = e2 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6239), (6253) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | (6254) all_36_0 = e2 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6247), (6254) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | (6255) $false % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6255) is inconsistent. % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | (6256) ~ (all_54_2 = e2) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | (6257) all_54_2 = e1 | all_54_2 = e0 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | (6258) all_54_9 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6238), (6258) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | (6259) all_8_0 = e3 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6244), (6259) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | (6260) $false % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6260) is inconsistent. % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | (6261) ~ (all_54_9 = e3) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | (6262) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6262) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (6263) all_54_9 = e2 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6238), (6263) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (6264) all_8_0 = e2 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6241), (6264) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (6265) ~ (all_52_4 = e2) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6243), (6264) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (6266) ~ (all_52_14 = e2) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6244), (6264) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (6267) ~ (e3 = e2) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6268) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6268) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6269) all_57_6 = e2 & op(e1, e3) = e2 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6144), (6269), (function-axioms) are % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #341. % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6270) all_57_7 = e2 & op(e1, e2) = e2 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6270) implies: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6271) all_57_7 = e2 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6272) op(e1, e2) = e2 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6273) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6273) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6274) all_57_12 = e2 & op(e0, e3) = e2 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6274) implies: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6275) all_57_12 = e2 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (231), (233), (6155), % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6171), (6275) are inconsistent by sub-proof #133. % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6276) all_57_13 = e2 & op(e0, e2) = e2 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6276) implies: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6277) op(e0, e2) = e2 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6257) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6278) all_54_2 = e1 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6239), (6278) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6279) all_36_0 = e1 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6279) implies: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6280) all_36_0 = e1 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6246), (6280) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6281) ~ (e3 = e1) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6247), (6280) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6282) ~ (e2 = e1) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6232), (6280) imply: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6283) op(e3, e1) = e1 % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6284) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6284) gives: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6285) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6146), (6172), (6285), (function-axioms) are % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #335. % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6286) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5153), (6277), (6286), (function-axioms) are % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #157. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6287) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (39), (372), (5153), (6172), (6229), % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6272), (6283), (6287), (function-axioms) are % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #131. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6288) all_54_2 = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6231), (6239), (6288) are inconsistent by % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #242. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6289) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6289) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6290) all_57_14 = e2 & op(e0, e1) = e2 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6290) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6291) all_57_14 = e2 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6292) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6292) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6293) all_57_4 = e1 & op(e3, e1) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6293) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6294) op(e3, e1) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6295) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6295) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6296) all_57_12 = e1 & op(e0, e3) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6296) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6297) all_57_12 = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6298) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6298) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6299) all_57_0 = e0 & op(e3, e3) = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6299) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6300) op(e3, e3) = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6146), (6300), (function-axioms) are % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6301) all_57_2 = e0 & op(e2, e3) = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6301) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6302) op(e2, e3) = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_38_0, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (6152), (6302) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6303) all_38_0 = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6151), (6303) imply: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6304) $false % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6304) is inconsistent. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6305) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6305) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6306) all_57_6 = e0 & op(e1, e3) = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6306) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6307) all_57_6 = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6308) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6308) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6309) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6309) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6310) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6310) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6311) ~ (all_56_3 = e3) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6312) op(e2, e3) = all_56_3 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6172), (6311), (6312), (function-axioms) are % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #347. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6313) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6313) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6314) op(e3, e3) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (235), (237), (6297), % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6307), (6314), (function-axioms) are inconsistent % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #585. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6315) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (5153), (6146), (6315), % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #136. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6316) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (39), (372), (5153), (6172), (6229), % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6272), (6294), (6316), (function-axioms) are % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #131. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6317) all_57_12 = e0 & op(e0, e3) = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6297), (6317) are inconsistent by sub-proof % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #584. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6318) all_57_13 = e1 & op(e0, e2) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5146), (6318), (function-axioms) are % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #178. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6319) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (371), (6291), (6319), % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #350. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6320) all_57_5 = e1 & op(e2, e1) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5147), (6320), (function-axioms) are % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #161. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6321) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6321) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6322) all_57_8 = e1 & op(e1, e1) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6322) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6323) op(e1, e1) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (6229), (6323), (function-axioms) are % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6324) all_57_14 = e1 & op(e0, e1) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6324) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6325) all_57_14 = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6291), (6325) are inconsistent by sub-proof % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #560. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6326) all_57_15 = e2 & op(e0, e0) = e2 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6326) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6327) op(e0, e0) = e2 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6328) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6328) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6329) all_57_9 = e3 & op(e3, e0) = e3 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6329) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6330) all_57_9 = e3 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6331) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6331) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6332) all_57_0 = e0 & op(e3, e3) = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6332) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6333) op(e3, e3) = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6146), (6333), (function-axioms) are % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6334) all_57_1 = e0 & op(e3, e2) = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6334) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6335) all_57_1 = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6336) op(e3, e2) = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6337) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6337) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6338) all_57_9 = e1 & op(e3, e0) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6338) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6339) all_57_9 = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (169), (238), (6146), (6220), % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6232), (6335), (6339), (function-axioms) are % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #344. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6340) all_57_10 = e1 & op(e2, e0) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6340) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6341) op(e2, e0) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5148), (6341), (function-axioms) are % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6342) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6342) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6343) all_57_11 = e1 & op(e1, e0) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6343) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6344) all_57_11 = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6345) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (6146), (6336), (6345), % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #241. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6346) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6346) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6347) all_57_4 = e1 & op(e3, e1) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6347) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6348) all_57_4 = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6349) op(e3, e1) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6350) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6350) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6351) all_57_6 = e0 & op(e1, e3) = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6351) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6352) all_57_6 = e0 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6353) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6353) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6354) all_57_0 = e1 & op(e3, e3) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6354) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6355) op(e3, e3) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (170), (232), % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236), (238), (6220), (6265), (6348), (6355), % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #162. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6356) all_57_2 = e1 & op(e2, e3) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5143), (6356), (function-axioms) are % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #676. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6357) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6357) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6358) all_57_6 = e1 & op(e1, e3) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6352), (6358) are inconsistent by sub-proof % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #130. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6359) all_57_12 = e1 & op(e0, e3) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6359) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6360) all_57_12 = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6361) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6361) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6362) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6362) gives: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6363) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6363) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6364) ~ (all_56_3 = e3) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6365) op(e2, e3) = all_56_3 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6172), (6364), (6365), (function-axioms) are % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #347. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6366) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6366) implies: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6367) op(e3, e3) = e1 % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (235), (237), % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6360), (6367), (function-axioms) are inconsistent % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #583. % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6368) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (5153), (6146), (6368), % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #136. % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.67/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6369) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6369) gives: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6370) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6272), (6349), (6370), (function-axioms) are % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #132. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6371) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (39), (372), (5153), (6174), (6327), % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6371), (function-axioms) are inconsistent by % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #156. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6372) all_57_7 = e0 & op(e1, e2) = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6372) implies: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6373) all_57_7 = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6271), (6373) imply: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6374) e2 = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6374) implies: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6375) e2 = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (6375) imply: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6376) $false % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6376) is inconsistent. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6377) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6377) gives: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6378) all_57_8 = e0 & op(e1, e1) = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6378) implies: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6379) op(e1, e1) = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6229), (6379), (function-axioms) are % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6380) all_57_11 = e0 & op(e1, e0) = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6380) implies: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6381) all_57_11 = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6344), (6381) imply: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6382) e1 = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (6382) imply: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6383) $false % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6383) is inconsistent. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6384) all_57_9 = e1 & op(e3, e0) = e1 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6384) implies: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6385) all_57_9 = e1 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (169), (238), (6146), (6220), % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6232), (6335), (6385), (function-axioms) are % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #344. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6386) all_57_15 = e1 & op(e0, e0) = e1 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6386) implies: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6387) op(e0, e0) = e1 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6327), (6387), (function-axioms) are % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6388) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6388) gives: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6389) all_57_4 = e0 & op(e3, e1) = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6231), (6232), (6389), (function-axioms) are % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #332. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6390) all_57_9 = e0 & op(e3, e0) = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6390) implies: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6391) all_57_9 = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6330), (6391) are inconsistent by sub-proof % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #670. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6392) all_57_10 = e3 & op(e2, e0) = e3 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6168), (6392), (function-axioms) are % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6393) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6393) gives: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6394) all_57_11 = e3 & op(e1, e0) = e3 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6394) implies: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6395) all_57_11 = e3 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6396) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6396) gives: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6397) all_57_6 = e0 & op(e1, e3) = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6397) implies: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6398) all_57_6 = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6399) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6399) gives: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6400) all_57_6 = e1 & op(e1, e3) = e1 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6398), (6400) are inconsistent by sub-proof % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #130. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6401) all_57_7 = e1 & op(e1, e2) = e1 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6271), (6401) are inconsistent by sub-proof % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #727. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6402) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6402) gives: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6403) all_57_8 = e1 & op(e1, e1) = e1 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6403) implies: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6404) op(e1, e1) = e1 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (6229), (6404), (function-axioms) are % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6405) all_57_11 = e1 & op(e1, e0) = e1 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6405) implies: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6406) all_57_11 = e1 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6395), (6406) are inconsistent by sub-proof % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #167. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6407) all_57_7 = e0 & op(e1, e2) = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6271), (6407) are inconsistent by sub-proof % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #664. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6408) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6408) gives: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6409) all_57_8 = e0 & op(e1, e1) = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6409) implies: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6410) all_57_8 = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6228), (6410) imply: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6411) e3 = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (6411) imply: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6412) $false % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6412) is inconsistent. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6413) all_57_11 = e0 & op(e1, e0) = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6395), (6413) are inconsistent by sub-proof % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #129. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6414) all_57_15 = e3 & op(e0, e0) = e3 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6414) implies: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6415) op(e0, e0) = e3 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6327), (6415), (function-axioms) are % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6416) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (372), (6266), (6416), % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | #513. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (6417) all_54_9 = e1 | all_54_9 = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6234), (6238), (6245), (6417) are inconsistent by % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #155. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | (6418) ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | $i(all_8_1) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6229), (6418), (function-axioms) are inconsistent % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #128. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | (6419) ~ (all_36_1 = e2) & op(e3, e3) = all_36_1 & % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | $i(all_36_1) % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6146), (6419), (function-axioms) are inconsistent % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | by sub-proof #342. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | (6420) all_57_14 = e3 & op(e0, e1) = e3 % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (6221), (6420), (function-axioms) are % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #652. % 133.82/19.27 | | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | End of split % 133.82/19.27 | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | (6421) all_20_2 = e2 % 133.82/19.27 | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | COMBINE_EQS: (318), (6421) imply: % 133.82/19.27 | | | | | | | | | | | | | | | | (6422) all_4_2 = e2 % 133.82/19.27 | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | REDUCE: (367), (6422) imply: % 133.82/19.27 | | | | | | | | | | | | | | | | (6423) ~ (all_52_11 = e2) % 133.82/19.27 | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | REDUCE: (369), (6422) imply: % 133.82/19.27 | | | | | | | | | | | | | | | | (6424) ~ (all_52_13 = e2) % 133.82/19.27 | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | REDUCE: (36), (6422) imply: % 133.82/19.27 | | | | | | | | | | | | | | | | (6425) op(e0, e0) = e2 % 133.82/19.27 | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 133.82/19.27 | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | Case 1: % 133.82/19.27 | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | (6426) all_54_7 = e3 % 133.82/19.27 | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (6426) imply: % 133.82/19.27 | | | | | | | | | | | | | | | | | (6427) all_52_13 = e3 % 133.82/19.27 | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | REDUCE: (6168), (6427) imply: % 133.82/19.27 | | | | | | | | | | | | | | | | | (6428) $false % 133.82/19.27 | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | CLOSE: (6428) is inconsistent. % 133.82/19.27 | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | Case 2: % 133.82/19.27 | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | (6429) ~ (all_54_7 = e3) % 133.82/19.27 | | | | | | | | | | | | | | | | | (6430) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 133.82/19.27 | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 133.82/19.27 | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | Case 1: % 133.82/19.27 | | | | | | | | | | | | | | | | | | % 133.82/19.27 | | | | | | | | | | | | | | | | | | (6431) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 133.82/19.27 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 133.82/19.27 | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (5152), (6143), (6431), % 133.84/19.27 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.84/19.27 | | | | | | | | | | | | | | | | | | #127. % 133.84/19.27 | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.27 | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | (6432) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 133.84/19.27 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 133.84/19.27 | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | BETA: splitting (6432) gives: % 133.84/19.27 | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | (6433) all_57_5 = e2 & op(e2, e1) = e2 % 133.84/19.27 | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | ALPHA: (6433) implies: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | (6434) all_57_5 = e2 % 133.84/19.27 | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | BETA: splitting (6430) gives: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | (6435) all_54_7 = e2 % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (6435) imply: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | (6436) all_52_13 = e2 % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | REDUCE: (6424), (6436) imply: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | (6437) $false % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | CLOSE: (6437) is inconsistent. % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | (6438) ~ (all_54_7 = e2) % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | (6439) all_54_7 = e1 | all_54_7 = e0 % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6439) gives: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6440) all_54_7 = e1 % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (6440) imply: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6441) all_52_13 = e1 % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5148), (6441) imply: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6442) $false % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | CLOSE: (6442) is inconsistent. % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6443) all_54_7 = e0 % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (6443) imply: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6444) all_52_13 = e0 % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (6444) imply: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6445) ~ (all_52_12 = e0) % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6168), (6444) imply: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6446) ~ (e3 = e0) % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6424), (6444) imply: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6447) ~ (e2 = e0) % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5148), (6444) imply: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6448) ~ (e1 = e0) % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (6444) imply: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | (6449) op(e2, e0) = e0 % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | (6450) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6450) gives: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | (6451) all_57_6 = e2 & op(e1, e3) = e2 % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6144), (6451), (function-axioms) are % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #341. % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | (6452) all_57_7 = e2 & op(e1, e2) = e2 % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6452) implies: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | (6453) op(e1, e2) = e2 % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | (6454) ~ (all_28_2 = e3) % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (316), (6454) imply: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | (6455) ~ (all_6_2 = e3) % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | (6456) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6456) gives: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (6457) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6146), (6449), (6457), (function-axioms) are % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #274. % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (6458) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (5153), (6146), (6458), % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | #136. % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (6459) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6459) gives: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (6460) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6460) gives: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6461) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6461) implies: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6462) op(e1, e1) = e3 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (6455), (6462), (function-axioms) are % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771. % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6463) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6463) implies: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6464) ~ (all_56_13 = e2) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6465) op(e1, e2) = all_56_13 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6453), (6464), (6465), (function-axioms) are % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #165. % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (6466) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (39), (91), (157), (190), % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (246), (332), (364), (372), (6171), (6423), % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (6425), (6434), (6449), (6466), (function-axioms) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #138. % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | (6467) all_28_2 = e3 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (6467) imply: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | (6468) all_6_2 = e3 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6468) implies: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | (6469) all_6_2 = e3 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (6469) imply: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | (6470) all_36_2 = e3 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (6469) imply: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | (6471) ~ (all_52_14 = e3) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (6472) ~ (all_36_2 = e3) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6470), (6472) imply: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (6473) $false % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6473) is inconsistent. % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (6474) ( ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_36_0)) | ( ~ (all_36_1 = e2) & op(e3, e3) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | = all_36_1 & $i(all_36_1)) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (6475) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6475) gives: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6476) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6146), (6449), (6476), (function-axioms) are % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #274. % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6477) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (5153), (6146), (6477), % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | #136. % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (6478) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6478) gives: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6479) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6479) gives: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6480) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6480) implies: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6481) ~ (all_56_17 = e1) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6482) op(e3, e1) = all_56_17 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (160), (164), (168), % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214), (232), (234), (6146), (6168), (6425), % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6445), (6471), (6474), (6481), (6482), % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #328. % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6483) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6483) implies: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6484) ~ (all_56_13 = e2) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6485) op(e1, e2) = all_56_13 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6453), (6484), (6485), (function-axioms) are % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #165. % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6486) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (39), (91), (157), (190), % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (246), (332), (364), (372), (6171), (6423), % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6425), (6434), (6449), (6486), (function-axioms) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #138. % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | (6487) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (164), (208), % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | (212), (214), (372), (6168), (6425), (6487), % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | #268. % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | (6488) all_57_10 = e2 & op(e2, e0) = e2 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | ALPHA: (6488) implies: % 133.84/19.28 | | | | | | | | | | | | | | | | | | | (6489) op(e2, e0) = e2 % 133.84/19.28 | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6424), (6489), (function-axioms) are % 133.84/19.28 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 133.84/19.28 | | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | (6490) all_57_3 = e3 & op(e2, e2) = e3 % 133.84/19.28 | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | ALPHA: (6490) implies: % 133.84/19.28 | | | | | | | | | | | | | | | (6491) op(e2, e2) = e3 % 133.84/19.28 | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | REF_CLOSE: (8), (5153), (6491), (function-axioms) are % 133.84/19.28 | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 133.84/19.28 | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | (6492) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 133.84/19.28 | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 133.84/19.28 | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | BETA: splitting (6492) gives: % 133.84/19.28 | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | Case 1: % 133.84/19.28 | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | (6493) all_57_5 = e3 & op(e2, e1) = e3 % 133.84/19.28 | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | REF_CLOSE: (165), (6167), (6493), (function-axioms) are % 133.84/19.28 | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 133.84/19.28 | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | (6494) all_57_10 = e3 & op(e2, e0) = e3 % 133.84/19.28 | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | | REF_CLOSE: (164), (6168), (6494), (function-axioms) are % 133.84/19.28 | | | | | | | | | | | | | | | inconsistent by sub-proof #749. % 133.84/19.28 | | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | (6495) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 133.84/19.28 | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | | REF_CLOSE: (6151), (6157), (6162), (6163), (6495) are % 133.84/19.28 | | | | | | | | | | | | | inconsistent by sub-proof #126. % 133.84/19.28 | | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | (6496) all_57_2 = e2 & op(e2, e3) = e2 % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | ALPHA: (6496) implies: % 133.84/19.28 | | | | | | | | | | | | (6497) op(e2, e3) = e2 % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | REF_CLOSE: (167), (6143), (6497), (function-axioms) are % 133.84/19.28 | | | | | | | | | | | | inconsistent by sub-proof #779. % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | (6498) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 133.84/19.28 | | | | | | | | | | | e2 & op(e0, e3) = e2) % 133.84/19.28 | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | BETA: splitting (6498) gives: % 133.84/19.28 | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | Case 1: % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | (6499) all_57_6 = e2 & op(e1, e3) = e2 % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | REF_CLOSE: (163), (6144), (6499), (function-axioms) are % 133.84/19.28 | | | | | | | | | | | | inconsistent by sub-proof #341. % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | (6500) all_57_12 = e2 & op(e0, e3) = e2 % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | ALPHA: (6500) implies: % 133.84/19.28 | | | | | | | | | | | | (6501) all_57_12 = e2 % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237), % 133.84/19.28 | | | | | | | | | | | | (6146), (6501), (function-axioms) are inconsistent % 133.84/19.28 | | | | | | | | | | | | by sub-proof #290. % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | | % 133.84/19.28 | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | (6502) ~ (all_38_1 = e1) & op(e2, e2) = all_38_1 & % 133.84/19.28 | | | | | | | | | | $i(all_38_1) % 133.84/19.28 | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | REF_CLOSE: (5153), (6502), (function-axioms) are inconsistent % 133.84/19.28 | | | | | | | | | | by sub-proof #125. % 133.84/19.28 | | | | | | | | | | % 133.84/19.28 | | | | | | | | | End of split % 133.84/19.28 | | | | | | | | | % 133.84/19.28 | | | | | | | | End of split % 133.84/19.28 | | | | | | | | % 133.84/19.28 | | | | | | | End of split % 133.84/19.28 | | | | | | | % 133.84/19.28 | | | | | | Case 2: % 133.84/19.28 | | | | | | | % 133.84/19.28 | | | | | | | (6503) all_10_2 = e0 % 133.84/19.28 | | | | | | | % 133.84/19.28 | | | | | | | COMBINE_EQS: (319), (6503) imply: % 133.84/19.28 | | | | | | | (6504) all_24_2 = e0 % 133.84/19.28 | | | | | | | % 133.84/19.28 | | | | | | | REDUCE: (336), (6503) imply: % 133.84/19.28 | | | | | | | (6505) ~ (all_52_1 = e0) % 133.84/19.28 | | | | | | | % 133.84/19.28 | | | | | | | REDUCE: (338), (6503) imply: % 133.84/19.28 | | | | | | | (6506) ~ (all_52_2 = e0) % 133.84/19.28 | | | | | | | % 133.84/19.28 | | | | | | | REDUCE: (340), (6503) imply: % 133.84/19.28 | | | | | | | (6507) ~ (all_52_3 = e0) % 133.84/19.28 | | | | | | | % 133.84/19.28 | | | | | | | REDUCE: (342), (6503) imply: % 133.84/19.28 | | | | | | | (6508) ~ (all_52_4 = e0) % 133.84/19.28 | | | | | | | % 133.84/19.28 | | | | | | | REDUCE: (45), (6503) imply: % 133.84/19.28 | | | | | | | (6509) op(e3, e3) = e0 % 133.84/19.28 | | | | | | | % 133.84/19.28 | | | | | | | BETA: splitting (61) gives: % 133.84/19.28 | | | | | | | % 133.84/19.28 | | | | | | | Case 1: % 133.84/19.28 | | | | | | | | % 133.84/19.28 | | | | | | | | (6510) ~ (all_20_2 = e2) % 133.84/19.28 | | | | | | | | % 133.84/19.28 | | | | | | | | REDUCE: (318), (6510) imply: % 133.84/19.28 | | | | | | | | (6511) ~ (all_4_2 = e2) % 133.84/19.28 | | | | | | | | % 133.84/19.28 | | | | | | | | BETA: splitting (73) gives: % 133.84/19.28 | | | | | | | | % 133.84/19.28 | | | | | | | | Case 1: % 133.84/19.28 | | | | | | | | | % 133.84/19.28 | | | | | | | | | (6512) ~ (all_28_2 = e3) % 133.84/19.28 | | | | | | | | | % 133.84/19.28 | | | | | | | | | REDUCE: (316), (6512) imply: % 133.84/19.28 | | | | | | | | | (6513) ~ (all_6_2 = e3) % 133.84/19.28 | | | | | | | | | % 133.84/19.28 | | | | | | | | | BETA: splitting (82) gives: % 133.84/19.28 | | | | | | | | | % 133.84/19.28 | | | | | | | | | Case 1: % 133.84/19.28 | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | (6514) ~ (all_34_2 = e3) % 133.84/19.28 | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | REDUCE: (307), (6514) imply: % 133.84/19.28 | | | | | | | | | | (6515) ~ (all_4_2 = e3) % 133.84/19.28 | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | BETA: splitting (189) gives: % 133.84/19.28 | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | Case 1: % 133.84/19.28 | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | (6516) all_54_15 = e3 % 133.84/19.28 | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | COMBINE_EQS: (245), (6516) imply: % 133.84/19.28 | | | | | | | | | | | (6517) all_4_2 = e3 % 133.84/19.28 | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | REDUCE: (6515), (6517) imply: % 133.84/19.28 | | | | | | | | | | | (6518) $false % 133.84/19.28 | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | CLOSE: (6518) is inconsistent. % 133.84/19.28 | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | (6519) ~ (all_54_15 = e3) % 133.84/19.28 | | | | | | | | | | | (6520) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 133.84/19.28 | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | BETA: splitting (6520) gives: % 133.84/19.28 | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | Case 1: % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | (6521) all_54_15 = e2 % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | COMBINE_EQS: (245), (6521) imply: % 133.84/19.28 | | | | | | | | | | | | (6522) all_4_2 = e2 % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | REDUCE: (6511), (6522) imply: % 133.84/19.28 | | | | | | | | | | | | (6523) $false % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | CLOSE: (6523) is inconsistent. % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | Case 2: % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | (6524) ~ (all_54_15 = e2) % 133.84/19.28 | | | | | | | | | | | | (6525) all_54_15 = e1 | all_54_15 = e0 % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | BETA: splitting (6525) gives: % 133.84/19.28 | | | | | | | | | | | | % 133.84/19.28 | | | | | | | | | | | | Case 1: % 133.84/19.28 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | (6526) all_54_15 = e1 % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | COMBINE_EQS: (245), (6526) imply: % 133.84/19.29 | | | | | | | | | | | | | (6527) all_4_2 = e1 % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | REDUCE: (371), (6527) imply: % 133.84/19.29 | | | | | | | | | | | | | (6528) $false % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | CLOSE: (6528) is inconsistent. % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | Case 2: % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | (6529) all_54_15 = e0 % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | COMBINE_EQS: (245), (6529) imply: % 133.84/19.29 | | | | | | | | | | | | | (6530) all_4_2 = e0 % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | REDUCE: (369), (6530) imply: % 133.84/19.29 | | | | | | | | | | | | | (6531) ~ (all_52_13 = e0) % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | REDUCE: (6515), (6530) imply: % 133.84/19.29 | | | | | | | | | | | | | (6532) ~ (e3 = e0) % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | REDUCE: (6511), (6530) imply: % 133.84/19.29 | | | | | | | | | | | | | (6533) ~ (e2 = e0) % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | REDUCE: (371), (6530) imply: % 133.84/19.29 | | | | | | | | | | | | | (6534) ~ (e1 = e0) % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | REDUCE: (36), (6530) imply: % 133.84/19.29 | | | | | | | | | | | | | (6535) op(e0, e0) = e0 % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | Case 1: % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | (6536) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.84/19.29 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.84/19.29 | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.84/19.29 | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.84/19.29 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.84/19.29 | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.84/19.29 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.84/19.29 | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.84/19.29 | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.84/19.29 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.84/19.29 | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.84/19.29 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.84/19.29 | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.84/19.29 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.29 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.84/19.29 | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.84/19.29 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.29 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.29 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.84/19.29 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | BETA: splitting (6536) gives: % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | Case 1: % 133.84/19.29 | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | (6537) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.84/19.29 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.84/19.29 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.84/19.29 | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.84/19.29 | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.84/19.29 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.84/19.29 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.84/19.29 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.84/19.29 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.84/19.29 | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.84/19.29 | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.84/19.29 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.84/19.29 | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6509), (6537), (function-axioms) are % 133.84/19.29 | | | | | | | | | | | | | | | inconsistent by sub-proof #229. % 133.84/19.29 | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | Case 2: % 133.84/19.29 | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | (6538) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.84/19.29 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.84/19.29 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.84/19.29 | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.84/19.29 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.29 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.84/19.29 | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.84/19.29 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.84/19.29 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.29 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.29 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.84/19.29 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.84/19.29 | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | BETA: splitting (6538) gives: % 133.84/19.29 | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | Case 1: % 133.84/19.29 | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | (6539) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.84/19.29 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.84/19.29 | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 133.84/19.29 | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.84/19.29 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.84/19.29 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.84/19.29 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.84/19.29 | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | ALPHA: (6539) implies: % 133.84/19.29 | | | | | | | | | | | | | | | | (6540) ~ (all_56_31 = e0) % 133.84/19.29 | | | | | | | | | | | | | | | | (6541) op(e0, e0) = all_56_31 % 133.84/19.29 | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | REF_CLOSE: (6535), (6540), (6541), (function-axioms) are % 133.84/19.29 | | | | | | | | | | | | | | | | inconsistent by sub-proof #712. % 133.84/19.29 | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | Case 2: % 133.84/19.29 | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | (6542) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.84/19.29 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.84/19.29 | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.29 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.29 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 133.84/19.29 | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.29 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.84/19.29 | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | ALPHA: (6542) implies: % 133.84/19.29 | | | | | | | | | | | | | | | | (6543) op(e2, e2) = e3 % 133.84/19.29 | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5153), (6543), (function-axioms) are % 133.84/19.29 | | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 133.84/19.29 | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | End of split % 133.84/19.29 | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | End of split % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | Case 2: % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | (6544) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.84/19.29 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.29 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.29 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.84/19.29 | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.84/19.29 | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.84/19.29 | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.84/19.29 | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.84/19.29 | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.84/19.29 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.84/19.29 | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.84/19.29 | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.84/19.29 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.84/19.29 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.84/19.29 | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.84/19.29 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.84/19.29 | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.84/19.29 | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.84/19.29 | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.84/19.29 | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.84/19.29 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.84/19.29 | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.84/19.29 | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.84/19.29 | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.84/19.29 | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.84/19.29 | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.84/19.29 | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.29 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.84/19.29 | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.84/19.29 | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.84/19.29 | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.84/19.29 | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.84/19.29 | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.84/19.29 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.84/19.29 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.84/19.29 | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.84/19.29 | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.84/19.29 | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.84/19.29 | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.84/19.29 | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.84/19.29 | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.84/19.29 | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.84/19.29 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.84/19.29 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.84/19.29 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.84/19.29 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.84/19.29 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.84/19.29 | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (103), (110), (117), (160), % 133.84/19.29 | | | | | | | | | | | | | | (165), (194), (197), (218), (259), (334), (362), % 133.84/19.29 | | | | | | | | | | | | | | (372), (5142), (5148), (5153), (6513), (6531), % 133.84/19.29 | | | | | | | | | | | | | | (6535), (6544), (function-axioms) are inconsistent % 133.84/19.29 | | | | | | | | | | | | | | by sub-proof #135. % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | End of split % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | End of split % 133.84/19.29 | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | End of split % 133.84/19.29 | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | End of split % 133.84/19.29 | | | | | | | | | | % 133.84/19.29 | | | | | | | | | Case 2: % 133.84/19.29 | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | (6545) all_34_2 = e3 % 133.84/19.29 | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | COMBINE_EQS: (307), (6545) imply: % 133.84/19.29 | | | | | | | | | | (6546) all_4_2 = e3 % 133.84/19.29 | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | SIMP: (6546) implies: % 133.84/19.29 | | | | | | | | | | (6547) all_4_2 = e3 % 133.84/19.29 | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | REDUCE: (360), (6547) imply: % 133.84/19.29 | | | | | | | | | | (6548) ~ (all_52_7 = e3) % 133.84/19.29 | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | REDUCE: (367), (6547) imply: % 133.84/19.29 | | | | | | | | | | (6549) ~ (all_52_11 = e3) % 133.84/19.29 | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | REDUCE: (368), (6547) imply: % 133.84/19.29 | | | | | | | | | | (6550) ~ (all_52_12 = e3) % 133.84/19.29 | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | REDUCE: (370), (6547) imply: % 133.84/19.29 | | | | | | | | | | (6551) ~ (all_52_14 = e3) % 133.84/19.29 | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | REDUCE: (36), (6547) imply: % 133.84/19.29 | | | | | | | | | | (6552) op(e0, e0) = e3 % 133.84/19.29 | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | BETA: splitting (91) gives: % 133.84/19.29 | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | Case 1: % 133.84/19.29 | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | (6553) ~ (all_40_2 = e0) % 133.84/19.29 | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | REDUCE: (332), (6553) imply: % 133.84/19.29 | | | | | | | | | | | (6554) ~ (all_6_2 = e0) % 133.84/19.29 | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | BETA: splitting (206) gives: % 133.84/19.29 | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | Case 1: % 133.84/19.29 | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | (6555) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.84/19.29 | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.84/19.29 | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.84/19.29 | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.84/19.29 | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.84/19.29 | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.84/19.29 | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.84/19.29 | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.84/19.29 | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.84/19.29 | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.84/19.29 | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.84/19.29 | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.84/19.29 | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.84/19.29 | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.84/19.29 | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.84/19.29 | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.84/19.29 | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.84/19.29 | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.84/19.29 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.29 | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.84/19.29 | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.84/19.29 | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.84/19.29 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.84/19.29 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.29 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.29 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.84/19.29 | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.29 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.84/19.29 | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | BETA: splitting (6555) gives: % 133.84/19.29 | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | Case 1: % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | (6556) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.84/19.29 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.84/19.29 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.84/19.29 | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.84/19.29 | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.84/19.29 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.84/19.29 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.84/19.29 | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.84/19.29 | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.84/19.29 | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.84/19.29 | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.84/19.29 | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.84/19.29 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.84/19.29 | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6509), (6556), (function-axioms) are % 133.84/19.29 | | | | | | | | | | | | | inconsistent by sub-proof #229. % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | Case 2: % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | (6557) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.84/19.29 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.84/19.29 | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.84/19.29 | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.84/19.29 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.29 | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.84/19.29 | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.84/19.29 | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.84/19.29 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.84/19.29 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.29 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.29 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.84/19.29 | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.29 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | REF_CLOSE: (8), (168), (5153), (6550), (6557), % 133.84/19.29 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.84/19.29 | | | | | | | | | | | | | #190. % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | End of split % 133.84/19.29 | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | Case 2: % 133.84/19.29 | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | (6558) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.84/19.29 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.84/19.29 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.29 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.29 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.84/19.29 | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.29 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.84/19.29 | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.84/19.29 | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.84/19.29 | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.84/19.29 | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.84/19.29 | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.84/19.29 | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.84/19.29 | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.84/19.29 | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.84/19.29 | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.84/19.29 | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.84/19.29 | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.84/19.29 | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.84/19.29 | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.84/19.29 | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.84/19.29 | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.84/19.29 | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.84/19.29 | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.84/19.29 | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.84/19.29 | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.84/19.29 | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.84/19.29 | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.84/19.29 | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.84/19.29 | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.84/19.29 | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.84/19.29 | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.29 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.84/19.29 | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.84/19.29 | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.29 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.84/19.29 | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.84/19.29 | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.84/19.29 | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.84/19.29 | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.84/19.29 | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.84/19.29 | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.84/19.29 | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.84/19.29 | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.84/19.29 | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.84/19.29 | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.84/19.29 | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.84/19.29 | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.84/19.29 | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.84/19.29 | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.84/19.29 | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.84/19.29 | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.84/19.29 | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.84/19.29 | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.84/19.29 | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.84/19.29 | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.84/19.29 | | | | | | | | | | | | & $i(all_56_29)))) % 133.84/19.29 | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | BETA: splitting (6558) gives: % 133.84/19.29 | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | Case 1: % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | (6559) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.84/19.29 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.84/19.29 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.29 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.29 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.84/19.29 | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.29 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.84/19.29 | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.84/19.29 | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.84/19.29 | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.84/19.29 | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.84/19.29 | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.84/19.29 | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.84/19.29 | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | BETA: splitting (6559) gives: % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | Case 1: % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | (6560) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.84/19.29 | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.29 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.29 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 133.84/19.29 | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | ALPHA: (6560) implies: % 133.84/19.29 | | | | | | | | | | | | | | (6561) op(e1, e1) = e3 % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | REF_CLOSE: (39), (6513), (6561), (function-axioms) are % 133.84/19.29 | | | | | | | | | | | | | | inconsistent by sub-proof #771. % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | Case 2: % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | (6562) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.84/19.29 | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 133.84/19.29 | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.84/19.29 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.84/19.29 | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | ALPHA: (6562) implies: % 133.84/19.29 | | | | | | | | | | | | | | (6563) ~ (all_56_21 = e1) % 133.84/19.29 | | | | | | | | | | | | | | (6564) op(e1, e1) = all_56_21 % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | REF_CLOSE: (39), (194), (334), (372), (6513), (6554), (6563), % 133.84/19.29 | | | | | | | | | | | | | | (6564), (function-axioms) are inconsistent by % 133.84/19.29 | | | | | | | | | | | | | | sub-proof #124. % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | End of split % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | Case 2: % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | (6565) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.84/19.29 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.84/19.29 | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.84/19.29 | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.84/19.29 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.29 | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.84/19.29 | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.84/19.29 | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.84/19.29 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.84/19.29 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.84/19.29 | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.84/19.29 | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.84/19.29 | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.84/19.29 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.84/19.29 | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.84/19.29 | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.84/19.29 | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.84/19.29 | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.84/19.29 | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.84/19.29 | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.84/19.29 | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.84/19.29 | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.84/19.29 | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.84/19.29 | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.84/19.29 | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.84/19.29 | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.84/19.29 | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.84/19.29 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.84/19.29 | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.84/19.29 | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.84/19.29 | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.84/19.29 | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.84/19.29 | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.84/19.29 | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.84/19.29 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.29 | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.84/19.29 | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.84/19.29 | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.84/19.29 | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.84/19.29 | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.84/19.29 | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.84/19.29 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.84/19.29 | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.84/19.29 | | | | | | | | | | | | | & $i(all_56_29)))) % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | BETA: splitting (6565) gives: % 133.84/19.29 | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | Case 1: % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | (6566) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.84/19.29 | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.84/19.29 | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.84/19.29 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.84/19.29 | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | ALPHA: (6566) implies: % 133.84/19.29 | | | | | | | | | | | | | | (6567) op(e2, e2) = e0 % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | REF_CLOSE: (4), (5153), (6567), (function-axioms) are % 133.84/19.29 | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | Case 2: % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | (6568) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.84/19.29 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.84/19.29 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.84/19.29 | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.84/19.29 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.84/19.29 | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.84/19.29 | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.84/19.29 | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.84/19.29 | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.84/19.29 | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.84/19.29 | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.84/19.29 | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.84/19.29 | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.84/19.29 | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.84/19.29 | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.84/19.29 | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.84/19.29 | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.84/19.29 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.84/19.29 | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.84/19.29 | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.84/19.29 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.84/19.29 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.84/19.29 | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.84/19.29 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.84/19.29 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.84/19.29 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.84/19.29 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.84/19.29 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.84/19.29 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.84/19.29 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.84/19.29 | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | BETA: splitting (6568) gives: % 133.84/19.29 | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | Case 1: % 133.84/19.29 | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | (6569) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.84/19.29 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.84/19.29 | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.84/19.29 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.84/19.29 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 133.84/19.29 | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.84/19.29 | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | ALPHA: (6569) implies: % 133.84/19.29 | | | | | | | | | | | | | | | (6570) op(e1, e1) = e2 % 133.84/19.29 | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | REF_CLOSE: (39), (372), (6570), (function-axioms) are % 133.84/19.29 | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 133.84/19.29 | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | Case 2: % 133.84/19.29 | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | (6571) op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.84/19.29 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.84/19.29 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 133.84/19.29 | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.84/19.29 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 133.84/19.29 | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.84/19.29 | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 133.84/19.29 | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 133.84/19.29 | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.84/19.29 | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.84/19.29 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.84/19.29 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.84/19.29 | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.84/19.29 | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.84/19.29 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.84/19.29 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.84/19.29 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.84/19.29 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 133.84/19.29 | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 133.84/19.29 | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 133.84/19.29 | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 133.84/19.29 | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 133.84/19.29 | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.84/19.29 | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_29))) % 133.84/19.29 | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | ALPHA: (6571) implies: % 133.84/19.29 | | | | | | | | | | | | | | | (6572) op(e0, e0) = all_56_31 % 133.84/19.29 | | | | | | | | | | | | | | | (6573) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.84/19.29 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.84/19.29 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.29 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.29 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.84/19.29 | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.84/19.29 | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.84/19.29 | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.84/19.29 | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.84/19.29 | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.84/19.29 | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.84/19.29 | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.84/19.29 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.84/19.29 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 133.84/19.29 | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.84/19.29 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.84/19.29 | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.84/19.29 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.84/19.29 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.84/19.29 | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.84/19.29 | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.84/19.29 | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.84/19.29 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.84/19.29 | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 133.84/19.29 | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | Case 1: % 133.84/19.29 | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | (6574) all_54_10 = e3 % 133.84/19.29 | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | REF_CLOSE: (334), (6513), (6574) are inconsistent by % 133.84/19.29 | | | | | | | | | | | | | | | | sub-proof #742. % 133.84/19.29 | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | Case 2: % 133.84/19.29 | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | (6575) ~ (all_54_10 = e3) % 133.84/19.29 | | | | | | | | | | | | | | | | (6576) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 133.84/19.29 | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | BETA: splitting (6576) gives: % 133.84/19.29 | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | Case 1: % 133.84/19.29 | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | (6577) all_54_10 = e2 % 133.84/19.29 | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (372), (6577) are inconsistent by sub-proof % 133.84/19.29 | | | | | | | | | | | | | | | | | #741. % 133.84/19.29 | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | Case 2: % 133.84/19.29 | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | (6578) ~ (all_54_10 = e2) % 133.84/19.29 | | | | | | | | | | | | | | | | | (6579) all_54_10 = e1 | all_54_10 = e0 % 133.84/19.29 | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | BETA: splitting (6579) gives: % 133.84/19.29 | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.29 | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | (6580) all_54_10 = e1 % 133.84/19.29 | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (6580) imply: % 133.84/19.29 | | | | | | | | | | | | | | | | | | (6581) all_6_2 = e1 % 133.84/19.29 | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | SIMP: (6581) implies: % 133.84/19.29 | | | | | | | | | | | | | | | | | | (6582) all_6_2 = e1 % 133.84/19.29 | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | REDUCE: (348), (6582) imply: % 133.84/19.29 | | | | | | | | | | | | | | | | | | (6583) ~ (all_52_2 = e1) % 133.84/19.29 | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | REDUCE: (366), (6582) imply: % 133.84/19.29 | | | | | | | | | | | | | | | | | | (6584) ~ (all_52_14 = e1) % 133.84/19.29 | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | REDUCE: (6513), (6582) imply: % 133.84/19.29 | | | | | | | | | | | | | | | | | | (6585) ~ (e3 = e1) % 133.84/19.29 | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | REDUCE: (372), (6582) imply: % 133.84/19.29 | | | | | | | | | | | | | | | | | | (6586) ~ (e2 = e1) % 133.84/19.29 | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 133.84/19.29 | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.29 | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | (6587) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 133.84/19.29 | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 133.84/19.29 | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | BETA: splitting (6587) gives: % 133.84/19.29 | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | (6588) all_57_9 = e1 & op(e3, e0) = e1 % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | ALPHA: (6588) implies: % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | (6589) all_57_9 = e1 % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | (6590) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6590) gives: % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | (6591) all_57_0 = e1 & op(e3, e3) = e1 % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6591) implies: % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | (6592) op(e3, e3) = e1 % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236), % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | (238), (6508), (6589), (6592), (function-axioms) % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #686. % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | (6593) all_57_2 = e1 & op(e2, e3) = e1 % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5143), (6593), (function-axioms) are % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #676. % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.29 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | (6594) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6594) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | (6595) all_57_6 = e1 & op(e1, e3) = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6595) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | (6596) op(e1, e3) = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6583), (6596), (function-axioms) are % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #725. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | (6597) all_57_12 = e1 & op(e0, e3) = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6597) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | (6598) all_57_12 = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6573) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6599) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6599) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6600) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6600) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6601) op(e0, e3) = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (6507), (6601), (function-axioms) are % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6602) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6602) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6603) all_56_31 = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6572), (6603) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6604) op(e0, e0) = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (211), (6548), (6549), % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6598), (6604), (function-axioms) are inconsistent % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #123. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6605) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6605) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6606) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6606) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6607) op(e1, e0) = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (6584), (6607), (function-axioms) are % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #327. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6608) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6608) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6609) ~ (all_56_21 = e1) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6610) op(e1, e1) = all_56_21 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (194), (334), (372), (6513), (6554), (6609), % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6610), (function-axioms) are inconsistent by % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #124. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6611) all_57_10 = e1 & op(e2, e0) = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | ALPHA: (6611) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6612) op(e2, e0) = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5148), (6612), (function-axioms) are % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6613) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | BETA: splitting (6613) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6614) all_57_11 = e1 & op(e1, e0) = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | ALPHA: (6614) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6615) op(e1, e0) = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (6584), (6615), (function-axioms) are % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #327. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6616) all_57_15 = e1 & op(e0, e0) = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | ALPHA: (6616) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6617) op(e0, e0) = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6552), (6617), (function-axioms) are % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | (6618) all_54_10 = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (6554), (6618) are inconsistent by % 133.84/19.30 | | | | | | | | | | | | | | | | | | sub-proof #506. % 133.84/19.30 | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | (6619) all_40_2 = e0 % 133.84/19.30 | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | COMBINE_EQS: (332), (6619) imply: % 133.84/19.30 | | | | | | | | | | | (6620) all_6_2 = e0 % 133.84/19.30 | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | SIMP: (6620) implies: % 133.84/19.30 | | | | | | | | | | | (6621) all_6_2 = e0 % 133.84/19.30 | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | COMBINE_EQS: (295), (6621) imply: % 133.84/19.30 | | | | | | | | | | | (6622) all_46_2 = e0 % 133.84/19.30 | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | REDUCE: (359), (6621) imply: % 133.84/19.30 | | | | | | | | | | | (6623) ~ (all_52_6 = e0) % 133.84/19.30 | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | REDUCE: (362), (6621) imply: % 133.84/19.30 | | | | | | | | | | | (6624) ~ (all_52_9 = e0) % 133.84/19.30 | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | REDUCE: (6513), (6621) imply: % 133.84/19.30 | | | | | | | | | | | (6625) ~ (e3 = e0) % 133.84/19.30 | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | REDUCE: (372), (6621) imply: % 133.84/19.30 | | | | | | | | | | | (6626) ~ (e2 = e0) % 133.84/19.30 | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | REDUCE: (39), (6621) imply: % 133.84/19.30 | | | | | | | | | | | (6627) op(e1, e1) = e0 % 133.84/19.30 | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | BETA: splitting (100) gives: % 133.84/19.30 | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | (6628) ~ (all_46_2 = e0) % 133.84/19.30 | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | REDUCE: (6622), (6628) imply: % 133.84/19.30 | | | | | | | | | | | | (6629) $false % 133.84/19.30 | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | CLOSE: (6629) is inconsistent. % 133.84/19.30 | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | (6630) ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 & % 133.84/19.30 | | | | | | | | | | | | $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0) % 133.84/19.30 | | | | | | | | | | | | = all_46_1 & $i(all_46_1)) % 133.84/19.30 | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | BETA: splitting (103) gives: % 133.84/19.30 | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | (6631) ~ (all_48_2 = e1) % 133.84/19.30 | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | REDUCE: (5142), (6631) imply: % 133.84/19.30 | | | | | | | | | | | | | (6632) $false % 133.84/19.30 | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | CLOSE: (6632) is inconsistent. % 133.84/19.30 | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | (6633) ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & % 133.84/19.30 | | | | | | | | | | | | | $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1) % 133.84/19.30 | | | | | | | | | | | | | = all_48_1 & $i(all_48_1)) % 133.84/19.30 | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | BETA: splitting (6630) gives: % 133.84/19.30 | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | (6634) ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 & % 133.84/19.30 | | | | | | | | | | | | | | $i(all_46_0) % 133.84/19.30 | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | ALPHA: (6634) implies: % 133.84/19.30 | | | | | | | | | | | | | | (6635) ~ (all_46_0 = e2) % 133.84/19.30 | | | | | | | | | | | | | | (6636) op(e0, e1) = all_46_0 % 133.84/19.30 | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | BETA: splitting (223) gives: % 133.84/19.30 | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | (6637) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 % 133.84/19.30 | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 133.84/19.30 | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (5153), (6505), (6637), % 133.84/19.30 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.84/19.30 | | | | | | | | | | | | | | | #152. % 133.84/19.30 | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | (6638) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = % 133.84/19.30 | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) % 133.84/19.30 | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | BETA: splitting (6638) gives: % 133.84/19.30 | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | (6639) all_57_5 = e0 & op(e2, e1) = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6624), (6639), (function-axioms) are % 133.84/19.30 | | | | | | | | | | | | | | | | inconsistent by sub-proof #455. % 133.84/19.30 | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | (6640) all_57_10 = e0 & op(e2, e0) = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | ALPHA: (6640) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | (6641) all_57_10 = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | (6642) op(e2, e0) = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | (6643) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 133.84/19.30 | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (224), (225), % 133.84/19.30 | | | | | | | | | | | | | | | | | (226), (6508), (6641), (6642), (6643), % 133.84/19.30 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.84/19.30 | | | | | | | | | | | | | | | | | #445. % 133.84/19.30 | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | (6644) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 133.84/19.30 | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 133.84/19.30 | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | BETA: splitting (6644) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | (6645) all_57_7 = e0 & op(e1, e2) = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (6623), (6645), (function-axioms) are % 133.84/19.30 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #505. % 133.84/19.30 | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | (6646) all_57_13 = e0 & op(e0, e2) = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | ALPHA: (6646) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | (6647) all_57_13 = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | | | (6648) op(e0, e2) = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | BETA: splitting (6633) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6649) ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & % 133.84/19.30 | | | | | | | | | | | | | | | | | | | $i(all_48_0) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | ALPHA: (6649) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6650) ~ (all_48_0 = e3) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6651) op(e1, e2) = all_48_0 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11, % 133.84/19.30 | | | | | | | | | | | | | | | | | | | all_46_0, e1, e0, simplifying with (157), (6636) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6652) all_52_11 = all_46_0 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0, % 133.84/19.30 | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (158), (6648) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6653) all_52_7 = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, % 133.84/19.30 | | | | | | | | | | | | | | | | | | | all_48_0, e2, e1, simplifying with (162), (6651) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6654) all_52_6 = all_48_0 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 133.84/19.30 | | | | | | | | | | | | | | | | | | | e0, e0, e2, simplifying with (164), (6642) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6655) all_52_13 = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (6654) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6656) all_54_9 = all_48_0 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | REDUCE: (143), (6654) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6657) ~ (all_52_2 = all_48_0) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | REDUCE: (126), (6654) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6658) ~ (all_52_14 = all_48_0) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | SIMP: (6658) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6659) ~ (all_52_14 = all_48_0) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | REDUCE: (6623), (6654) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6660) ~ (all_48_0 = e0) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | REDUCE: (110), (6655) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6661) ~ (all_52_14 = e0) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | SIMP: (6661) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | (6662) ~ (all_52_14 = e0) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6663) all_54_9 = e3 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6650), (6656), (6663) are inconsistent by % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | sub-proof #176. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6664) ~ (all_54_9 = e3) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | (6665) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6665) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | (6666) all_54_9 = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6656), (6666) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | (6667) all_48_0 = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | SIMP: (6667) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | (6668) all_48_0 = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6657), (6668) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | (6669) ~ (all_52_2 = e2) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6659), (6668) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | (6670) ~ (all_52_14 = e2) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | REDUCE: (6650), (6668) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | (6671) ~ (e3 = e2) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | (6672) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6672) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6673) all_57_9 = e2 & op(e3, e0) = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6673) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6674) all_57_9 = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6675) all_54_11 = e3 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (6551), (6675) are inconsistent by % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #260. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | (6676) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6676) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | (6677) all_54_11 = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (6670), (6677) are inconsistent by % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #259. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | (6678) all_54_11 = e1 | all_54_11 = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6678) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (6679) all_54_11 = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (6679) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (6680) all_52_14 = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6680) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (6681) all_52_14 = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (6681) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (6682) ~ (all_52_2 = e1) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6683) all_54_8 = e3 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (6683) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6684) all_52_2 = e3 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (6684) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6685) ~ (all_52_1 = e3) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (6684) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6686) ~ (all_52_3 = e3) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6686) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6687) ~ (all_52_3 = e3) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6688) all_54_4 = e3 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (6685), (6688) are inconsistent by % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #481. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6689) ~ (all_54_4 = e3) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6690) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6690) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6691) all_54_4 = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (6691) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6692) all_52_1 = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6692) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6693) all_52_1 = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (6693) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6694) ~ (all_52_3 = e2) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6694) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6695) ~ (all_52_3 = e2) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (6693) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6696) op(e2, e3) = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6697) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6697) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6698) all_57_0 = e1 & op(e3, e3) = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6698) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6699) op(e3, e3) = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (39), (169), (170), (232), (361), % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6508), (6627), (6674), (6699), (function-axioms) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #487. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6700) all_57_2 = e1 & op(e2, e3) = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6700) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6701) op(e2, e3) = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6696), (6701), (function-axioms) are % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #450. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6702) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6702) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6703) all_57_6 = e1 & op(e1, e3) = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (163), (192), (248), (6507), (6687), % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6695), (6703), (function-axioms) are inconsistent % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #422. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6704) all_57_12 = e1 & op(e0, e3) = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6704) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6705) all_57_12 = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6706) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6706) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6707) all_57_12 = e2 & op(e0, e3) = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6707) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6708) all_57_12 = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6705), (6708) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6709) e2 = e1 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (6709) imply: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6710) $false % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6710) is inconsistent. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6711) all_57_13 = e2 & op(e0, e2) = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6647), (6711) are inconsistent by sub-proof % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #122. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6712) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6712) gives: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6713) all_57_14 = e2 & op(e0, e1) = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6713) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6714) op(e0, e1) = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6635), (6636), (6714), (function-axioms) are % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #759. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6715) all_57_15 = e2 & op(e0, e0) = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6715) implies: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6716) op(e0, e0) = e2 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (211), (6548), (6549), % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6705), (6716), (function-axioms) are inconsistent % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #123. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6717) all_54_4 = e1 | all_54_4 = e0 % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (5143), (6505), (6717) are inconsistent by % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #153. % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.84/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6718) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (6506), (6669), (6682), (6718) are % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #429. % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (6719) all_54_11 = e0 % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (6662), (6719) are inconsistent by % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #258. % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6720) all_57_10 = e2 & op(e2, e0) = e2 % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6720) implies: % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6721) op(e2, e0) = e2 % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6642), (6721), (function-axioms) are % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #451. % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | (6722) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6722) gives: % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6723) all_57_11 = e2 & op(e1, e0) = e2 % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (6670), (6723), (function-axioms) are % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #514. % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6724) all_57_15 = e2 & op(e0, e0) = e2 % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6724) implies: % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | (6725) op(e0, e0) = e2 % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6552), (6725), (function-axioms) are % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634. % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | (6726) all_54_9 = e1 | all_54_9 = e0 % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (5145), (6623), (6726) are inconsistent by % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | sub-proof #168. % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.30 | | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.30 | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.30 | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | (6727) ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 & % 133.90/19.30 | | | | | | | | | | | | | | | | | | | $i(all_48_1) % 133.90/19.30 | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6627), (6727), (function-axioms) are inconsistent % 133.90/19.30 | | | | | | | | | | | | | | | | | | | by sub-proof #187. % 133.90/19.30 | | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | | End of split % 133.90/19.30 | | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | | End of split % 133.90/19.30 | | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | | End of split % 133.90/19.30 | | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | | End of split % 133.90/19.30 | | | | | | | | | | | | | | | % 133.90/19.30 | | | | | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | (6728) ~ (all_46_1 = e3) & op(e0, e0) = all_46_1 & % 133.90/19.31 | | | | | | | | | | | | | | $i(all_46_1) % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | REF_CLOSE: (6552), (6728), (function-axioms) are inconsistent % 133.90/19.31 | | | | | | | | | | | | | | by sub-proof #758. % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | % 133.90/19.31 | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | % 133.90/19.31 | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | % 133.90/19.31 | | | | | | | | | (6729) all_28_2 = e3 % 133.90/19.31 | | | | | | | | | (6730) ( ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 & % 133.90/19.31 | | | | | | | | | $i(all_28_0)) | ( ~ (all_28_1 = e0) & op(e3, e3) = % 133.90/19.31 | | | | | | | | | all_28_1 & $i(all_28_1)) % 133.90/19.31 | | | | | | | | | % 133.90/19.31 | | | | | | | | | COMBINE_EQS: (316), (6729) imply: % 133.90/19.31 | | | | | | | | | (6731) all_6_2 = e3 % 133.90/19.31 | | | | | | | | | % 133.90/19.31 | | | | | | | | | REDUCE: (348), (6731) imply: % 133.90/19.31 | | | | | | | | | (6732) ~ (all_52_2 = e3) % 133.90/19.31 | | | | | | | | | % 133.90/19.31 | | | | | | | | | REDUCE: (359), (6731) imply: % 133.90/19.31 | | | | | | | | | (6733) ~ (all_52_6 = e3) % 133.90/19.31 | | | | | | | | | % 133.90/19.31 | | | | | | | | | REDUCE: (39), (6731) imply: % 133.90/19.31 | | | | | | | | | (6734) op(e1, e1) = e3 % 133.90/19.31 | | | | | | | | | % 133.90/19.31 | | | | | | | | | BETA: splitting (6730) gives: % 133.90/19.31 | | | | | | | | | % 133.90/19.31 | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | (6735) ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 & % 133.90/19.31 | | | | | | | | | | $i(all_28_0) % 133.90/19.31 | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | ALPHA: (6735) implies: % 133.90/19.31 | | | | | | | | | | (6736) ~ (all_28_0 = e2) % 133.90/19.31 | | | | | | | | | | (6737) op(e3, e1) = all_28_0 % 133.90/19.31 | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | BETA: splitting (5141) gives: % 133.90/19.31 | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | (6738) ~ (all_8_0 = e0) & op(e1, e2) = all_8_0 & % 133.90/19.31 | | | | | | | | | | | $i(all_8_0) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | ALPHA: (6738) implies: % 133.90/19.31 | | | | | | | | | | | (6739) ~ (all_8_0 = e0) % 133.90/19.31 | | | | | | | | | | | (6740) op(e1, e2) = all_8_0 % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, % 133.90/19.31 | | | | | | | | | | | all_8_0, e2, e1, simplifying with (162), (6740) % 133.90/19.31 | | | | | | | | | | | gives: % 133.90/19.31 | | | | | | | | | | | (6741) all_52_6 = all_8_0 % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 133.90/19.31 | | | | | | | | | | | all_28_0, e1, e3, simplifying with (169), (6737) % 133.90/19.31 | | | | | | | | | | | gives: % 133.90/19.31 | | | | | | | | | | | (6742) all_52_8 = all_28_0 % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | COMBINE_EQS: (257), (6741) imply: % 133.90/19.31 | | | | | | | | | | | (6743) all_54_9 = all_8_0 % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | REDUCE: (143), (6741) imply: % 133.90/19.31 | | | | | | | | | | | (6744) ~ (all_52_2 = all_8_0) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | REDUCE: (136), (6741) imply: % 133.90/19.31 | | | | | | | | | | | (6745) ~ (all_52_4 = all_8_0) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | REDUCE: (6733), (6741) imply: % 133.90/19.31 | | | | | | | | | | | (6746) ~ (all_8_0 = e3) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | REDUCE: (5145), (6741) imply: % 133.90/19.31 | | | | | | | | | | | (6747) ~ (all_8_0 = e1) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | BETA: splitting (195) gives: % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | (6748) all_54_9 = e3 % 133.90/19.31 | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | COMBINE_EQS: (6743), (6748) imply: % 133.90/19.31 | | | | | | | | | | | | (6749) all_8_0 = e3 % 133.90/19.31 | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | REDUCE: (6746), (6749) imply: % 133.90/19.31 | | | | | | | | | | | | (6750) $false % 133.90/19.31 | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | CLOSE: (6750) is inconsistent. % 133.90/19.31 | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | (6751) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 133.90/19.31 | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | BETA: splitting (6751) gives: % 133.90/19.31 | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | (6752) all_54_9 = e2 % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | COMBINE_EQS: (6743), (6752) imply: % 133.90/19.31 | | | | | | | | | | | | | (6753) all_8_0 = e2 % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | REDUCE: (6744), (6753) imply: % 133.90/19.31 | | | | | | | | | | | | | (6754) ~ (all_52_2 = e2) % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | REDUCE: (6745), (6753) imply: % 133.90/19.31 | | | | | | | | | | | | | (6755) ~ (all_52_4 = e2) % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | BETA: splitting (196) gives: % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | (6756) all_54_8 = e3 % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | REF_CLOSE: (258), (6732), (6756) are inconsistent by % 133.90/19.31 | | | | | | | | | | | | | | sub-proof #121. % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | (6757) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | BETA: splitting (6757) gives: % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | (6758) all_54_8 = e2 % 133.90/19.31 | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | REF_CLOSE: (258), (6754), (6758) are inconsistent by % 133.90/19.31 | | | | | | | | | | | | | | | sub-proof #430. % 133.90/19.31 | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | (6759) ~ (all_54_8 = e2) % 133.90/19.31 | | | | | | | | | | | | | | | (6760) all_54_8 = e1 | all_54_8 = e0 % 133.90/19.31 | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | BETA: splitting (6760) gives: % 133.90/19.31 | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | (6761) all_54_8 = e1 % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (6761) imply: % 133.90/19.31 | | | | | | | | | | | | | | | | (6762) all_52_2 = e1 % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | SIMP: (6762) implies: % 133.90/19.31 | | | | | | | | | | | | | | | | (6763) all_52_2 = e1 % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | REDUCE: (141), (6763) imply: % 133.90/19.31 | | | | | | | | | | | | | | | | (6764) ~ (all_52_14 = e1) % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | SIMP: (6764) implies: % 133.90/19.31 | | | | | | | | | | | | | | | | (6765) ~ (all_52_14 = e1) % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | REDUCE: (6754), (6763) imply: % 133.90/19.31 | | | | | | | | | | | | | | | | (6766) ~ (e2 = e1) % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | (6767) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 133.90/19.31 | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 133.90/19.31 | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | BETA: splitting (6767) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | (6768) all_57_9 = e1 & op(e3, e0) = e1 % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | ALPHA: (6768) implies: % 133.90/19.31 | | | | | | | | | | | | | | | | | | (6769) all_57_9 = e1 % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | (6770) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 133.90/19.31 | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (6770) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6771) all_57_0 = e2 & op(e3, e3) = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (6771) implies: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6772) op(e3, e3) = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6509), (6772), (function-axioms) are % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6773) all_57_1 = e2 & op(e3, e2) = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (6755), (6773), (function-axioms) are % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #396. % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | (6774) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 133.90/19.31 | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (6774) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6775) all_57_4 = e2 & op(e3, e1) = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6736), (6737), (6775), (function-axioms) are % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #218. % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6776) all_57_9 = e2 & op(e3, e0) = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (6776) implies: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6777) all_57_9 = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6769), (6777) imply: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6778) e2 = e1 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (6778) imply: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6779) $false % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | CLOSE: (6779) is inconsistent. % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | (6780) all_57_10 = e1 & op(e2, e0) = e1 % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | ALPHA: (6780) implies: % 133.90/19.31 | | | | | | | | | | | | | | | | | | (6781) op(e2, e0) = e1 % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5148), (6781), (function-axioms) are % 133.90/19.31 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180. % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | (6782) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 133.90/19.31 | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.90/19.31 | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | BETA: splitting (6782) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | (6783) all_57_11 = e1 & op(e1, e0) = e1 % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | ALPHA: (6783) implies: % 133.90/19.31 | | | | | | | | | | | | | | | | | | (6784) op(e1, e0) = e1 % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (6765), (6784), (function-axioms) are % 133.90/19.31 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #327. % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | (6785) all_57_15 = e1 & op(e0, e0) = e1 % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | ALPHA: (6785) implies: % 133.90/19.31 | | | | | | | | | | | | | | | | | | (6786) op(e0, e0) = e1 % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (6786), (function-axioms) are % 133.90/19.31 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354. % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | (6787) all_54_8 = e0 % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | REF_CLOSE: (258), (6506), (6787) are inconsistent by % 133.90/19.31 | | | | | | | | | | | | | | | | sub-proof #475. % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | (6788) all_54_9 = e1 | all_54_9 = e0 % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | REF_CLOSE: (6739), (6743), (6747), (6788) are inconsistent by % 133.90/19.31 | | | | | | | | | | | | | sub-proof #155. % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | (6789) ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 & % 133.90/19.31 | | | | | | | | | | | $i(all_8_1) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | REF_CLOSE: (6734), (6789), (function-axioms) are inconsistent % 133.90/19.31 | | | | | | | | | | | by sub-proof #128. % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | % 133.90/19.31 | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | (6790) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 & % 133.90/19.31 | | | | | | | | | | $i(all_28_1) % 133.90/19.31 | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | REF_CLOSE: (6509), (6790), (function-axioms) are inconsistent % 133.90/19.31 | | | | | | | | | | by sub-proof #211. % 133.90/19.31 | | | | | | | | | | % 133.90/19.31 | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | % 133.90/19.31 | | | | | | | | End of split % 133.90/19.31 | | | | | | | | % 133.90/19.31 | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | % 133.90/19.31 | | | | | | | | (6791) all_20_2 = e2 % 133.90/19.31 | | | | | | | | (6792) ( ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 & % 133.90/19.31 | | | | | | | | $i(all_20_0)) | ( ~ (all_20_1 = e1) & op(e2, e2) = % 133.90/19.31 | | | | | | | | all_20_1 & $i(all_20_1)) % 133.90/19.31 | | | | | | | | % 133.90/19.31 | | | | | | | | COMBINE_EQS: (318), (6791) imply: % 133.90/19.31 | | | | | | | | (6793) all_4_2 = e2 % 133.90/19.31 | | | | | | | | % 133.90/19.31 | | | | | | | | SIMP: (6793) implies: % 133.90/19.31 | | | | | | | | (6794) all_4_2 = e2 % 133.90/19.31 | | | | | | | | % 133.90/19.31 | | | | | | | | REDUCE: (349), (6794) imply: % 133.90/19.31 | | | | | | | | (6795) ~ (all_52_3 = e2) % 133.90/19.31 | | | | | | | | % 133.90/19.31 | | | | | | | | REDUCE: (367), (6794) imply: % 133.90/19.31 | | | | | | | | (6796) ~ (all_52_11 = e2) % 133.90/19.31 | | | | | | | | % 133.90/19.31 | | | | | | | | REDUCE: (368), (6794) imply: % 133.90/19.31 | | | | | | | | (6797) ~ (all_52_12 = e2) % 133.90/19.31 | | | | | | | | % 133.90/19.31 | | | | | | | | REDUCE: (369), (6794) imply: % 133.90/19.31 | | | | | | | | (6798) ~ (all_52_13 = e2) % 133.90/19.31 | | | | | | | | % 133.90/19.31 | | | | | | | | REDUCE: (370), (6794) imply: % 133.90/19.31 | | | | | | | | (6799) ~ (all_52_14 = e2) % 133.90/19.31 | | | | | | | | % 133.90/19.31 | | | | | | | | REDUCE: (36), (6794) imply: % 133.90/19.31 | | | | | | | | (6800) op(e0, e0) = e2 % 133.90/19.31 | | | | | | | | % 133.90/19.31 | | | | | | | | BETA: splitting (67) gives: % 133.90/19.31 | | | | | | | | % 133.90/19.31 | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | % 133.90/19.31 | | | | | | | | | (6801) ~ (all_24_2 = e0) % 133.90/19.31 | | | | | | | | | % 133.90/19.31 | | | | | | | | | REDUCE: (6504), (6801) imply: % 133.90/19.31 | | | | | | | | | (6802) $false % 133.90/19.31 | | | | | | | | | % 133.90/19.31 | | | | | | | | | CLOSE: (6802) is inconsistent. % 133.90/19.31 | | | | | | | | | % 133.90/19.31 | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | % 133.90/19.31 | | | | | | | | | (6803) ( ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 & % 133.90/19.31 | | | | | | | | | $i(all_24_0)) | ( ~ (all_24_1 = e2) & op(e0, e0) = % 133.90/19.31 | | | | | | | | | all_24_1 & $i(all_24_1)) % 133.90/19.31 | | | | | | | | | % 133.90/19.31 | | | | | | | | | BETA: splitting (6792) gives: % 133.90/19.31 | | | | | | | | | % 133.90/19.31 | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | (6804) ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 & % 133.90/19.31 | | | | | | | | | | $i(all_20_0) % 133.90/19.31 | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | ALPHA: (6804) implies: % 133.90/19.31 | | | | | | | | | | (6805) ~ (all_20_0 = e3) % 133.90/19.31 | | | | | | | | | | (6806) op(e2, e0) = all_20_0 % 133.90/19.31 | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | BETA: splitting (6803) gives: % 133.90/19.31 | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | (6807) ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 & % 133.90/19.31 | | | | | | | | | | | $i(all_24_0) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | ALPHA: (6807) implies: % 133.90/19.31 | | | | | | | | | | | (6808) ~ (all_24_0 = e1) % 133.90/19.31 | | | | | | | | | | | (6809) op(e0, e3) = all_24_0 % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, % 133.90/19.31 | | | | | | | | | | | all_24_0, e3, e0, simplifying with (159), (6809) % 133.90/19.31 | | | | | | | | | | | gives: % 133.90/19.31 | | | | | | | | | | | (6810) all_52_3 = all_24_0 % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 133.90/19.31 | | | | | | | | | | | all_20_0, e0, e2, simplifying with (164), (6806) % 133.90/19.31 | | | | | | | | | | | gives: % 133.90/19.31 | | | | | | | | | | | (6811) all_52_13 = all_20_0 % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | COMBINE_EQS: (248), (6810) imply: % 133.90/19.31 | | | | | | | | | | | (6812) all_54_12 = all_24_0 % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | COMBINE_EQS: (259), (6811) imply: % 133.90/19.31 | | | | | | | | | | | (6813) all_54_7 = all_20_0 % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | REDUCE: (148), (6810) imply: % 133.90/19.31 | | | | | | | | | | | (6814) ~ (all_52_1 = all_24_0) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | REDUCE: (145), (6811) imply: % 133.90/19.31 | | | | | | | | | | | (6815) ~ (all_52_1 = all_20_0) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | REDUCE: (144), (6810) imply: % 133.90/19.31 | | | | | | | | | | | (6816) ~ (all_52_2 = all_24_0) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | REDUCE: (140), (6810) imply: % 133.90/19.31 | | | | | | | | | | | (6817) ~ (all_52_7 = all_24_0) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | SIMP: (6817) implies: % 133.90/19.31 | | | | | | | | | | | (6818) ~ (all_52_7 = all_24_0) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | REDUCE: (139), (6810) imply: % 133.90/19.31 | | | | | | | | | | | (6819) ~ (all_52_11 = all_24_0) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | SIMP: (6819) implies: % 133.90/19.31 | | | | | | | | | | | (6820) ~ (all_52_11 = all_24_0) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | REDUCE: (6795), (6810) imply: % 133.90/19.31 | | | | | | | | | | | (6821) ~ (all_24_0 = e2) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | REDUCE: (6507), (6810) imply: % 133.90/19.31 | | | | | | | | | | | (6822) ~ (all_24_0 = e0) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | REDUCE: (117), (6811) imply: % 133.90/19.31 | | | | | | | | | | | (6823) ~ (all_52_9 = all_20_0) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | REDUCE: (6798), (6811) imply: % 133.90/19.31 | | | | | | | | | | | (6824) ~ (all_20_0 = e2) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | REDUCE: (5148), (6811) imply: % 133.90/19.31 | | | | | | | | | | | (6825) ~ (all_20_0 = e1) % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | BETA: splitting (209) gives: % 133.90/19.31 | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | (6826) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 133.90/19.31 | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 133.90/19.31 | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | BETA: splitting (6826) gives: % 133.90/19.31 | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | (6827) all_57_12 = e1 & op(e0, e3) = e1 % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | ALPHA: (6827) implies: % 133.90/19.31 | | | | | | | | | | | | | (6828) all_57_12 = e1 % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | REF_CLOSE: (157), (158), (192), (211), (6800), (6808), % 133.90/19.31 | | | | | | | | | | | | | (6812), (6818), (6820), (6821), (6822), (6828), % 133.90/19.31 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.90/19.31 | | | | | | | | | | | | | #120. % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | (6829) all_57_13 = e1 & op(e0, e2) = e1 % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | REF_CLOSE: (158), (5146), (6829), (function-axioms) are % 133.90/19.31 | | | | | | | | | | | | | inconsistent by sub-proof #178. % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | End of split % 133.90/19.31 | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | (6830) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 133.90/19.31 | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.90/19.31 | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | BETA: splitting (6830) gives: % 133.90/19.31 | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | (6831) all_57_14 = e1 & op(e0, e1) = e1 % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | ALPHA: (6831) implies: % 133.90/19.31 | | | | | | | | | | | | | (6832) all_57_14 = e1 % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | BETA: splitting (192) gives: % 133.90/19.31 | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | (6833) all_54_12 = e3 % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | COMBINE_EQS: (6812), (6833) imply: % 133.90/19.31 | | | | | | | | | | | | | | (6834) all_24_0 = e3 % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | SIMP: (6834) implies: % 133.90/19.31 | | | | | | | | | | | | | | (6835) all_24_0 = e3 % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | REDUCE: (6814), (6835) imply: % 133.90/19.31 | | | | | | | | | | | | | | (6836) ~ (all_52_1 = e3) % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | REDUCE: (6816), (6835) imply: % 133.90/19.31 | | | | | | | | | | | | | | (6837) ~ (all_52_2 = e3) % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | REDUCE: (6818), (6835) imply: % 133.90/19.31 | | | | | | | | | | | | | | (6838) ~ (all_52_7 = e3) % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | REDUCE: (6820), (6835) imply: % 133.90/19.31 | | | | | | | | | | | | | | (6839) ~ (all_52_11 = e3) % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | BETA: splitting (208) gives: % 133.90/19.31 | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | (6840) all_57_15 = e0 & op(e0, e0) = e0 % 133.90/19.31 | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | ALPHA: (6840) implies: % 133.90/19.31 | | | | | | | | | | | | | | | (6841) op(e0, e0) = e0 % 133.90/19.31 | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | REF_CLOSE: (5), (6800), (6841), (function-axioms) are % 133.90/19.31 | | | | | | | | | | | | | | | inconsistent by sub-proof #714. % 133.90/19.31 | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | (6842) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 133.90/19.31 | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 133.90/19.31 | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 133.90/19.31 | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 133.90/19.31 | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 133.90/19.31 | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | ALPHA: (6842) implies: % 133.90/19.31 | | | | | | | | | | | | | | | (6843) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 133.90/19.31 | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 133.90/19.31 | | | | | | | | | | | | | | | e1) = e0) % 133.90/19.31 | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 133.90/19.31 | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | (6844) all_54_7 = e3 % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | REF_CLOSE: (6805), (6813), (6844) are inconsistent by % 133.90/19.31 | | | | | | | | | | | | | | | | sub-proof #119. % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | (6845) ~ (all_54_7 = e3) % 133.90/19.31 | | | | | | | | | | | | | | | | (6846) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | (6847) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 133.90/19.31 | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 133.90/19.31 | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (5143), (6509), (6847), % 133.90/19.31 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.90/19.31 | | | | | | | | | | | | | | | | | #118. % 133.90/19.31 | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | (6848) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 133.90/19.31 | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 133.90/19.31 | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | BETA: splitting (6848) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | (6849) all_57_6 = e1 & op(e1, e3) = e1 % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | ALPHA: (6849) implies: % 133.90/19.31 | | | | | | | | | | | | | | | | | | (6850) op(e1, e3) = e1 % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | (6851) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 133.90/19.31 | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (167), (6509), (6836), (6851), % 133.90/19.31 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.90/19.31 | | | | | | | | | | | | | | | | | | | #210. % 133.90/19.31 | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | (6852) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 133.90/19.31 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 133.90/19.31 | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (6852) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6853) all_57_6 = e3 & op(e1, e3) = e3 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6837), (6853), (function-axioms) are % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #761. % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6854) all_57_12 = e3 & op(e0, e3) = e3 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (6854) implies: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6855) all_57_12 = e3 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | (6856) op(e0, e3) = e3 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | (6857) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6857) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | (6858) all_57_6 = e2 & op(e1, e3) = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6858) implies: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | (6859) op(e1, e3) = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (6850), (6859), (function-axioms) are % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #517. % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | (6860) all_57_7 = e2 & op(e1, e2) = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6860) implies: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | (6861) all_57_7 = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6843) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | (6862) all_57_12 = e0 & op(e0, e3) = e0 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6862) implies: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | (6863) op(e0, e3) = e0 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (6507), (6863), (function-axioms) are % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219. % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | (6864) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6864) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | (6865) all_57_13 = e0 & op(e0, e2) = e0 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6865) implies: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | (6866) all_57_13 = e0 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | (6867) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2) % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6867) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (6868) all_57_0 = e2 & op(e3, e3) = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6868) implies: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (6869) op(e3, e3) = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6509), (6869), (function-axioms) are % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (6870) all_57_2 = e2 & op(e2, e3) = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6870) implies: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (6871) all_57_2 = e2 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6872) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6872) gives: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6873) all_57_1 = e3 & op(e3, e2) = e3 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6873) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6874) all_57_1 = e3 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6846) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6875) all_54_7 = e2 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6813), (6875) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6876) all_20_0 = e2 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6824), (6876) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6877) $false % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6877) is inconsistent. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6878) ~ (all_54_7 = e2) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6879) all_54_7 = e1 | all_54_7 = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6880) all_54_4 = e3 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (6836), (6880) are inconsistent by % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #481. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6881) ~ (all_54_4 = e3) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6882) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6883) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6883) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6884) all_57_0 = e2 & op(e3, e3) = e2 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6884) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6885) op(e3, e3) = e2 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (231), (233), (6855), % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6871), (6885), (function-axioms) are inconsistent % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #489. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6886) all_57_1 = e2 & op(e3, e2) = e2 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (208), (209), % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (6800), (6839), (6855), (6874), (6886), % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #207. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6887) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6887) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6888) all_57_4 = e2 & op(e3, e1) = e2 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6888) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6889) all_57_4 = e2 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6879) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6890) all_54_7 = e1 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6813), (6890) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6891) all_20_0 = e1 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6825), (6891) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6892) $false % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6892) is inconsistent. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6893) all_54_7 = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6813), (6893) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6894) all_20_0 = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6823), (6894) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6895) ~ (all_52_9 = e0) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6805), (6894) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6896) ~ (e3 = e0) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6824), (6894) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6897) ~ (e2 = e0) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6825), (6894) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6898) ~ (e1 = e0) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6899) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (5144), (6509), (6899), % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #117. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6900) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6900) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6901) all_57_4 = e1 & op(e3, e1) = e1 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6889), (6901) are inconsistent by sub-proof % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #462. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6902) all_57_9 = e1 & op(e3, e0) = e1 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6902) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6903) all_57_9 = e1 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6904) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6904) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6905) all_57_2 = e0 & op(e2, e3) = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (6505), (6905), (function-axioms) are % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #225. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6906) all_57_3 = e0 & op(e2, e2) = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6906) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6907) all_57_3 = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6908) op(e2, e2) = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6909) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (5144), (6908), (6909), % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #564. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6910) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6910) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6911) all_57_7 = e1 & op(e1, e2) = e1 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6911) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6912) all_57_7 = e1 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6872) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6913) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6913) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6914) all_57_1 = e2 & op(e3, e2) = e2 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6874), (6914) are inconsistent by sub-proof % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #563. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6915) all_57_3 = e2 & op(e2, e2) = e2 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6915) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6916) all_57_3 = e2 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6907), (6916) are inconsistent by sub-proof % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #679. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6917) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6917) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6861), (6912) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6918) e2 = e1 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (6918) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6919) $false % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6919) is inconsistent. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6920) all_57_13 = e2 & op(e0, e2) = e2 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6866), (6920) are inconsistent by sub-proof % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #122. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6921) all_57_3 = e3 & op(e2, e2) = e3 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6921) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6922) op(e2, e2) = e3 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6908), (6922), (function-axioms) are % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6923) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6923) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6924) all_57_7 = e3 & op(e1, e2) = e3 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6924) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6925) all_57_7 = e3 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6912), (6925) are inconsistent by sub-proof % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #390. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6926) all_57_13 = e3 & op(e0, e2) = e3 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6926) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6927) all_57_13 = e3 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6866), (6927) are inconsistent by sub-proof % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #484. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6928) all_57_13 = e1 & op(e0, e2) = e1 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6928) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6929) all_57_13 = e1 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6866), (6929) are inconsistent by sub-proof % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #681. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6930) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6930) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6931) all_57_5 = e0 & op(e2, e1) = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6895), (6931), (function-axioms) are % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #455. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6932) all_57_10 = e0 & op(e2, e0) = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6932) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6933) all_57_10 = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6934) op(e2, e0) = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6882) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6935) all_54_4 = e2 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (6935) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6936) all_52_1 = e2 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (6936) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6937) ~ (all_52_9 = e2) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6937) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6938) ~ (all_52_9 = e2) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6939) all_54_6 = e3 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (6939) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6940) all_52_9 = e3 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (6940) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6941) ~ (all_6_2 = e3) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6941) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6942) ~ (all_6_2 = e3) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (6940) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6943) op(e2, e1) = e3 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6944) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6944) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6945) all_57_4 = e0 & op(e3, e1) = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6945) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6946) all_57_4 = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (221), (222), % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (6832), (6942), (6946), (function-axioms) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #558. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6947) all_57_5 = e0 & op(e2, e1) = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6895), (6947), (function-axioms) are % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #455. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6948) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6948) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6949) all_57_8 = e0 & op(e1, e1) = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6949) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6950) op(e1, e1) = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6951) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6951) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6952) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (231), (232), % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (236), (238), (6508), (6855), (6871), % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6903), (6952), (function-axioms) are inconsistent % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #116. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6953) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5153), (6856), (6953), (function-axioms) are % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #115. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6954) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6954) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6955) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6955) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6956) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6956) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6957) op(e1, e1) = e3 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6950), (6957), (function-axioms) are % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6958) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6943), (6958), (function-axioms) are % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #114. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6959) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (39), (91), (157), (190), (246), % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332), (364), (372), (5153), (6796), (6800), % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6934), (6959), (function-axioms) are inconsistent % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #154. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6960) all_57_14 = e0 & op(e0, e1) = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6960) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6961) all_57_14 = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6832), (6961) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6962) e1 = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6962) implies: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6963) e1 = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5152), (6963) imply: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6964) all_57_3 = e0 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6965) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (5153), (6836), (6965), % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #166. % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6966) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6933), (6934), (6964), (6966), (function-axioms) % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #447. % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6967) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (5147), (6895), (6938), (6967) are % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #478. % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6968) all_54_4 = e1 | all_54_4 = e0 % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (163), (268), (6505), (6850), (6968), % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #243. % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6969) all_57_9 = e2 & op(e3, e0) = e2 % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (6797), (6969), (function-axioms) are % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6970) all_57_3 = e3 & op(e2, e2) = e3 % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6970) implies: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6971) op(e2, e2) = e3 % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5153), (6971), (function-axioms) are % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6972) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6972) gives: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6973) all_57_7 = e3 & op(e1, e2) = e3 % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6973) implies: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6974) all_57_7 = e3 % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6861), (6974) imply: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6975) e3 = e2 % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6855), (6975) imply: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6976) all_57_12 = e2 % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (208), (209), % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (6800), (6839), (6976), (function-axioms) % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #458. % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6977) all_57_13 = e3 & op(e0, e2) = e3 % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (6838), (6977), (function-axioms) are % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #556. % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | (6978) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6978) gives: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (6979) all_57_6 = e2 & op(e1, e3) = e2 % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6979) implies: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (6980) op(e1, e3) = e2 % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (6850), (6980), (function-axioms) are % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #517. % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (6981) all_57_12 = e2 & op(e0, e3) = e2 % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6981) implies: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (6982) all_57_12 = e2 % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (208), (209), % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (6800), (6839), (6982), (function-axioms) % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #458. % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | (6983) all_57_14 = e0 & op(e0, e1) = e0 % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6983) implies: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | (6984) all_57_14 = e0 % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6832), (6984) are inconsistent by sub-proof % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | #221. % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | (6985) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (372), (6799), (6985), % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | #513. % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | Case 2: % 133.90/19.33 | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | (6986) all_57_12 = e1 & op(e0, e3) = e1 % 133.90/19.33 | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | ALPHA: (6986) implies: % 133.90/19.33 | | | | | | | | | | | | | | | | | | (6987) all_57_12 = e1 % 133.90/19.33 | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (211), (6800), (6838), % 133.90/19.33 | | | | | | | | | | | | | | | | | | (6839), (6987), (function-axioms) are inconsistent % 133.90/19.33 | | | | | | | | | | | | | | | | | | by sub-proof #123. % 133.90/19.33 | | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | Case 2: % 133.90/19.33 | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | (6988) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 133.90/19.33 | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | | REF_CLOSE: (6808), (6812), (6821), (6822), (6988) are % 133.90/19.33 | | | | | | | | | | | | | | inconsistent by sub-proof #205. % 133.90/19.33 | | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | Case 2: % 133.90/19.33 | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | (6989) all_57_15 = e1 & op(e0, e0) = e1 % 133.90/19.33 | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | ALPHA: (6989) implies: % 133.90/19.33 | | | | | | | | | | | | | (6990) op(e0, e0) = e1 % 133.90/19.33 | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | | REF_CLOSE: (6), (6800), (6990), (function-axioms) are % 133.90/19.33 | | | | | | | | | | | | | inconsistent by sub-proof #636. % 133.90/19.33 | | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | Case 2: % 133.90/19.33 | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | (6991) ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 & % 133.90/19.33 | | | | | | | | | | | $i(all_24_1) % 133.90/19.33 | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | | REF_CLOSE: (6800), (6991), (function-axioms) are inconsistent % 133.90/19.33 | | | | | | | | | | | by sub-proof #204. % 133.90/19.33 | | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | | % 133.90/19.33 | | | | | | | | | Case 2: % 133.90/19.33 | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | (6992) ~ (all_20_1 = e1) & op(e2, e2) = all_20_1 & % 133.90/19.33 | | | | | | | | | | $i(all_20_1) % 133.90/19.33 | | | | | | | | | | % 133.90/19.33 | | | | | | | | | | REF_CLOSE: (5153), (6992), (function-axioms) are inconsistent % 133.90/19.33 | | | | | | | | | | by sub-proof #113. % 133.90/19.33 | | | | | | | | | | % 133.90/19.33 | | | | | | | | | End of split % 133.90/19.33 | | | | | | | | | % 133.90/19.33 | | | | | | | | End of split % 133.90/19.33 | | | | | | | | % 133.90/19.33 | | | | | | | End of split % 133.90/19.33 | | | | | | | % 133.90/19.33 | | | | | | End of split % 133.90/19.33 | | | | | | % 133.90/19.33 | | | | | End of split % 133.90/19.33 | | | | | % 133.90/19.33 | | | | Case 2: % 133.90/19.33 | | | | | % 133.90/19.33 | | | | | (6993) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, % 133.90/19.33 | | | | | e0) = e1) % 133.90/19.33 | | | | | % 133.90/19.33 | | | | | REF_CLOSE: (164), (165), (5147), (5148), (6993), (function-axioms) are % 133.90/19.33 | | | | | inconsistent by sub-proof #112. % 133.90/19.33 | | | | | % 133.90/19.33 | | | | End of split % 133.90/19.33 | | | | % 133.90/19.33 | | | End of split % 133.90/19.33 | | | % 133.90/19.33 | | Case 2: % 133.90/19.33 | | | % 133.90/19.33 | | | (6994) all_6_2 = e2 % 133.90/19.33 | | | (6995) ( ~ (all_6_0 = e0) & op(e2, e1) = all_6_0 & $i(all_6_0)) | ( ~ % 133.90/19.33 | | | (all_6_1 = e3) & op(e2, e2) = all_6_1 & $i(all_6_1)) % 133.90/19.33 | | | % 133.90/19.33 | | | COMBINE_EQS: (324), (6994) imply: % 133.90/19.33 | | | (6996) all_18_2 = e2 % 133.90/19.33 | | | % 133.90/19.33 | | | REDUCE: (348), (6994) imply: % 133.90/19.33 | | | (6997) ~ (all_52_2 = e2) % 133.90/19.33 | | | % 133.90/19.33 | | | REDUCE: (359), (6994) imply: % 133.90/19.33 | | | (6998) ~ (all_52_6 = e2) % 133.90/19.33 | | | % 133.90/19.33 | | | REDUCE: (361), (6994) imply: % 133.90/19.33 | | | (6999) ~ (all_52_8 = e2) % 133.90/19.33 | | | % 133.90/19.33 | | | REDUCE: (362), (6994) imply: % 133.90/19.33 | | | (7000) ~ (all_52_9 = e2) % 133.90/19.33 | | | % 133.90/19.33 | | | REDUCE: (364), (6994) imply: % 133.90/19.33 | | | (7001) ~ (all_52_11 = e2) % 133.90/19.33 | | | % 133.90/19.33 | | | REDUCE: (366), (6994) imply: % 133.97/19.33 | | | (7002) ~ (all_52_14 = e2) % 133.97/19.33 | | | % 133.97/19.33 | | | BETA: splitting (221) gives: % 133.97/19.33 | | | % 133.97/19.33 | | | Case 1: % 133.97/19.33 | | | | % 133.97/19.33 | | | | (7003) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, % 133.97/19.33 | | | | e1) = e2) % 133.97/19.33 | | | | % 133.97/19.33 | | | | REF_CLOSE: (165), (169), (6999), (7000), (7003), (function-axioms) are % 133.97/19.33 | | | | inconsistent by sub-proof #441. % 133.97/19.33 | | | | % 133.97/19.33 | | | Case 2: % 133.97/19.33 | | | | % 133.97/19.33 | | | | (7004) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, % 133.97/19.33 | | | | e1) = e2) % 133.97/19.33 | | | | % 133.97/19.33 | | | | BETA: splitting (7004) gives: % 133.97/19.33 | | | | % 133.97/19.33 | | | | Case 1: % 133.97/19.33 | | | | | % 133.97/19.33 | | | | | (7005) all_57_8 = e2 & op(e1, e1) = e2 % 133.97/19.33 | | | | | % 133.97/19.33 | | | | | ALPHA: (7005) implies: % 133.97/19.33 | | | | | (7006) all_57_8 = e2 % 133.97/19.33 | | | | | (7007) op(e1, e1) = e2 % 133.97/19.33 | | | | | % 133.97/19.33 | | | | | BETA: splitting (43) gives: % 133.97/19.33 | | | | | % 133.97/19.33 | | | | | Case 1: % 133.97/19.33 | | | | | | % 133.97/19.33 | | | | | | (7008) ~ (all_8_2 = e1) % 133.97/19.33 | | | | | | % 133.97/19.33 | | | | | | BETA: splitting (46) gives: % 133.97/19.33 | | | | | | % 133.97/19.33 | | | | | | Case 1: % 133.97/19.33 | | | | | | | % 133.97/19.33 | | | | | | | (7009) ~ (all_10_2 = e0) % 133.97/19.33 | | | | | | | % 133.97/19.33 | | | | | | | BETA: splitting (52) gives: % 133.97/19.33 | | | | | | | % 133.97/19.33 | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | % 133.97/19.33 | | | | | | | | (7010) ~ (all_14_2 = e3) % 133.97/19.33 | | | | | | | | % 133.97/19.33 | | | | | | | | REDUCE: (329), (7010) imply: % 133.97/19.33 | | | | | | | | (7011) ~ (all_8_2 = e3) % 133.97/19.33 | | | | | | | | % 133.97/19.33 | | | | | | | | BETA: splitting (58) gives: % 133.97/19.33 | | | | | | | | % 133.97/19.33 | | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | | % 133.97/19.33 | | | | | | | | | (7012) ~ (all_18_2 = e2) % 133.97/19.33 | | | | | | | | | % 133.97/19.33 | | | | | | | | | REDUCE: (6996), (7012) imply: % 133.97/19.33 | | | | | | | | | (7013) $false % 133.97/19.33 | | | | | | | | | % 133.97/19.33 | | | | | | | | | CLOSE: (7013) is inconsistent. % 133.97/19.33 | | | | | | | | | % 133.97/19.33 | | | | | | | | Case 2: % 133.97/19.33 | | | | | | | | | % 133.97/19.33 | | | | | | | | | (7014) ( ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 & % 133.97/19.33 | | | | | | | | | $i(all_18_0)) | ( ~ (all_18_1 = e0) & op(e2, e2) = % 133.97/19.33 | | | | | | | | | all_18_1 & $i(all_18_1)) % 133.97/19.33 | | | | | | | | | % 133.97/19.33 | | | | | | | | | BETA: splitting (55) gives: % 133.97/19.33 | | | | | | | | | % 133.97/19.33 | | | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | (7015) ~ (all_16_2 = e2) % 133.97/19.33 | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | REDUCE: (327), (7015) imply: % 133.97/19.33 | | | | | | | | | | (7016) ~ (all_10_2 = e2) % 133.97/19.33 | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | BETA: splitting (61) gives: % 133.97/19.33 | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | (7017) ~ (all_20_2 = e2) % 133.97/19.33 | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | REDUCE: (318), (7017) imply: % 133.97/19.33 | | | | | | | | | | | (7018) ~ (all_4_2 = e2) % 133.97/19.33 | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | BETA: splitting (79) gives: % 133.97/19.33 | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | (7019) ~ (all_32_2 = e1) % 133.97/19.33 | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | REDUCE: (312), (7019) imply: % 133.97/19.33 | | | | | | | | | | | | (7020) ~ (all_10_2 = e1) % 133.97/19.33 | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | BETA: splitting (204) gives: % 133.97/19.33 | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | (7021) all_54_0 = e3 % 133.97/19.33 | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | COMBINE_EQS: (278), (7021) imply: % 133.97/19.33 | | | | | | | | | | | | | (7022) all_10_2 = e3 % 133.97/19.33 | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | REDUCE: (336), (7022) imply: % 133.97/19.33 | | | | | | | | | | | | | (7023) ~ (all_52_1 = e3) % 133.97/19.33 | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | REDUCE: (342), (7022) imply: % 133.97/19.33 | | | | | | | | | | | | | (7024) ~ (all_52_4 = e3) % 133.97/19.33 | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | REDUCE: (344), (7022) imply: % 133.97/19.33 | | | | | | | | | | | | | (7025) ~ (all_52_8 = e3) % 133.97/19.33 | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | REDUCE: (346), (7022) imply: % 133.97/19.33 | | | | | | | | | | | | | (7026) ~ (all_52_12 = e3) % 133.97/19.33 | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | REDUCE: (45), (7022) imply: % 133.97/19.33 | | | | | | | | | | | | | (7027) op(e3, e3) = e3 % 133.97/19.33 | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | BETA: splitting (76) gives: % 133.97/19.33 | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | (7028) ~ (all_30_2 = e0) % 133.97/19.33 | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | REDUCE: (309), (7028) imply: % 133.97/19.33 | | | | | | | | | | | | | | (7029) ~ (all_8_2 = e0) % 133.97/19.33 | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | BETA: splitting (199) gives: % 133.97/19.33 | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | (7030) all_54_5 = e3 % 133.97/19.33 | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | REF_CLOSE: (267), (7011), (7030) are inconsistent by % 133.97/19.33 | | | | | | | | | | | | | | | sub-proof #554. % 133.97/19.33 | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | Case 2: % 133.97/19.33 | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | (7031) ~ (all_54_5 = e3) % 133.97/19.33 | | | | | | | | | | | | | | | (7032) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 133.97/19.33 | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | BETA: splitting (7032) gives: % 133.97/19.33 | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | (7033) all_54_5 = e2 % 133.97/19.33 | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7033) imply: % 133.97/19.33 | | | | | | | | | | | | | | | | (7034) all_8_2 = e2 % 133.97/19.33 | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | SIMP: (7034) implies: % 133.97/19.33 | | | | | | | | | | | | | | | | (7035) all_8_2 = e2 % 133.97/19.33 | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | REDUCE: (347), (7035) imply: % 133.97/19.33 | | | | | | | | | | | | | | | | (7036) ~ (all_52_1 = e2) % 133.97/19.33 | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | REDUCE: (358), (7035) imply: % 133.97/19.33 | | | | | | | | | | | | | | | | (7037) ~ (all_52_13 = e2) % 133.97/19.33 | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | REDUCE: (7011), (7035) imply: % 133.97/19.33 | | | | | | | | | | | | | | | | (7038) ~ (e3 = e2) % 133.97/19.33 | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 133.97/19.33 | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | (7039) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 133.97/19.33 | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 133.97/19.33 | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | BETA: splitting (7039) gives: % 133.97/19.33 | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | (7040) all_57_9 = e2 & op(e3, e0) = e2 % 133.97/19.33 | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | ALPHA: (7040) implies: % 133.97/19.33 | | | | | | | | | | | | | | | | | | (7041) all_57_9 = e2 % 133.97/19.33 | | | | | | | | | | | | | | | | | | (7042) op(e3, e0) = e2 % 133.97/19.33 | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 133.97/19.33 | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | (7043) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | BETA: splitting (7043) gives: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | (7044) all_57_2 = e2 & op(e2, e3) = e2 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | ALPHA: (7044) implies: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | (7045) op(e2, e3) = e2 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (7036), (7045), (function-axioms) are % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #779. % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | (7046) all_57_3 = e2 & op(e2, e2) = e2 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | ALPHA: (7046) implies: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | (7047) all_57_3 = e2 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | (7048) op(e2, e2) = e2 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (7049) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7049) gives: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (7050) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7050) gives: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | (7051) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7051) implies: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | (7052) op(e3, e3) = e2 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234), % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | (238), (7024), (7041), (7052), (function-axioms) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #250. % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | (7053) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7053) implies: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | (7054) op(e3, e3) = e1 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7027), (7054), (function-axioms) are % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #775. % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (7055) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (168), (7011), (7042), (7055), % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | #110. % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (7056) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7056) gives: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (7057) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (7057), % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | #108. % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (7058) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7058) gives: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | (7059) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.97/19.33 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7059) implies: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7060) op(e2, e0) = e2 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7037), (7060), (function-axioms) are % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7061) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7061) gives: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7062) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7062) implies: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7063) ~ (all_56_11 = e2) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7064) op(e2, e2) = all_56_11 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7048), (7063), (7064), (function-axioms) are % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #531. % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7065) op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7065) implies: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7066) op(e0, e0) = all_56_31 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7067) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (39), (45), (100), (118), (157), (160), % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (163), (164), (165), (167), (189), (190), (204), % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (218), (226), (245), (246), (278), (295), (336), % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (338), (364), (369), (370), (371), (7009), (7016), % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7018), (7020), (7047), (7066), (7067), % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | #744. % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.34 | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | (7068) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (7000), (7037), (7068), % 133.97/19.34 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.34 | | | | | | | | | | | | | | | | | | | #625. % 133.97/19.34 | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | End of split % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | (7069) all_57_10 = e2 & op(e2, e0) = e2 % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | ALPHA: (7069) implies: % 133.97/19.34 | | | | | | | | | | | | | | | | | | (7070) op(e2, e0) = e2 % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7037), (7070), (function-axioms) are % 133.97/19.34 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | End of split % 133.97/19.34 | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | Case 2: % 133.97/19.34 | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | (7071) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 133.97/19.34 | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 133.97/19.34 | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | BETA: splitting (7071) gives: % 133.97/19.34 | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | (7072) all_57_11 = e2 & op(e1, e0) = e2 % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (7002), (7072), (function-axioms) are % 133.97/19.34 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #514. % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | (7073) all_57_15 = e2 & op(e0, e0) = e2 % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (7018), (7073), (function-axioms) are % 133.97/19.34 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #107. % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | End of split % 133.97/19.34 | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | End of split % 133.97/19.34 | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | Case 2: % 133.97/19.34 | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | (7074) all_54_5 = e1 | all_54_5 = e0 % 133.97/19.34 | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | REF_CLOSE: (267), (7008), (7029), (7074) are inconsistent by % 133.97/19.34 | | | | | | | | | | | | | | | | sub-proof #624. % 133.97/19.34 | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | End of split % 133.97/19.34 | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | End of split % 133.97/19.34 | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | Case 2: % 133.97/19.34 | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | (7075) all_30_2 = e0 % 133.97/19.34 | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | COMBINE_EQS: (309), (7075) imply: % 133.97/19.34 | | | | | | | | | | | | | | (7076) all_8_2 = e0 % 133.97/19.34 | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | SIMP: (7076) implies: % 133.97/19.34 | | | | | | | | | | | | | | (7077) all_8_2 = e0 % 133.97/19.34 | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | REDUCE: (347), (7077) imply: % 133.97/19.34 | | | | | | | | | | | | | | (7078) ~ (all_52_1 = e0) % 133.97/19.34 | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | REDUCE: (356), (7077) imply: % 133.97/19.34 | | | | | | | | | | | | | | (7079) ~ (all_52_9 = e0) % 133.97/19.34 | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | REDUCE: (42), (7077) imply: % 133.97/19.34 | | | | | | | | | | | | | | (7080) op(e2, e2) = e0 % 133.97/19.34 | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | BETA: splitting (7014) gives: % 133.97/19.34 | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | Case 1: % 133.97/19.34 | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | (7081) ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 & % 133.97/19.34 | | | | | | | | | | | | | | | $i(all_18_0) % 133.97/19.34 | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | ALPHA: (7081) implies: % 133.97/19.34 | | | | | | | | | | | | | | | (7082) ~ (all_18_0 = e3) % 133.97/19.34 | | | | | | | | | | | | | | | (7083) op(e2, e1) = all_18_0 % 133.97/19.34 | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, % 133.97/19.34 | | | | | | | | | | | | | | | all_18_0, e1, e2, simplifying with (165), (7083) % 133.97/19.34 | | | | | | | | | | | | | | | gives: % 133.97/19.34 | | | | | | | | | | | | | | | (7084) all_52_9 = all_18_0 % 133.97/19.34 | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | COMBINE_EQS: (260), (7084) imply: % 133.97/19.34 | | | | | | | | | | | | | | | (7085) all_54_6 = all_18_0 % 133.97/19.34 | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | REDUCE: (146), (7084) imply: % 133.97/19.34 | | | | | | | | | | | | | | | (7086) ~ (all_52_1 = all_18_0) % 133.97/19.34 | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | REDUCE: (123), (7084) imply: % 133.97/19.34 | | | | | | | | | | | | | | | (7087) ~ (all_52_8 = all_18_0) % 133.97/19.34 | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | REDUCE: (7000), (7084) imply: % 133.97/19.34 | | | | | | | | | | | | | | | (7088) ~ (all_18_0 = e2) % 133.97/19.34 | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | REDUCE: (7079), (7084) imply: % 133.97/19.34 | | | | | | | | | | | | | | | (7089) ~ (all_18_0 = e0) % 133.97/19.34 | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 133.97/19.34 | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | Case 1: % 133.97/19.34 | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | (7090) all_54_6 = e3 % 133.97/19.34 | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | COMBINE_EQS: (7085), (7090) imply: % 133.97/19.34 | | | | | | | | | | | | | | | | (7091) all_18_0 = e3 % 133.97/19.34 | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | REDUCE: (7082), (7091) imply: % 133.97/19.34 | | | | | | | | | | | | | | | | (7092) $false % 133.97/19.34 | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | CLOSE: (7092) is inconsistent. % 133.97/19.34 | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | Case 2: % 133.97/19.34 | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | (7093) ~ (all_54_6 = e3) % 133.97/19.34 | | | | | | | | | | | | | | | | (7094) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 133.97/19.34 | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | BETA: splitting (7094) gives: % 133.97/19.34 | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | Case 1: % 133.97/19.34 | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | (7095) all_54_6 = e2 % 133.97/19.34 | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | COMBINE_EQS: (7085), (7095) imply: % 133.97/19.34 | | | | | | | | | | | | | | | | | (7096) all_18_0 = e2 % 133.97/19.34 | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | REDUCE: (7088), (7096) imply: % 133.97/19.34 | | | | | | | | | | | | | | | | | (7097) $false % 133.97/19.34 | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | CLOSE: (7097) is inconsistent. % 133.97/19.34 | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | Case 2: % 133.97/19.34 | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | (7098) all_54_6 = e1 | all_54_6 = e0 % 133.97/19.34 | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | BETA: splitting (7098) gives: % 133.97/19.34 | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | (7099) all_54_6 = e1 % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7085), (7099) imply: % 133.97/19.34 | | | | | | | | | | | | | | | | | | (7100) all_18_0 = e1 % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | REDUCE: (7086), (7100) imply: % 133.97/19.34 | | | | | | | | | | | | | | | | | | (7101) ~ (all_52_1 = e1) % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | REDUCE: (7087), (7100) imply: % 133.97/19.34 | | | | | | | | | | | | | | | | | | (7102) ~ (all_52_8 = e1) % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | REDUCE: (7082), (7100) imply: % 133.97/19.34 | | | | | | | | | | | | | | | | | | (7103) ~ (e3 = e1) % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | REDUCE: (7083), (7100) imply: % 133.97/19.34 | | | | | | | | | | | | | | | | | | (7104) op(e2, e1) = e1 % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 133.97/19.34 | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | (7105) all_54_4 = e3 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7105) imply: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | (7106) all_52_1 = e3 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | REDUCE: (7023), (7106) imply: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | (7107) $false % 133.97/19.34 | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | CLOSE: (7107) is inconsistent. % 133.97/19.34 | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | (7108) ~ (all_54_4 = e3) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | (7109) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | BETA: splitting (7109) gives: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | (7110) all_54_4 = e2 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7110) imply: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | (7111) all_52_1 = e2 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (7111) imply: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | (7112) ~ (all_52_13 = e2) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | SIMP: (7112) implies: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | (7113) ~ (all_52_13 = e2) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | REDUCE: (7023), (7111) imply: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | (7114) ~ (e3 = e2) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (7115) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7115) gives: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (7116) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (7027), (7116), (function-axioms) are % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623. % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (7117) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7117) gives: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7118) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7118) implies: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7119) op(e3, e0) = e3 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (7026), (7119), (function-axioms) are % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #733. % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7120) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7120) implies: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7121) op(e2, e2) = e3 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (39), (45), (165), (168), (169), (202), % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (204), (206), (270), (278), (344), (346), (361), % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (371), (6999), (7000), (7007), (7009), (7016), % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7020), (7102), (7104), (7121), (function-axioms) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #104. % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (7122) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7122) gives: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (7123) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (7123), % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | #108. % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (7124) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7124) gives: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7125) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7125) implies: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7126) op(e2, e0) = e2 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7113), (7126), (function-axioms) are % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (7127) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7127) gives: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7128) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7128) implies: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7129) ~ (all_56_19 = e1) % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7130) op(e2, e1) = all_56_19 % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7104), (7129), (7130), (function-axioms) are % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106. % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | (7131) op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.34 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7131) implies: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (7132) op(e0, e0) = all_56_31 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (7133) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (39), (169), (202), (270), (361), (371), % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (6999), (7025), (7027), (7102), (7104), (7132), % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (7133), (function-axioms) are inconsistent by % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #105. % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | (7134) all_54_4 = e1 | all_54_4 = e0 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7078), (7101), (7134) are inconsistent by % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | sub-proof #153. % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.35 | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | End of split % 133.97/19.35 | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.35 | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | (7135) all_54_6 = e0 % 133.97/19.35 | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7085), (7135) imply: % 133.97/19.35 | | | | | | | | | | | | | | | | | | (7136) all_18_0 = e0 % 133.97/19.35 | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | REDUCE: (7089), (7136) imply: % 133.97/19.35 | | | | | | | | | | | | | | | | | | (7137) $false % 133.97/19.35 | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | CLOSE: (7137) is inconsistent. % 133.97/19.35 | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | End of split % 133.97/19.35 | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | End of split % 133.97/19.35 | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | End of split % 133.97/19.35 | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | Case 2: % 133.97/19.35 | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | (7138) ~ (all_18_1 = e0) & op(e2, e2) = all_18_1 & % 133.97/19.35 | | | | | | | | | | | | | | | $i(all_18_1) % 133.97/19.35 | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | REF_CLOSE: (7080), (7138), (function-axioms) are inconsistent % 133.97/19.35 | | | | | | | | | | | | | | | by sub-proof #103. % 133.97/19.35 | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | End of split % 133.97/19.35 | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | End of split % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | Case 2: % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | (7139) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | REF_CLOSE: (278), (7009), (7016), (7020), (7139) are % 133.97/19.35 | | | | | | | | | | | | | inconsistent by sub-proof #777. % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | End of split % 133.97/19.35 | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | Case 2: % 133.97/19.35 | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | (7140) all_32_2 = e1 % 133.97/19.35 | | | | | | | | | | | | (7141) ( ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 & % 133.97/19.35 | | | | | | | | | | | | $i(all_32_0)) | ( ~ (all_32_1 = e2) & op(e1, e1) % 133.97/19.35 | | | | | | | | | | | | = all_32_1 & $i(all_32_1)) % 133.97/19.35 | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | COMBINE_EQS: (312), (7140) imply: % 133.97/19.35 | | | | | | | | | | | | (7142) all_10_2 = e1 % 133.97/19.35 | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | REDUCE: (336), (7142) imply: % 133.97/19.35 | | | | | | | | | | | | (7143) ~ (all_52_1 = e1) % 133.97/19.35 | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | REDUCE: (338), (7142) imply: % 133.97/19.35 | | | | | | | | | | | | (7144) ~ (all_52_2 = e1) % 133.97/19.35 | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | REDUCE: (340), (7142) imply: % 133.97/19.35 | | | | | | | | | | | | (7145) ~ (all_52_3 = e1) % 133.97/19.35 | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | REDUCE: (45), (7142) imply: % 133.97/19.35 | | | | | | | | | | | | (7146) op(e3, e3) = e1 % 133.97/19.35 | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | BETA: splitting (7141) gives: % 133.97/19.35 | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | (7147) ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 & % 133.97/19.35 | | | | | | | | | | | | | $i(all_32_0) % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | ALPHA: (7147) implies: % 133.97/19.35 | | | | | | | | | | | | | (7148) ~ (all_32_0 = e0) % 133.97/19.35 | | | | | | | | | | | | | (7149) op(e1, e3) = all_32_0 % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 133.97/19.35 | | | | | | | | | | | | | all_32_0, e3, e1, simplifying with (163), (7149) % 133.97/19.35 | | | | | | | | | | | | | gives: % 133.97/19.35 | | | | | | | | | | | | | (7150) all_52_2 = all_32_0 % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | COMBINE_EQS: (258), (7150) imply: % 133.97/19.35 | | | | | | | | | | | | | (7151) all_54_8 = all_32_0 % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | REDUCE: (149), (7150) imply: % 133.97/19.35 | | | | | | | | | | | | | (7152) ~ (all_52_1 = all_32_0) % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | REDUCE: (144), (7150) imply: % 133.97/19.35 | | | | | | | | | | | | | (7153) ~ (all_52_3 = all_32_0) % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | SIMP: (7153) implies: % 133.97/19.35 | | | | | | | | | | | | | (7154) ~ (all_52_3 = all_32_0) % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | REDUCE: (143), (7150) imply: % 133.97/19.35 | | | | | | | | | | | | | (7155) ~ (all_52_6 = all_32_0) % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | SIMP: (7155) implies: % 133.97/19.35 | | | | | | | | | | | | | (7156) ~ (all_52_6 = all_32_0) % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | REDUCE: (141), (7150) imply: % 133.97/19.35 | | | | | | | | | | | | | (7157) ~ (all_52_14 = all_32_0) % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | SIMP: (7157) implies: % 133.97/19.35 | | | | | | | | | | | | | (7158) ~ (all_52_14 = all_32_0) % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | REDUCE: (6997), (7150) imply: % 133.97/19.35 | | | | | | | | | | | | | (7159) ~ (all_32_0 = e2) % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | REDUCE: (7144), (7150) imply: % 133.97/19.35 | | | | | | | | | | | | | (7160) ~ (all_32_0 = e1) % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | BETA: splitting (196) gives: % 133.97/19.35 | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | (7161) all_54_8 = e3 % 133.97/19.35 | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | COMBINE_EQS: (7151), (7161) imply: % 133.97/19.35 | | | | | | | | | | | | | | (7162) all_32_0 = e3 % 133.97/19.35 | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | REDUCE: (7152), (7162) imply: % 133.97/19.35 | | | | | | | | | | | | | | (7163) ~ (all_52_1 = e3) % 133.97/19.35 | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | REDUCE: (7154), (7162) imply: % 133.97/19.35 | | | | | | | | | | | | | | (7164) ~ (all_52_3 = e3) % 133.97/19.35 | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | REDUCE: (7156), (7162) imply: % 133.97/19.35 | | | | | | | | | | | | | | (7165) ~ (all_52_6 = e3) % 133.97/19.35 | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | REDUCE: (7158), (7162) imply: % 133.97/19.35 | | | | | | | | | | | | | | (7166) ~ (all_52_14 = e3) % 133.97/19.35 | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | BETA: splitting (218) gives: % 133.97/19.35 | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | (7167) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 133.97/19.35 | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 133.97/19.35 | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | BETA: splitting (7167) gives: % 133.97/19.35 | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | (7168) all_57_6 = e3 & op(e1, e3) = e3 % 133.97/19.35 | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | ALPHA: (7168) implies: % 133.97/19.35 | | | | | | | | | | | | | | | | (7169) all_57_6 = e3 % 133.97/19.35 | | | | | | | | | | | | | | | | (7170) op(e1, e3) = e3 % 133.97/19.35 | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | BETA: splitting (76) gives: % 133.97/19.35 | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | (7171) ~ (all_30_2 = e0) % 133.97/19.35 | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | REDUCE: (309), (7171) imply: % 133.97/19.35 | | | | | | | | | | | | | | | | | (7172) ~ (all_8_2 = e0) % 133.97/19.35 | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | BETA: splitting (199) gives: % 133.97/19.35 | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | (7173) all_54_5 = e3 % 133.97/19.35 | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7173) imply: % 133.97/19.35 | | | | | | | | | | | | | | | | | | (7174) all_8_2 = e3 % 133.97/19.35 | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | REDUCE: (7011), (7174) imply: % 133.97/19.35 | | | | | | | | | | | | | | | | | | (7175) $false % 133.97/19.35 | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | CLOSE: (7175) is inconsistent. % 133.97/19.35 | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.35 | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | (7176) ~ (all_54_5 = e3) % 133.97/19.35 | | | | | | | | | | | | | | | | | | (7177) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 133.97/19.35 | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | BETA: splitting (7177) gives: % 133.97/19.35 | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | (7178) all_54_5 = e2 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7178) imply: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | (7179) all_8_2 = e2 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | REDUCE: (347), (7179) imply: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | (7180) ~ (all_52_1 = e2) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | REDUCE: (350), (7179) imply: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | (7181) ~ (all_52_4 = e2) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | REDUCE: (354), (7179) imply: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | (7182) ~ (all_52_7 = e2) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | REDUCE: (358), (7179) imply: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | (7183) ~ (all_52_13 = e2) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | REDUCE: (7011), (7179) imply: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | (7184) ~ (e3 = e2) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | (7185) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7185) gives: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | (7186) all_57_9 = e2 & op(e3, e0) = e2 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7186) implies: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | (7187) op(e3, e0) = e2 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | (7188) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7188) gives: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | (7189) all_57_1 = e2 & op(e3, e2) = e2 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (7181), (7189), (function-axioms) are % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #396. % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | (7190) all_57_3 = e2 & op(e2, e2) = e2 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7190) implies: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | (7191) all_57_3 = e2 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | (7192) op(e2, e2) = e2 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (7193) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7193) gives: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | (7194) all_57_12 = e2 & op(e0, e3) = e2 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7194) implies: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | (7195) all_57_12 = e2 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (7196) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7196) gives: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7197) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237), % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7170), (7195), (7197), (function-axioms) are % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #102. % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7198) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (168), (7011), (7187), (7198), % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | #110. % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (7199) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7199) gives: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7200) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (7200), % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | #108. % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7201) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7201) gives: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7202) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7202) implies: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7203) op(e2, e0) = e2 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7183), (7203), (function-axioms) are % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7204) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7204) gives: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7205) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7205) implies: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7206) ~ (all_56_11 = e2) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7207) op(e2, e2) = all_56_11 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7192), (7206), (7207), (function-axioms) are % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #531. % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7208) op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7208) implies: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7209) op(e0, e0) = all_56_31 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7210) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7211) all_54_4 = e3 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7211) imply: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7212) all_52_1 = e3 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7163), (7212) imply: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7213) $false % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7213) is inconsistent. % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7214) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7214) gives: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7215) all_54_4 = e2 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7215) imply: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7216) all_52_1 = e2 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7180), (7216) imply: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7217) $false % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7217) is inconsistent. % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7218) ~ (all_54_4 = e2) % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7219) all_54_4 = e1 | all_54_4 = e0 % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7219) gives: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7220) all_54_4 = e1 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7220) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7221) all_52_1 = e1 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7143), (7221) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7222) $false % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7222) is inconsistent. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7223) all_54_4 = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7223) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7224) all_52_1 = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (7224) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7225) ~ (all_52_3 = e0) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7225) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7226) ~ (all_52_3 = e0) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7180), (7224) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7227) ~ (e2 = e0) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (159), (164), (165), (167), (225), % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371), (7000), (7007), (7180), (7183), (7191), % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7192), (7209), (7210), (7226), (function-axioms) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #101. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | (7228) all_57_13 = e2 & op(e0, e2) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (7182), (7228), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #100. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | (7229) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7229) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | (7230) all_57_14 = e2 & op(e0, e1) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7001), (7230), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | (7231) all_57_15 = e2 & op(e0, e0) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (7018), (7231), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #107. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7232) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7232) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7233) all_57_7 = e2 & op(e1, e2) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (6998), (7233), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7234) all_57_13 = e2 & op(e0, e2) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (7182), (7234), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #100. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7235) all_57_10 = e2 & op(e2, e0) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7235) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7236) op(e2, e0) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7183), (7236), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | (7237) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7237) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7238) all_57_11 = e2 & op(e1, e0) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7238) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7239) all_57_11 = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (215), (216), (7006), % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7169), (7239) are inconsistent by sub-proof #572. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7240) all_57_15 = e2 & op(e0, e0) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (7018), (7240), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #107. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | (7241) all_54_5 = e1 | all_54_5 = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (7008), (7172), (7241) are inconsistent by % 133.97/19.36 | | | | | | | | | | | | | | | | | | | sub-proof #624. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | (7242) all_30_2 = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (7242) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | (7243) all_8_2 = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | SIMP: (7243) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | (7244) all_8_2 = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | REDUCE: (347), (7244) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | (7245) ~ (all_52_1 = e0) % 133.97/19.36 | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | REDUCE: (350), (7244) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | (7246) ~ (all_52_4 = e0) % 133.97/19.36 | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | REDUCE: (356), (7244) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | (7247) ~ (all_52_9 = e0) % 133.97/19.36 | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | REDUCE: (42), (7244) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | (7248) op(e2, e2) = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | (7249) all_54_4 = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7249) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | (7250) all_52_1 = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | REDUCE: (7163), (7250) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | (7251) $false % 133.97/19.36 | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | CLOSE: (7251) is inconsistent. % 133.97/19.36 | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | (7252) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | BETA: splitting (7252) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | (7253) all_54_4 = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7253) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | (7254) all_52_1 = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | REDUCE: (148), (7254) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | (7255) ~ (all_52_3 = e2) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | SIMP: (7255) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | (7256) ~ (all_52_3 = e2) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | REDUCE: (145), (7254) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | (7257) ~ (all_52_13 = e2) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | SIMP: (7257) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | (7258) ~ (all_52_13 = e2) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | (7259) all_54_12 = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (7164), (7259) are inconsistent by % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | sub-proof #424. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | (7260) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7260) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7261) all_54_12 = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (7256), (7261) are inconsistent by % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | sub-proof #423. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7262) ~ (all_54_12 = e2) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | (7263) all_54_12 = e1 | all_54_12 = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7263) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7264) all_54_12 = e1 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (7145), (7264) are inconsistent by % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | sub-proof #99. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7265) all_54_12 = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (7265) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7266) all_52_3 = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | SIMP: (7266) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7267) all_52_3 = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (7267) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7268) ~ (all_4_2 = e0) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | SIMP: (7268) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7269) ~ (all_4_2 = e0) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7256), (7267) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7270) ~ (e2 = e0) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7145), (7267) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | (7271) ~ (e1 = e0) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7272) all_54_15 = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (7272) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7273) all_4_2 = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7273) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7274) all_4_2 = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (7274) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7275) all_34_2 = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (7274) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7276) ~ (all_52_7 = e3) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (7274) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7277) op(e0, e0) = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | (7278) ~ (all_34_2 = e3) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7275), (7278) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | (7279) $false % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7279) is inconsistent. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | (7280) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | = all_34_1 & $i(all_34_1)) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | (7281) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7281) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (7282) all_57_4 = e0 & op(e3, e1) = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7282) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (7283) all_57_4 = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7284) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7284) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7285) all_57_1 = e3 & op(e3, e2) = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7285) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7286) all_57_1 = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (236), (7146), (7280), (7283), % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7286), (function-axioms) are inconsistent by % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #550. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7287) all_57_3 = e3 & op(e2, e2) = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7287) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7288) op(e2, e2) = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7248), (7288), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7289) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (7165), (7276), (7289), % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | #555. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (7290) all_57_5 = e0 & op(e2, e1) = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7247), (7290), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #455. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | (7291) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7291) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (7292) all_57_8 = e0 & op(e1, e1) = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7292) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (7293) op(e1, e1) = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7007), (7293), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #98. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (7294) all_57_14 = e0 & op(e0, e1) = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7294) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (7295) all_57_14 = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7296) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7296) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7297) all_57_12 = e1 & op(e0, e3) = e1 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7297) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7298) all_57_12 = e1 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (235), (237), % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7146), (7298), (function-axioms) are inconsistent % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #583. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7299) all_57_13 = e1 & op(e0, e2) = e1 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7299) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7300) all_57_13 = e1 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7301) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7301) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7302) all_57_9 = e2 & op(e3, e0) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7302) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7303) all_57_9 = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7304) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7304) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7305) all_57_12 = e2 & op(e0, e3) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7256), (7305), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #97. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7306) all_57_13 = e2 & op(e0, e2) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7306) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7307) all_57_13 = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7300), (7307) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7308) e2 = e1 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7308) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7309) e2 = e1 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7303), (7309) imply: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7310) all_57_9 = e1 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236), % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (7146), (7246), (7310), (function-axioms) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #686. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7311) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7311) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7312) all_57_14 = e2 & op(e0, e1) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7001), (7312), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7313) all_57_15 = e2 & op(e0, e0) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7313) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7314) op(e0, e0) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7277), (7314), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7315) all_57_10 = e2 & op(e2, e0) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7315) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7316) op(e2, e0) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7258), (7316), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7317) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7317) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7318) all_57_11 = e2 & op(e1, e0) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7318) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7319) all_57_11 = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (215), (216), (7006), % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7169), (7319) are inconsistent by sub-proof #572. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7320) all_57_15 = e2 & op(e0, e0) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7320) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7321) op(e0, e0) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7277), (7321), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7322) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7322) gives: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7323) all_57_14 = e1 & op(e0, e1) = e1 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7323) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7324) all_57_14 = e1 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7295), (7324) are inconsistent by sub-proof % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #221. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7325) all_57_15 = e1 & op(e0, e0) = e1 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7325) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7326) op(e0, e0) = e1 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7277), (7326), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | (7327) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (7018), (7269), (7327) are % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #746. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | (7328) all_54_4 = e1 | all_54_4 = e0 % 133.97/19.36 | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7143), (7245), (7328) are inconsistent by % 133.97/19.36 | | | | | | | | | | | | | | | | | | | sub-proof #153. % 133.97/19.36 | | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | (7329) all_57_7 = e3 & op(e1, e2) = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | ALPHA: (7329) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | (7330) op(e1, e2) = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | REF_CLOSE: (162), (7165), (7330), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | inconsistent by sub-proof #654. % 133.97/19.36 | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | (7331) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 133.97/19.36 | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 133.97/19.36 | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | BETA: splitting (7331) gives: % 133.97/19.36 | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | (7332) all_57_8 = e3 & op(e1, e1) = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | ALPHA: (7332) implies: % 133.97/19.36 | | | | | | | | | | | | | | | | (7333) op(e1, e1) = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7007), (7333), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | inconsistent by sub-proof #109. % 133.97/19.36 | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | (7334) all_57_11 = e3 & op(e1, e0) = e3 % 133.97/19.36 | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | | REF_CLOSE: (160), (7166), (7334), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | | inconsistent by sub-proof #750. % 133.97/19.36 | | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | (7335) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 133.97/19.36 | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | REF_CLOSE: (7148), (7151), (7159), (7160), (7335) are % 133.97/19.36 | | | | | | | | | | | | | | inconsistent by sub-proof #96. % 133.97/19.36 | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | (7336) ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 & % 133.97/19.36 | | | | | | | | | | | | | $i(all_32_1) % 133.97/19.36 | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | REF_CLOSE: (7007), (7336), (function-axioms) are inconsistent % 133.97/19.36 | | | | | | | | | | | | | by sub-proof #95. % 133.97/19.36 | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | End of split % 133.97/19.36 | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | (7337) all_20_2 = e2 % 133.97/19.36 | | | | | | | | | | | (7338) ( ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 & % 133.97/19.36 | | | | | | | | | | | $i(all_20_0)) | ( ~ (all_20_1 = e1) & op(e2, e2) % 133.97/19.36 | | | | | | | | | | | = all_20_1 & $i(all_20_1)) % 133.97/19.36 | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | COMBINE_EQS: (318), (7337) imply: % 133.97/19.36 | | | | | | | | | | | (7339) all_4_2 = e2 % 133.97/19.36 | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | SIMP: (7339) implies: % 133.97/19.36 | | | | | | | | | | | (7340) all_4_2 = e2 % 133.97/19.36 | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | REDUCE: (349), (7340) imply: % 133.97/19.36 | | | | | | | | | | | (7341) ~ (all_52_3 = e2) % 133.97/19.36 | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | REDUCE: (368), (7340) imply: % 133.97/19.36 | | | | | | | | | | | (7342) ~ (all_52_12 = e2) % 133.97/19.36 | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | REDUCE: (36), (7340) imply: % 133.97/19.36 | | | | | | | | | | | (7343) op(e0, e0) = e2 % 133.97/19.36 | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | BETA: splitting (235) gives: % 133.97/19.36 | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | (7344) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 133.97/19.36 | | | | | | | | | | | | & op(e2, e3) = e2) % 133.97/19.36 | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | BETA: splitting (7344) gives: % 133.97/19.36 | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | (7345) all_57_0 = e2 & op(e3, e3) = e2 % 133.97/19.36 | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | ALPHA: (7345) implies: % 133.97/19.36 | | | | | | | | | | | | | (7346) op(e3, e3) = e2 % 133.97/19.36 | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | REF_CLOSE: (45), (7016), (7346), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | inconsistent by sub-proof #536. % 133.97/19.36 | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | (7347) all_57_2 = e2 & op(e2, e3) = e2 % 133.97/19.36 | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | ALPHA: (7347) implies: % 133.97/19.36 | | | | | | | | | | | | | (7348) all_57_2 = e2 % 133.97/19.36 | | | | | | | | | | | | | (7349) op(e2, e3) = e2 % 133.97/19.36 | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | BETA: splitting (236) gives: % 133.97/19.36 | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | (7350) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 133.97/19.36 | | | | | | | | | | | | | | & op(e3, e2) = e2) % 133.97/19.36 | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | BETA: splitting (7350) gives: % 133.97/19.36 | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | Case 1: % 133.97/19.36 | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | (7351) all_57_0 = e2 & op(e3, e3) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | ALPHA: (7351) implies: % 133.97/19.36 | | | | | | | | | | | | | | | (7352) op(e3, e3) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | REF_CLOSE: (45), (7016), (7352), (function-axioms) are % 133.97/19.36 | | | | | | | | | | | | | | | inconsistent by sub-proof #536. % 133.97/19.36 | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | Case 2: % 133.97/19.36 | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | (7353) all_57_1 = e2 & op(e3, e2) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | ALPHA: (7353) implies: % 133.97/19.36 | | | | | | | | | | | | | | | (7354) op(e3, e2) = e2 % 133.97/19.36 | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2, % 133.97/19.36 | | | | | | | | | | | | | | | e3, e2, simplifying with (167), (7349) gives: % 133.97/19.36 | | | | | | | | | | | | | | | (7355) all_52_1 = e2 % 133.97/19.36 | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2, % 133.97/19.36 | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (7354) gives: % 133.97/19.36 | | | | | | | | | | | | | | | (7356) all_52_4 = e2 % 133.97/19.36 | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | REDUCE: (146), (7355) imply: % 133.97/19.36 | | | | | | | | | | | | | | | (7357) ~ (all_52_9 = e2) % 133.97/19.36 | | | | | | | | | | | | | | | % 133.97/19.36 | | | | | | | | | | | | | | | REDUCE: (134), (7356) imply: % 133.97/19.37 | | | | | | | | | | | | | | | (7358) ~ (all_52_8 = e2) % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | REDUCE: (342), (7356) imply: % 133.97/19.37 | | | | | | | | | | | | | | | (7359) ~ (all_10_2 = e2) % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | REDUCE: (350), (7356) imply: % 133.97/19.37 | | | | | | | | | | | | | | | (7360) ~ (all_8_2 = e2) % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | SIMP: (7360) implies: % 133.97/19.37 | | | | | | | | | | | | | | | (7361) ~ (all_8_2 = e2) % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | BETA: splitting (199) gives: % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | (7362) all_54_5 = e3 % 133.97/19.37 | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7362) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | (7363) all_8_2 = e3 % 133.97/19.37 | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | REDUCE: (7011), (7363) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | (7364) $false % 133.97/19.37 | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | CLOSE: (7364) is inconsistent. % 133.97/19.37 | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | (7365) ~ (all_54_5 = e3) % 133.97/19.37 | | | | | | | | | | | | | | | | (7366) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 133.97/19.37 | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | BETA: splitting (7366) gives: % 133.97/19.37 | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | (7367) all_54_5 = e2 % 133.97/19.37 | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7367) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | (7368) all_8_2 = e2 % 133.97/19.37 | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | REDUCE: (7361), (7368) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | (7369) $false % 133.97/19.37 | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | CLOSE: (7369) is inconsistent. % 133.97/19.37 | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | (7370) ~ (all_54_5 = e2) % 133.97/19.37 | | | | | | | | | | | | | | | | | (7371) all_54_5 = e1 | all_54_5 = e0 % 133.97/19.37 | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | BETA: splitting (7371) gives: % 133.97/19.37 | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7372) all_54_5 = e1 % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7372) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7373) all_8_2 = e1 % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (7008), (7373) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7374) $false % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | CLOSE: (7374) is inconsistent. % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7375) all_54_5 = e0 % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7375) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7376) all_8_2 = e0 % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (356), (7376) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7377) ~ (all_52_9 = e0) % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (7011), (7376) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7378) ~ (e3 = e0) % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (7361), (7376) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7379) ~ (e2 = e0) % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (7008), (7376) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7380) ~ (e1 = e0) % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (42), (7376) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7381) op(e2, e2) = e0 % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (79), (117), % 133.97/19.37 | | | | | | | | | | | | | | | | | | (123), (164), (165), (169), (198), (206), (224), % 133.97/19.37 | | | | | | | | | | | | | | | | | | (226), (231), (237), (260), (312), (6999), (7000), % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7007), (7009), (7014), (7016), (7338), (7343), % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7348), (7349), (7354), (7377), (7381), % 133.97/19.37 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.37 | | | | | | | | | | | | | | | | | | #90. % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | End of split % 133.97/19.37 | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | End of split % 133.97/19.37 | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | End of split % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | End of split % 133.97/19.37 | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | (7382) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 133.97/19.37 | | | | | | | | | | | | | | & op(e3, e0) = e2) % 133.97/19.37 | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | BETA: splitting (7382) gives: % 133.97/19.37 | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | (7383) all_57_4 = e2 & op(e3, e1) = e2 % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | REF_CLOSE: (169), (6999), (7383), (function-axioms) are % 133.97/19.37 | | | | | | | | | | | | | | | inconsistent by sub-proof #442. % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | (7384) all_57_9 = e2 & op(e3, e0) = e2 % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | REF_CLOSE: (168), (7342), (7384), (function-axioms) are % 133.97/19.37 | | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | End of split % 133.97/19.37 | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | End of split % 133.97/19.37 | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | End of split % 133.97/19.37 | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | (7385) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 133.97/19.37 | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 133.97/19.37 | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | BETA: splitting (7385) gives: % 133.97/19.37 | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | (7386) all_57_6 = e2 & op(e1, e3) = e2 % 133.97/19.37 | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | REF_CLOSE: (163), (6997), (7386), (function-axioms) are % 133.97/19.37 | | | | | | | | | | | | | inconsistent by sub-proof #341. % 133.97/19.37 | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | (7387) all_57_12 = e2 & op(e0, e3) = e2 % 133.97/19.37 | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | REF_CLOSE: (159), (7341), (7387), (function-axioms) are % 133.97/19.37 | | | | | | | | | | | | | inconsistent by sub-proof #97. % 133.97/19.37 | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | End of split % 133.97/19.37 | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | End of split % 133.97/19.37 | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | End of split % 133.97/19.37 | | | | | | | | | | % 133.97/19.37 | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | (7388) all_16_2 = e2 % 133.97/19.37 | | | | | | | | | | (7389) ( ~ (all_16_0 = e1) & op(e2, e3) = all_16_0 & % 133.97/19.37 | | | | | | | | | | $i(all_16_0)) | ( ~ (all_16_1 = e0) & op(e2, e2) % 133.97/19.37 | | | | | | | | | | = all_16_1 & $i(all_16_1)) % 133.97/19.37 | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | COMBINE_EQS: (327), (7388) imply: % 133.97/19.37 | | | | | | | | | | (7390) all_10_2 = e2 % 133.97/19.37 | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | SIMP: (7390) implies: % 133.97/19.37 | | | | | | | | | | (7391) all_10_2 = e2 % 133.97/19.37 | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | REDUCE: (336), (7391) imply: % 133.97/19.37 | | | | | | | | | | (7392) ~ (all_52_1 = e2) % 133.97/19.37 | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | REDUCE: (346), (7391) imply: % 133.97/19.37 | | | | | | | | | | (7393) ~ (all_52_12 = e2) % 133.97/19.37 | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | REDUCE: (45), (7391) imply: % 133.97/19.37 | | | | | | | | | | (7394) op(e3, e3) = e2 % 133.97/19.37 | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | BETA: splitting (61) gives: % 133.97/19.37 | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | (7395) ~ (all_20_2 = e2) % 133.97/19.37 | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | REDUCE: (318), (7395) imply: % 133.97/19.37 | | | | | | | | | | | (7396) ~ (all_4_2 = e2) % 133.97/19.37 | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | BETA: splitting (213) gives: % 133.97/19.37 | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | (7397) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 133.97/19.37 | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 133.97/19.37 | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | BETA: splitting (7397) gives: % 133.97/19.37 | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | (7398) all_57_9 = e2 & op(e3, e0) = e2 % 133.97/19.37 | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | REF_CLOSE: (168), (7393), (7398), (function-axioms) are % 133.97/19.37 | | | | | | | | | | | | | inconsistent by sub-proof #460. % 133.97/19.37 | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | (7399) all_57_10 = e2 & op(e2, e0) = e2 % 133.97/19.37 | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | ALPHA: (7399) implies: % 133.97/19.37 | | | | | | | | | | | | | (7400) all_57_10 = e2 % 133.97/19.37 | | | | | | | | | | | | | (7401) op(e2, e0) = e2 % 133.97/19.37 | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | BETA: splitting (210) gives: % 133.97/19.37 | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | (7402) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 133.97/19.37 | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 133.97/19.37 | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | BETA: splitting (7402) gives: % 133.97/19.37 | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | (7403) all_57_12 = e2 & op(e0, e3) = e2 % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | ALPHA: (7403) implies: % 133.97/19.37 | | | | | | | | | | | | | | | (7404) all_57_12 = e2 % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237), % 133.97/19.37 | | | | | | | | | | | | | | | (7394), (7404), (function-axioms) are inconsistent % 133.97/19.37 | | | | | | | | | | | | | | | by sub-proof #290. % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | (7405) all_57_13 = e2 & op(e0, e2) = e2 % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | ALPHA: (7405) implies: % 133.97/19.37 | | | | | | | | | | | | | | | (7406) all_57_13 = e2 % 133.97/19.37 | | | | | | | | | | | | | | | (7407) op(e0, e2) = e2 % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2, % 133.97/19.37 | | | | | | | | | | | | | | | e2, e0, simplifying with (158), (7407) gives: % 133.97/19.37 | | | | | | | | | | | | | | | (7408) all_52_7 = e2 % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 133.97/19.37 | | | | | | | | | | | | | | | e2, e0, e2, simplifying with (164), (7401) gives: % 133.97/19.37 | | | | | | | | | | | | | | | (7409) all_52_13 = e2 % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | REDUCE: (140), (7408) imply: % 133.97/19.37 | | | | | | | | | | | | | | | (7410) ~ (all_52_3 = e2) % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | REDUCE: (358), (7409) imply: % 133.97/19.37 | | | | | | | | | | | | | | | (7411) ~ (all_8_2 = e2) % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | SIMP: (7411) implies: % 133.97/19.37 | | | | | | | | | | | | | | | (7412) ~ (all_8_2 = e2) % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | REDUCE: (369), (7409) imply: % 133.97/19.37 | | | | | | | | | | | | | | | (7413) ~ (all_4_2 = e2) % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | BETA: splitting (199) gives: % 133.97/19.37 | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | (7414) all_54_5 = e3 % 133.97/19.37 | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7414) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | (7415) all_8_2 = e3 % 133.97/19.37 | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | REDUCE: (7011), (7415) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | (7416) $false % 133.97/19.37 | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | CLOSE: (7416) is inconsistent. % 133.97/19.37 | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | (7417) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 133.97/19.37 | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | BETA: splitting (7417) gives: % 133.97/19.37 | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | (7418) all_54_5 = e2 % 133.97/19.37 | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7418) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | (7419) all_8_2 = e2 % 133.97/19.37 | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | REDUCE: (7412), (7419) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | (7420) $false % 133.97/19.37 | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | CLOSE: (7420) is inconsistent. % 133.97/19.37 | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | (7421) ~ (all_54_5 = e2) % 133.97/19.37 | | | | | | | | | | | | | | | | | (7422) all_54_5 = e1 | all_54_5 = e0 % 133.97/19.37 | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | BETA: splitting (7422) gives: % 133.97/19.37 | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7423) all_54_5 = e1 % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7423) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7424) all_8_2 = e1 % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (7008), (7424) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7425) $false % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | CLOSE: (7425) is inconsistent. % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7426) all_54_5 = e0 % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7426) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7427) all_8_2 = e0 % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (347), (7427) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7428) ~ (all_52_1 = e0) % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (7412), (7427) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7429) ~ (e2 = e0) % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (7008), (7427) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7430) ~ (e1 = e0) % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | REDUCE: (42), (7427) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | (7431) op(e2, e2) = e0 % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | BETA: splitting (7389) gives: % 133.97/19.37 | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7432) ~ (all_16_0 = e1) & op(e2, e3) = all_16_0 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | $i(all_16_0) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | ALPHA: (7432) implies: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7433) ~ (all_16_0 = e1) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7434) op(e2, e3) = all_16_0 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, % 133.97/19.37 | | | | | | | | | | | | | | | | | | | all_16_0, e3, e2, simplifying with (167), (7434) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | gives: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7435) all_52_1 = all_16_0 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7435) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7436) all_54_4 = all_16_0 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | REDUCE: (149), (7435) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7437) ~ (all_52_2 = all_16_0) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | SIMP: (7437) implies: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7438) ~ (all_52_2 = all_16_0) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | REDUCE: (7392), (7435) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7439) ~ (all_16_0 = e2) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | REDUCE: (7428), (7435) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | (7440) ~ (all_16_0 = e0) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | (7441) all_54_4 = e3 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7436), (7441) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | (7442) all_16_0 = e3 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | SIMP: (7442) implies: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | (7443) all_16_0 = e3 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | REDUCE: (7438), (7443) imply: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | (7444) ~ (all_52_2 = e3) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | (7445) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7431), (7433), (7434), (7445), % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | #415. % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | (7446) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7446) gives: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | (7447) all_57_5 = e1 & op(e2, e1) = e1 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7447) implies: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | (7448) all_57_5 = e1 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | (7449) op(e2, e1) = e1 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (7450) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7450) gives: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (7451) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7451) gives: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7452) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7452) implies: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7453) ~ (all_56_19 = e1) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7454) op(e2, e1) = all_56_19 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7449), (7453), (7454), (function-axioms) are % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106. % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7455) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7455) implies: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7456) op(e3, e3) = e1 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7394), (7456), (function-axioms) are % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743. % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (7457) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7457) gives: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7458) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7458) implies: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7459) ~ (all_56_15 = e2) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7460) op(e0, e2) = all_56_15 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7407), (7459), (7460), (function-axioms) are % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609. % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7461) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7461) implies: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | (7462) op(e2, e2) = e3 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7431), (7462), (function-axioms) are % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (7463) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7463) gives: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (7464) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (7464), % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | #108. % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (7465) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.37 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7465) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | (7466) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7466) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | (7467) ~ (all_56_15 = e2) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | (7468) op(e0, e2) = all_56_15 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7407), (7467), (7468), (function-axioms) are % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | (7469) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7469) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (7470) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7470) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (7471) ~ (all_56_19 = e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (7472) op(e2, e1) = all_56_19 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7449), (7471), (7472), (function-axioms) are % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (7473) op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7473) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (7474) op(e0, e0) = all_56_31 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (7475) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7476) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7476) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7477) all_57_2 = e3 & op(e2, e3) = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7477) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7478) all_57_2 = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7479) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7479) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7480) all_57_12 = e1 & op(e0, e3) = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7480) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7481) all_57_12 = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7482) op(e0, e3) = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7483) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (7394), (7428), (7483), % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #89. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7484) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7484) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7485) all_57_6 = e0 & op(e1, e3) = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7485) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7486) op(e1, e3) = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (36), (7474) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7487) all_56_31 = all_4_2 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e1, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (7482) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7488) all_52_3 = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e0, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (7486) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7489) all_52_2 = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7444), (7489) imply: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7490) ~ (e3 = e0) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (7488) imply: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7491) ~ (all_4_2 = e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7410), (7488) imply: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7492) ~ (e2 = e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7475) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7493) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7493) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7494) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7494) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7495) all_56_31 = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7496) ~ (all_56_25 = e0) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7497) op(e3, e0) = all_56_25 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7487), (7495) imply: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7498) all_4_2 = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (7498) imply: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7499) op(e0, e0) = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7500) all_57_15 = e0 & op(e0, e0) = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7500) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7501) op(e0, e0) = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (7474), (7475), (7501), % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #710. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7502) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7502) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7503) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7504) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7504) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7505) all_57_6 = e3 & op(e1, e3) = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7444), (7505), (function-axioms) are % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #761. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7506) all_57_7 = e3 & op(e1, e2) = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7506) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7507) all_57_7 = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7508) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7508) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7509) all_57_4 = e3 & op(e3, e1) = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7509) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7510) op(e3, e1) = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7511) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7511) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7512) all_57_1 = e1 & op(e3, e2) = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7512) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7513) op(e3, e2) = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7514) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7394), (7513), (7514), % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #333. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7515) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7515) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7516) all_57_4 = e0 & op(e3, e1) = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7516) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7517) op(e3, e1) = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (7510), (7517), (function-axioms) are % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #600. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7518) all_57_9 = e0 & op(e3, e0) = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7518) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7519) op(e3, e0) = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7496), (7497), (7519), (function-axioms) are % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #642. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7520) all_57_3 = e1 & op(e2, e2) = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7520) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7521) op(e2, e2) = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7431), (7521), (function-axioms) are % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7522) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7522) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7523) all_57_7 = e1 & op(e1, e2) = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7523) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7524) all_57_7 = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7507), (7524) are inconsistent by sub-proof % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #390. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7525) all_57_13 = e1 & op(e0, e2) = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7406), (7525) are inconsistent by sub-proof % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #248. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7526) all_57_5 = e3 & op(e2, e1) = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (224), (7400), (7431), (7478), % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7526), (function-axioms) are inconsistent by % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #87. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7527) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7527) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7528) all_57_8 = e3 & op(e1, e1) = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7528) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7529) op(e1, e1) = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7007), (7529), (function-axioms) are % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7530) all_57_14 = e3 & op(e0, e1) = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7530) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7531) all_57_14 = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (7406), (7481), (7503), (7531) are % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #399. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7532) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7532) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7533) all_57_8 = e3 & op(e1, e1) = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7533) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7534) op(e1, e1) = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7007), (7534), (function-axioms) are % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7535) all_57_11 = e3 & op(e1, e0) = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7535) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7536) all_57_11 = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7537) all_57_15 = e0 & op(e0, e0) = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7537) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7538) op(e0, e0) = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7499), (7538), (function-axioms) are % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #715. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7502) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7539) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7539) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7540) all_57_9 = e0 & op(e3, e0) = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7540) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7541) all_57_9 = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7542) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7542) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7543) all_57_9 = e1 & op(e3, e0) = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7543) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7544) all_57_9 = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7541), (7544) are inconsistent by sub-proof % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #383. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7545) all_57_10 = e1 & op(e2, e0) = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7400), (7545) are inconsistent by sub-proof % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #270. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7546) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7546) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7547) all_57_11 = e1 & op(e1, e0) = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7536), (7547) are inconsistent by sub-proof % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #296. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7548) all_57_15 = e1 & op(e0, e0) = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7548) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7549) op(e0, e0) = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7499), (7549), (function-axioms) are % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7550) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7550) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7551) all_57_10 = e0 & op(e2, e0) = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7551) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7552) op(e2, e0) = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7401), (7552), (function-axioms) are % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #451. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7553) all_57_11 = e0 & op(e1, e0) = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7536), (7553) are inconsistent by sub-proof % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #129. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7554) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7554) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7555) ~ (all_56_19 = e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7556) op(e2, e1) = all_56_19 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7449), (7555), (7556), (function-axioms) are % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7557) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (371), (7007), (7487), (7557), % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #86. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7558) all_57_12 = e0 & op(e0, e3) = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7558) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7559) all_57_12 = e0 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7481), (7559) are inconsistent by sub-proof % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #581. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7560) all_57_13 = e1 & op(e0, e2) = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7560) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7561) all_57_13 = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7406), (7561) are inconsistent by sub-proof % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #567. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7562) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7562) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7563) all_57_14 = e1 & op(e0, e1) = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7563) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7564) all_57_14 = e1 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7565) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7565) gives: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7566) all_57_4 = e3 & op(e3, e1) = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7566) implies: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7567) all_57_4 = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7568) op(e3, e1) = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (169), (219), (220), % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7006), (7448), (7564), (7567), (7568), % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #82. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7569) all_57_5 = e3 & op(e2, e1) = e3 % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (224), (7400), (7431), (7478), % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7569), (function-axioms) are inconsistent by % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #87. % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7570) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 133.97/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (7007), (7564), (7570), % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #81. % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7571) all_57_15 = e1 & op(e0, e0) = e1 % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7571) implies: % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7572) op(e0, e0) = e1 % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (7572), (function-axioms) are % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354. % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7573) all_57_3 = e3 & op(e2, e2) = e3 % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7573) implies: % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7574) op(e2, e2) = e3 % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7431), (7574), (function-axioms) are % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7575) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7575) gives: % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7576) all_57_5 = e3 & op(e2, e1) = e3 % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7576) implies: % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7577) all_57_5 = e3 % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7448), (7577) imply: % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7578) e3 = e1 % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (7578) imply: % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7579) $false % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7579) is inconsistent. % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7580) all_57_10 = e3 & op(e2, e0) = e3 % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7580) implies: % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7581) op(e2, e0) = e3 % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (7401), (7581), (function-axioms) are % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #546. % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | (7582) all_57_10 = e1 & op(e2, e0) = e1 % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7400), (7582) are inconsistent by sub-proof % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | #270. % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | (7583) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7433), (7436), (7439), (7440), (7583) are % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #381. % 133.97/19.39 | | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | (7584) ~ (all_16_1 = e0) & op(e2, e2) = all_16_1 & % 133.97/19.39 | | | | | | | | | | | | | | | | | | | $i(all_16_1) % 133.97/19.39 | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7431), (7584), (function-axioms) are inconsistent % 133.97/19.39 | | | | | | | | | | | | | | | | | | | by sub-proof #380. % 133.97/19.39 | | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | (7585) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 133.97/19.39 | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | BETA: splitting (7585) gives: % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | Case 1: % 133.97/19.39 | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | (7586) all_57_14 = e2 & op(e0, e1) = e2 % 133.97/19.39 | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | REF_CLOSE: (157), (7001), (7586), (function-axioms) are % 133.97/19.39 | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 133.97/19.39 | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | (7587) all_57_15 = e2 & op(e0, e0) = e2 % 133.97/19.39 | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | REF_CLOSE: (36), (7396), (7587), (function-axioms) are % 133.97/19.39 | | | | | | | | | | | | | | | inconsistent by sub-proof #107. % 133.97/19.39 | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | (7588) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 133.97/19.39 | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | BETA: splitting (7588) gives: % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | Case 1: % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | (7589) all_57_11 = e2 & op(e1, e0) = e2 % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | REF_CLOSE: (160), (7002), (7589), (function-axioms) are % 133.97/19.39 | | | | | | | | | | | | | inconsistent by sub-proof #514. % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | (7590) all_57_15 = e2 & op(e0, e0) = e2 % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | REF_CLOSE: (36), (7396), (7590), (function-axioms) are % 133.97/19.39 | | | | | | | | | | | | | inconsistent by sub-proof #107. % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | (7591) all_20_2 = e2 % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | COMBINE_EQS: (318), (7591) imply: % 133.97/19.39 | | | | | | | | | | | (7592) all_4_2 = e2 % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | REDUCE: (369), (7592) imply: % 133.97/19.39 | | | | | | | | | | | (7593) ~ (all_52_13 = e2) % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | REDUCE: (36), (7592) imply: % 133.97/19.39 | | | | | | | | | | | (7594) op(e0, e0) = e2 % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | BETA: splitting (225) gives: % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | Case 1: % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | (7595) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 133.97/19.39 | | | | | | | | | | | | & op(e2, e2) = e2) % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | BETA: splitting (7595) gives: % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | Case 1: % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | (7596) all_57_2 = e2 & op(e2, e3) = e2 % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | ALPHA: (7596) implies: % 133.97/19.39 | | | | | | | | | | | | | (7597) op(e2, e3) = e2 % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | REF_CLOSE: (167), (7392), (7597), (function-axioms) are % 133.97/19.39 | | | | | | | | | | | | | inconsistent by sub-proof #779. % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | (7598) all_57_3 = e2 & op(e2, e2) = e2 % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | ALPHA: (7598) implies: % 133.97/19.39 | | | | | | | | | | | | | (7599) op(e2, e2) = e2 % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e2, % 133.97/19.39 | | | | | | | | | | | | | e2, e2, simplifying with (42), (7599) gives: % 133.97/19.39 | | | | | | | | | | | | | (7600) all_8_2 = e2 % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | REDUCE: (7011), (7600) imply: % 133.97/19.39 | | | | | | | | | | | | | (7601) ~ (e3 = e2) % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | Case 1: % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | (7602) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.97/19.39 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.39 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.97/19.39 | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.97/19.39 | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.39 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.39 | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.97/19.39 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.39 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.97/19.39 | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.97/19.39 | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.39 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.97/19.39 | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.97/19.39 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.39 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.97/19.39 | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.39 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.39 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.39 | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.97/19.39 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.39 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.39 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.39 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.97/19.39 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (42), (7011), (7394), (7599), (7602), % 133.97/19.39 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.39 | | | | | | | | | | | | | | #80. % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | (7603) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.97/19.39 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.39 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.39 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.39 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.97/19.39 | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.97/19.39 | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.97/19.39 | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.97/19.39 | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.97/19.39 | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.97/19.39 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.97/19.39 | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.97/19.39 | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.97/19.39 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.39 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.97/19.39 | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.39 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.97/19.39 | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.97/19.39 | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.97/19.39 | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.97/19.39 | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.39 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.97/19.39 | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.97/19.39 | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.97/19.39 | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.97/19.39 | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.97/19.39 | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.97/19.39 | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.39 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.97/19.39 | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.97/19.39 | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.97/19.39 | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.97/19.39 | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.97/19.39 | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.39 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.39 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.97/19.39 | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.97/19.39 | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.97/19.39 | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.97/19.39 | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.97/19.39 | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.97/19.39 | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.97/19.39 | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.39 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.39 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.39 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.39 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.39 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.39 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.39 | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | BETA: splitting (7603) gives: % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | Case 1: % 133.97/19.39 | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | (7604) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.97/19.39 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.39 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.39 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.39 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.97/19.39 | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.97/19.39 | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.97/19.39 | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.97/19.39 | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.97/19.39 | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.97/19.39 | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.97/19.39 | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.97/19.39 | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (7604), % 133.97/19.39 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.39 | | | | | | | | | | | | | | | #108. % 133.97/19.39 | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | (7605) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.97/19.39 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.39 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.97/19.39 | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.39 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.39 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.39 | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.39 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.39 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.97/19.39 | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.39 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.97/19.39 | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.39 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.39 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.97/19.39 | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.97/19.39 | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.39 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.97/19.39 | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.97/19.39 | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.97/19.39 | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.97/19.39 | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.97/19.39 | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.97/19.39 | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.39 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.97/19.39 | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.97/19.39 | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.39 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.39 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.39 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.39 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.39 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.39 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.39 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.39 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.39 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.39 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.39 | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.39 | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | BETA: splitting (7605) gives: % 133.97/19.39 | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | Case 1: % 133.97/19.39 | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | (7606) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.97/19.39 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.97/19.39 | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.97/19.39 | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.39 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.97/19.39 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.39 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.97/19.39 | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | ALPHA: (7606) implies: % 133.97/19.39 | | | | | | | | | | | | | | | | (7607) op(e2, e0) = e2 % 133.97/19.39 | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7593), (7607), (function-axioms) are % 133.97/19.39 | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 133.97/19.39 | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | (7608) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.39 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.39 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.97/19.39 | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.39 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.97/19.39 | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.97/19.39 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.39 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.39 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.97/19.39 | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.97/19.39 | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.39 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.97/19.39 | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.97/19.39 | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.97/19.39 | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.97/19.39 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.97/19.39 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.97/19.39 | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.97/19.39 | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.97/19.39 | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.39 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.97/19.39 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.97/19.39 | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.97/19.39 | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.39 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.39 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.39 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.39 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.39 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.97/19.39 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.39 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.39 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.39 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.39 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.39 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.39 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.39 | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.39 | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | BETA: splitting (7608) gives: % 133.97/19.39 | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | Case 1: % 133.97/19.39 | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | (7609) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.39 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.97/19.39 | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.39 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.39 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 133.97/19.39 | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.97/19.39 | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | ALPHA: (7609) implies: % 133.97/19.39 | | | | | | | | | | | | | | | | | (7610) ~ (all_56_11 = e2) % 133.97/19.39 | | | | | | | | | | | | | | | | | (7611) op(e2, e2) = all_56_11 % 133.97/19.39 | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | REF_CLOSE: (7599), (7610), (7611), (function-axioms) are % 133.97/19.39 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #531. % 133.97/19.39 | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | (7612) op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.39 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.97/19.39 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 133.97/19.39 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.39 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 133.97/19.39 | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.97/19.39 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 133.97/19.39 | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.39 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.39 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.97/19.39 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.97/19.39 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.39 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.39 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 133.97/19.39 | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 133.97/19.39 | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 133.97/19.39 | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.97/19.39 | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_29))) % 133.97/19.39 | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | ALPHA: (7612) implies: % 133.97/19.39 | | | | | | | | | | | | | | | | | (7613) op(e0, e0) = all_56_31 % 133.97/19.39 | | | | | | | | | | | | | | | | | (7614) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.97/19.39 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.39 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.39 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.39 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.97/19.39 | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.97/19.39 | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.97/19.39 | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.97/19.39 | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.97/19.39 | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.97/19.39 | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.97/19.39 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 133.97/19.39 | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.39 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.97/19.39 | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.97/19.39 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.39 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.97/19.39 | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.97/19.39 | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.97/19.39 | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.39 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.97/19.39 | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (91), (157), (190), (246), (332), % 133.97/19.39 | | | | | | | | | | | | | | | | | (364), (7001), (7594), (7599), (7613), (7614), % 133.97/19.39 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.39 | | | | | | | | | | | | | | | | | #523. % 133.97/19.39 | | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | (7615) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 133.97/19.39 | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | REF_CLOSE: (164), (165), (7000), (7593), (7615), % 133.97/19.39 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.39 | | | | | | | | | | | | #625. % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | | % 133.97/19.39 | | | | | | | | | End of split % 133.97/19.39 | | | | | | | | | % 133.97/19.39 | | | | | | | | End of split % 133.97/19.39 | | | | | | | | % 133.97/19.39 | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | % 133.97/19.39 | | | | | | | | (7616) all_14_2 = e3 % 133.97/19.39 | | | | | | | | % 133.97/19.39 | | | | | | | | COMBINE_EQS: (329), (7616) imply: % 133.97/19.39 | | | | | | | | (7617) all_8_2 = e3 % 133.97/19.39 | | | | | | | | % 133.97/19.39 | | | | | | | | COMBINE_EQS: (322), (7617) imply: % 133.97/19.39 | | | | | | | | (7618) all_22_2 = e3 % 133.97/19.39 | | | | | | | | % 133.97/19.39 | | | | | | | | REDUCE: (347), (7617) imply: % 133.97/19.39 | | | | | | | | (7619) ~ (all_52_1 = e3) % 133.97/19.39 | | | | | | | | % 133.97/19.39 | | | | | | | | REDUCE: (350), (7617) imply: % 133.97/19.39 | | | | | | | | (7620) ~ (all_52_4 = e3) % 133.97/19.39 | | | | | | | | % 133.97/19.39 | | | | | | | | REDUCE: (352), (7617) imply: % 133.97/19.39 | | | | | | | | (7621) ~ (all_52_6 = e3) % 133.97/19.39 | | | | | | | | % 133.97/19.39 | | | | | | | | REDUCE: (354), (7617) imply: % 133.97/19.39 | | | | | | | | (7622) ~ (all_52_7 = e3) % 133.97/19.39 | | | | | | | | % 133.97/19.39 | | | | | | | | REDUCE: (356), (7617) imply: % 133.97/19.39 | | | | | | | | (7623) ~ (all_52_9 = e3) % 133.97/19.39 | | | | | | | | % 133.97/19.39 | | | | | | | | REDUCE: (358), (7617) imply: % 133.97/19.39 | | | | | | | | (7624) ~ (all_52_13 = e3) % 133.97/19.39 | | | | | | | | % 133.97/19.39 | | | | | | | | REDUCE: (42), (7617) imply: % 133.97/19.39 | | | | | | | | (7625) op(e2, e2) = e3 % 133.97/19.39 | | | | | | | | % 133.97/19.39 | | | | | | | | BETA: splitting (6995) gives: % 133.97/19.39 | | | | | | | | % 133.97/19.39 | | | | | | | | Case 1: % 133.97/19.39 | | | | | | | | | % 133.97/19.39 | | | | | | | | | (7626) ~ (all_6_0 = e0) & op(e2, e1) = all_6_0 & % 133.97/19.39 | | | | | | | | | $i(all_6_0) % 133.97/19.39 | | | | | | | | | % 133.97/19.39 | | | | | | | | | ALPHA: (7626) implies: % 133.97/19.39 | | | | | | | | | (7627) ~ (all_6_0 = e0) % 133.97/19.39 | | | | | | | | | (7628) op(e2, e1) = all_6_0 % 133.97/19.39 | | | | | | | | | % 133.97/19.39 | | | | | | | | | BETA: splitting (230) gives: % 133.97/19.39 | | | | | | | | | % 133.97/19.39 | | | | | | | | | Case 1: % 133.97/19.39 | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | (7629) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 133.97/19.39 | | | | | | | | | | & op(e2, e2) = e3) % 133.97/19.39 | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | BETA: splitting (7629) gives: % 133.97/19.39 | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | Case 1: % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | (7630) all_57_1 = e3 & op(e3, e2) = e3 % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | ALPHA: (7630) implies: % 133.97/19.39 | | | | | | | | | | | (7631) op(e3, e2) = e3 % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | REF_CLOSE: (170), (7620), (7631), (function-axioms) are % 133.97/19.39 | | | | | | | | | | | inconsistent by sub-proof #738. % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | (7632) all_57_3 = e3 & op(e2, e2) = e3 % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | ALPHA: (7632) implies: % 133.97/19.39 | | | | | | | | | | | (7633) all_57_3 = e3 % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, % 133.97/19.39 | | | | | | | | | | | all_6_0, e1, e2, simplifying with (165), (7628) % 133.97/19.39 | | | | | | | | | | | gives: % 133.97/19.39 | | | | | | | | | | | (7634) all_52_9 = all_6_0 % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | COMBINE_EQS: (260), (7634) imply: % 133.97/19.39 | | | | | | | | | | | (7635) all_54_6 = all_6_0 % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | REDUCE: (146), (7634) imply: % 133.97/19.39 | | | | | | | | | | | (7636) ~ (all_52_1 = all_6_0) % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | REDUCE: (123), (7634) imply: % 133.97/19.39 | | | | | | | | | | | (7637) ~ (all_52_8 = all_6_0) % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | REDUCE: (118), (7634) imply: % 133.97/19.39 | | | | | | | | | | | (7638) ~ (all_52_11 = all_6_0) % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | SIMP: (7638) implies: % 133.97/19.39 | | | | | | | | | | | (7639) ~ (all_52_11 = all_6_0) % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | REDUCE: (117), (7634) imply: % 133.97/19.39 | | | | | | | | | | | (7640) ~ (all_52_13 = all_6_0) % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | SIMP: (7640) implies: % 133.97/19.39 | | | | | | | | | | | (7641) ~ (all_52_13 = all_6_0) % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | REDUCE: (7623), (7634) imply: % 133.97/19.39 | | | | | | | | | | | (7642) ~ (all_6_0 = e3) % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | REDUCE: (7000), (7634) imply: % 133.97/19.39 | | | | | | | | | | | (7643) ~ (all_6_0 = e2) % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | BETA: splitting (198) gives: % 133.97/19.39 | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | Case 1: % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | (7644) all_54_6 = e3 % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | REF_CLOSE: (7635), (7642), (7644) are inconsistent by % 133.97/19.39 | | | | | | | | | | | | sub-proof #79. % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | (7645) ~ (all_54_6 = e3) % 133.97/19.39 | | | | | | | | | | | | (7646) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | BETA: splitting (7646) gives: % 133.97/19.39 | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | Case 1: % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | (7647) all_54_6 = e2 % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | REF_CLOSE: (7635), (7643), (7647) are inconsistent by % 133.97/19.39 | | | | | | | | | | | | | sub-proof #78. % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | Case 2: % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | (7648) ~ (all_54_6 = e2) % 133.97/19.39 | | | | | | | | | | | | | (7649) all_54_6 = e1 | all_54_6 = e0 % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | BETA: splitting (7649) gives: % 133.97/19.39 | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | Case 1: % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | (7650) all_54_6 = e1 % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | COMBINE_EQS: (7635), (7650) imply: % 133.97/19.39 | | | | | | | | | | | | | | (7651) all_6_0 = e1 % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | SIMP: (7651) implies: % 133.97/19.39 | | | | | | | | | | | | | | (7652) all_6_0 = e1 % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | REDUCE: (7636), (7652) imply: % 133.97/19.39 | | | | | | | | | | | | | | (7653) ~ (all_52_1 = e1) % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | REDUCE: (7637), (7652) imply: % 133.97/19.39 | | | | | | | | | | | | | | (7654) ~ (all_52_8 = e1) % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | REDUCE: (7639), (7652) imply: % 133.97/19.39 | | | | | | | | | | | | | | (7655) ~ (all_52_11 = e1) % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | REDUCE: (7641), (7652) imply: % 133.97/19.39 | | | | | | | | | | | | | | (7656) ~ (all_52_13 = e1) % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | REDUCE: (7642), (7652) imply: % 133.97/19.39 | | | | | | | | | | | | | | (7657) ~ (e3 = e1) % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | REDUCE: (7643), (7652) imply: % 133.97/19.39 | | | | | | | | | | | | | | (7658) ~ (e2 = e1) % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | BETA: splitting (224) gives: % 133.97/19.39 | | | | | | | | | | | | | | % 133.97/19.39 | | | | | | | | | | | | | | Case 1: % 133.97/19.39 | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | (7659) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 133.97/19.40 | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 133.97/19.40 | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (7625), (7653), (7659), % 133.97/19.40 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.40 | | | | | | | | | | | | | | | #77. % 133.97/19.40 | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | Case 2: % 133.97/19.40 | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | (7660) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 133.97/19.40 | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 133.97/19.40 | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | BETA: splitting (7660) gives: % 133.97/19.40 | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | (7661) all_57_5 = e1 & op(e2, e1) = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | ALPHA: (7661) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | (7662) all_57_5 = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | (7663) op(e2, e1) = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | BETA: splitting (55) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | (7664) ~ (all_16_2 = e2) % 133.97/19.40 | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | REDUCE: (327), (7664) imply: % 133.97/19.40 | | | | | | | | | | | | | | | | | (7665) ~ (all_10_2 = e2) % 133.97/19.40 | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | BETA: splitting (64) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | (7666) ~ (all_22_2 = e3) % 133.97/19.40 | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | REDUCE: (7618), (7666) imply: % 133.97/19.40 | | | | | | | | | | | | | | | | | | (7667) $false % 133.97/19.40 | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | CLOSE: (7667) is inconsistent. % 133.97/19.40 | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.40 | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | (7668) ( ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | $i(all_22_0)) | ( ~ (all_22_1 = e1) & op(e3, e3) % 133.97/19.40 | | | | | | | | | | | | | | | | | | = all_22_1 & $i(all_22_1)) % 133.97/19.40 | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | (7669) ~ (all_20_2 = e2) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | REDUCE: (318), (7669) imply: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | (7670) ~ (all_4_2 = e2) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7671) ~ (all_32_2 = e1) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | REDUCE: (312), (7671) imply: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7672) ~ (all_10_2 = e1) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (39), (45), (165), (168), (169), (202), % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (204), (206), (270), (278), (344), (346), (361), % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (371), (6999), (7000), (7007), (7009), (7625), % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7654), (7663), (7665), (7672), (function-axioms) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #104. % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7673) all_32_2 = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7674) ( ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | $i(all_32_0)) | ( ~ (all_32_1 = e2) & op(e1, e1) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | = all_32_1 & $i(all_32_1)) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (312), (7673) imply: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7675) all_10_2 = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | SIMP: (7675) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7676) all_10_2 = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (7676) imply: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7677) ~ (all_52_12 = e1) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (7676) imply: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | (7678) op(e3, e3) = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | (7679) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (7656), (7677), (7679), % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | #179. % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | (7680) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7680) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | (7681) all_57_11 = e1 & op(e1, e0) = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7681) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | (7682) all_57_11 = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | (7683) op(e1, e0) = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7674) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | (7684) ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | $i(all_32_0) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7684) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | (7685) ~ (all_32_0 = e0) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | (7686) op(e1, e3) = all_32_0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | (7687) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7687) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | (7688) all_57_6 = e3 & op(e1, e3) = e3 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7688) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | (7689) all_57_6 = e3 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | (7690) op(e1, e3) = e3 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (7691) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7691) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7692) all_57_12 = e1 & op(e0, e3) = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7692) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7693) all_57_12 = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (235), (237), % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7678), (7693), (function-axioms) are inconsistent % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #583. % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7694) all_57_13 = e1 & op(e0, e2) = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7694) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7695) all_57_13 = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7696) op(e0, e2) = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7697) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7697) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7698) all_57_1 = e2 & op(e3, e2) = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7698) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7699) all_57_1 = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7700) op(e3, e2) = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7701) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7701) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7702) all_57_1 = e0 & op(e3, e2) = e0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7699), (7702) are inconsistent by sub-proof % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #466. % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7703) all_57_3 = e0 & op(e2, e2) = e0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7703) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7704) op(e2, e2) = e0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7625), (7704), (function-axioms) are % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7705) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7705) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7706) all_57_7 = e0 & op(e1, e2) = e0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7706) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7707) op(e1, e2) = e0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7708) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7708) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7709) all_57_12 = e2 & op(e0, e3) = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7709) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7710) all_57_12 = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7668) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7711) ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_22_0) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7711) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7712) ~ (all_22_0 = e0) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7713) op(e3, e2) = all_22_0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7714) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7714) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7715) all_57_0 = e0 & op(e3, e3) = e0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7715) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7716) op(e3, e3) = e0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7678), (7716), (function-axioms) are % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7717) all_57_2 = e0 & op(e2, e3) = e0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7717) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7718) all_57_2 = e0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7719) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7719) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7720) all_57_2 = e2 & op(e2, e3) = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7718), (7720) are inconsistent by sub-proof % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #680. % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7721) all_57_3 = e2 & op(e2, e2) = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7721) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7722) all_57_3 = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (227), (228), % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (7621), (7699), (7722), (function-axioms) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #463. % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7723) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7723) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7724) all_57_5 = e2 & op(e2, e1) = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7724) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7725) op(e2, e1) = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7000), (7725), (function-axioms) are % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770. % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7726) all_57_10 = e2 & op(e2, e0) = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7726) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7727) op(e2, e0) = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e1, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (158), (7696) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7728) all_52_7 = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, e1, simplifying with (160), (7683) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7729) all_52_14 = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e0, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (162), (7707) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7730) all_52_6 = e0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (7690) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7731) all_52_2 = e3 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_32_0, e3, e1, simplifying with (163), (7686) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7732) all_52_2 = all_32_0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e2, simplifying with (164), (7727) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7733) all_52_13 = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (7700) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7734) all_52_4 = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_22_0, e2, e3, simplifying with (170), (7713) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7735) all_52_4 = all_22_0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7731), (7732) imply: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7736) all_32_0 = e3 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7734), (7735) imply: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7737) all_22_0 = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7737) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7738) all_22_0 = e2 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (7729), (7730) imply: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7739) ~ (e1 = e0) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7624), (7733) imply: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7740) ~ (e3 = e2) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7741) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7741) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7742) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237), % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7690), (7710), (7742), (function-axioms) are % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #102. % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7743) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7743) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7744) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7744) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7745) op(e3, e3) = e0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7678), (7745), (function-axioms) are % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7746) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7746) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7747) ~ (all_56_9 = e2) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7748) op(e3, e2) = all_56_9 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7700), (7747), (7748), (function-axioms) are % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7749) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7749) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7750) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (7750), % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #108. % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7751) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7751) gives: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7752) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7752) implies: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7753) op(e2, e2) = e0 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7625), (7753), (function-axioms) are % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7754) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.97/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7754) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7755) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7755) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7756) ~ (all_56_19 = e1) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7757) op(e2, e1) = all_56_19 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7663), (7756), (7757), (function-axioms) are % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7758) op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7758) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7759) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7759) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7760) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7663), (7700), (7760), (function-axioms) are % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #91. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7761) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7761) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7762) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7762) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7763) op(e1, e1) = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e0, e1, % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (7007), (7763) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7764) e2 = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (7764) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7765) $false % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7765) is inconsistent. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7766) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7766) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7767) ~ (all_56_5 = e3) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7768) op(e1, e3) = all_56_5 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7690), (7767), (7768), (function-axioms) are % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #724. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7769) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7769) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7770) all_57_6 = e0 & op(e1, e3) = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7689), (7770) are inconsistent by sub-proof % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #576. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7771) all_57_12 = e0 & op(e0, e3) = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7710), (7771) are inconsistent by sub-proof % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #578. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7772) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_22_1) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7678), (7772), (function-axioms) are inconsistent % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #305. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7773) all_57_13 = e2 & op(e0, e2) = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7773) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7774) all_57_13 = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (227), (228), (7633), % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7699), (7774) are inconsistent by sub-proof #301. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7775) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7775) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7776) all_57_14 = e2 & op(e0, e1) = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7001), (7776), (function-axioms) are % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7777) all_57_15 = e2 & op(e0, e0) = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (7670), (7777), (function-axioms) are % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #107. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7778) all_57_13 = e0 & op(e0, e2) = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7778) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7779) all_57_13 = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7695), (7779) are inconsistent by sub-proof % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #681. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7780) all_57_3 = e2 & op(e2, e2) = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7633), (7780) are inconsistent by sub-proof % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #375. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7781) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7781) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7782) all_57_7 = e2 & op(e1, e2) = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7782) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7783) all_57_7 = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7668) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7784) ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_22_0) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7784) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7785) ~ (all_22_0 = e0) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7786) op(e3, e2) = all_22_0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (227), (228), % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (236), (238), (7620), (7625), (7678), % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7783), (7785), (7786), (function-axioms) are % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #308. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7787) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_22_1) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7678), (7787), (function-axioms) are inconsistent % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #305. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7788) all_57_13 = e2 & op(e0, e2) = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7788) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7789) all_57_13 = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7695), (7789) are inconsistent by sub-proof % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #567. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (7790) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7790) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7791) all_57_14 = e1 & op(e0, e1) = e1 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7791) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7792) all_57_14 = e1 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (169), (219), % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (222), (7006), (7007), (7623), (7662), % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7792), (function-axioms) are inconsistent by % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #76. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7793) all_57_15 = e1 & op(e0, e0) = e1 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7793) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7794) op(e0, e0) = e1 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (7794), (function-axioms) are % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7795) all_57_7 = e3 & op(e1, e2) = e3 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7795) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7796) op(e1, e2) = e3 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (7621), (7796), (function-axioms) are % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | (7797) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7797) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7798) all_57_8 = e3 & op(e1, e1) = e3 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7798) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7799) op(e1, e1) = e3 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7007), (7799), (function-axioms) are % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7800) all_57_11 = e3 & op(e1, e0) = e3 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7800) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7801) all_57_11 = e3 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7682), (7801) are inconsistent by sub-proof % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | #167. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | (7802) ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | $i(all_32_1) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7007), (7802), (function-axioms) are inconsistent % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #95. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | (7803) all_57_15 = e1 & op(e0, e0) = e1 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7803) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | (7804) op(e0, e0) = e1 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (7804), (function-axioms) are % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | (7805) all_20_2 = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (318), (7805) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | (7806) all_4_2 = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | SIMP: (7806) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | (7807) all_4_2 = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (7807) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | (7808) all_26_2 = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | REDUCE: (368), (7807) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | (7809) ~ (all_52_12 = e2) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | REDUCE: (369), (7807) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | (7810) ~ (all_52_13 = e2) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | REDUCE: (36), (7807) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | (7811) op(e0, e0) = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | (7812) ~ (all_26_2 = e2) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | REDUCE: (7808), (7812) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | (7813) $false % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | CLOSE: (7813) is inconsistent. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | (7814) ( ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | $i(all_26_0)) | ( ~ (all_26_1 = e3) & op(e2, e2) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | = all_26_1 & $i(all_26_1)) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | (7815) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7815) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | (7816) all_57_1 = e2 & op(e3, e2) = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7816) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | (7817) all_57_1 = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | (7818) op(e3, e2) = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | (7819) all_54_7 = e3 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (7819) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | (7820) all_52_13 = e3 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7624), (7820) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | (7821) $false % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7821) is inconsistent. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | (7822) ~ (all_54_7 = e3) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | (7823) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7823) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | (7824) all_54_7 = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (7824) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | (7825) all_52_13 = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7810), (7825) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | (7826) $false % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7826) is inconsistent. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | (7827) ~ (all_54_7 = e2) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | (7828) all_54_7 = e1 | all_54_7 = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7828) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7829) all_54_7 = e1 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (7829) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7830) all_52_13 = e1 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7656), (7830) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7831) $false % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7831) is inconsistent. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7832) all_54_7 = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (7832) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7833) all_52_13 = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7624), (7833) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7834) ~ (e3 = e0) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7810), (7833) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7835) ~ (e2 = e0) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7656), (7833) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7836) ~ (e1 = e0) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (7833) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | (7837) op(e2, e0) = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7814) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (7838) ~ (all_26_0 = e1) & op(e2, e0) = all_26_0 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_0) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7838) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (7839) ~ (all_26_0 = e1) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (7840) op(e2, e0) = all_26_0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7841) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7841) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7842) all_57_0 = e0 & op(e3, e3) = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7842) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7843) op(e3, e3) = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (7009), (7843), (function-axioms) are % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #534. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7844) all_57_1 = e0 & op(e3, e2) = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7817), (7844) are inconsistent by sub-proof % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #466. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7845) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7845) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7846) all_57_4 = e0 & op(e3, e1) = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7846) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7847) all_57_4 = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7848) op(e3, e1) = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7849) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (165), (169), (7623), (7848), (7849), % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #420. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7850) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7850) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7851) all_57_8 = e3 & op(e1, e1) = e3 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7851) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7852) op(e1, e1) = e3 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7007), (7852), (function-axioms) are % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109. % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7853) all_57_14 = e3 & op(e0, e1) = e3 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7853) implies: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7854) op(e0, e1) = e3 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11, % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, e0, simplifying with (157), (7854) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7855) all_52_11 = e3 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_26_0, % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e2, simplifying with (7837), (7840) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7856) all_26_0 = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0, % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (7848) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7857) all_52_8 = e0 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2, % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (7818) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7858) all_52_4 = e2 % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (7857) imply: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7859) ~ (all_10_2 = e0) % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7860) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 133.97/19.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7860) gives: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7861) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7861) gives: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7862) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7862) implies: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7863) op(e3, e3) = e2 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234), % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (7620), (7817), (7847), (7863), % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #238. % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7864) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7864) implies: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7865) op(e3, e1) = e3 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (7848), (7865), (function-axioms) are % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #600. % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7866) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7866) gives: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7867) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7867) implies: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7868) op(e3, e3) = e0 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (7009), (7868), (function-axioms) are % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #534. % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7869) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7869) implies: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7870) ~ (all_56_9 = e2) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7871) op(e3, e2) = all_56_9 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7818), (7870), (7871), (function-axioms) are % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7872) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7872) gives: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7873) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (7873), % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #108. % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7874) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7874) gives: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7875) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7875) implies: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7876) op(e2, e2) = e0 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7625), (7876), (function-axioms) are % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7877) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7877) gives: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7878) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7878) implies: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7879) ~ (all_56_19 = e1) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7880) op(e2, e1) = all_56_19 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7663), (7879), (7880), (function-axioms) are % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106. % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7881) op(e0, e0) = all_56_31 & $i(all_56_31) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7881) implies: % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7882) op(e0, e0) = all_56_31 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7883) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 133.97/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (91), (157), (190), (246), (332), % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364), (7001), (7811), (7837), (7882), (7883), % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #273. % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7884) all_57_9 = e0 & op(e3, e0) = e0 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7884) implies: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7885) all_57_9 = e0 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (208), (212), % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214), (223), (224), (225), (7624), (7625), % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7633), (7811), (7837), (7885), (function-axioms) % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #291. % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (7886) ~ (all_26_1 = e3) & op(e2, e2) = all_26_1 & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_1) % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7886) implies: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (7887) ~ (all_26_1 = e3) % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (7888) op(e2, e2) = all_26_1 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7625), (7887), (7888), (function-axioms) are % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #334. % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | (7889) all_57_3 = e2 & op(e2, e2) = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7633), (7889) are inconsistent by sub-proof % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | #375. % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | (7890) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7890) gives: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | (7891) all_57_7 = e2 & op(e1, e2) = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (6998), (7891), (function-axioms) are % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515. % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | (7892) all_57_13 = e2 & op(e0, e2) = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7892) implies: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | (7893) all_57_13 = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | (7894) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7894) gives: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (7895) all_57_0 = e2 & op(e3, e3) = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7895) implies: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (7896) op(e3, e3) = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (7665), (7896), (function-axioms) are % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #536. % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (7897) all_57_1 = e2 & op(e3, e2) = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7897) implies: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (7898) all_57_1 = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (227), (228), (7633), % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (7893), (7898) are inconsistent by sub-proof #301. % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | (7899) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7899) gives: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (7900) all_57_4 = e2 & op(e3, e1) = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6999), (7900), (function-axioms) are % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442. % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | (7901) all_57_9 = e2 & op(e3, e0) = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (7809), (7901), (function-axioms) are % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | End of split % 134.25/19.42 | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | Case 2: % 134.25/19.42 | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | (7902) all_16_2 = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | COMBINE_EQS: (327), (7902) imply: % 134.25/19.42 | | | | | | | | | | | | | | | | | (7903) all_10_2 = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | SIMP: (7903) implies: % 134.25/19.42 | | | | | | | | | | | | | | | | | (7904) all_10_2 = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | REDUCE: (336), (7904) imply: % 134.25/19.42 | | | | | | | | | | | | | | | | | (7905) ~ (all_52_1 = e2) % 134.25/19.42 | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | REDUCE: (45), (7904) imply: % 134.25/19.42 | | | | | | | | | | | | | | | | | (7906) op(e3, e3) = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 134.25/19.42 | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.42 | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | (7907) all_54_4 = e3 % 134.25/19.42 | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7907) imply: % 134.25/19.42 | | | | | | | | | | | | | | | | | | (7908) all_52_1 = e3 % 134.25/19.42 | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | REDUCE: (7619), (7908) imply: % 134.25/19.42 | | | | | | | | | | | | | | | | | | (7909) $false % 134.25/19.42 | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | CLOSE: (7909) is inconsistent. % 134.25/19.42 | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.42 | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | (7910) ~ (all_54_4 = e3) % 134.25/19.42 | | | | | | | | | | | | | | | | | | (7911) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 134.25/19.42 | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | BETA: splitting (7911) gives: % 134.25/19.42 | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | (7912) all_54_4 = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7912) imply: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | (7913) all_52_1 = e2 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | REDUCE: (7905), (7913) imply: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | (7914) $false % 134.25/19.42 | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | CLOSE: (7914) is inconsistent. % 134.25/19.42 | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | (7915) ~ (all_54_4 = e2) % 134.25/19.42 | | | | | | | | | | | | | | | | | | | (7916) all_54_4 = e1 | all_54_4 = e0 % 134.25/19.42 | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | (7917) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7917) gives: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | (7918) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.25/19.42 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (7620), (7906), (7918), % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | #254. % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (7919) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (7905), (7906), (7919), % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | #443. % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (7920) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7920) gives: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (7921) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (7921), % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | #108. % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (7922) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7922) gives: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | (7923) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7923) implies: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | (7924) op(e2, e2) = e0 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7625), (7924), (function-axioms) are % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | (7925) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7925) gives: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (7926) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7926) implies: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (7927) ~ (all_56_19 = e1) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (7928) op(e2, e1) = all_56_19 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7663), (7927), (7928), (function-axioms) are % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106. % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (7929) op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7929) implies: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (7930) op(e0, e0) = all_56_31 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (7931) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7916) gives: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7932) all_54_4 = e1 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7932) imply: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7933) all_52_1 = e1 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7653), (7933) imply: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7934) $false % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7934) is inconsistent. % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7935) all_54_4 = e0 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7935) imply: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7936) all_52_1 = e0 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (7936) imply: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7937) ~ (all_52_3 = e0) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7937) implies: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7938) ~ (all_52_3 = e0) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (7936) imply: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7939) ~ (all_52_13 = e0) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7939) implies: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7940) ~ (all_52_13 = e0) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7619), (7936) imply: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7941) ~ (e3 = e0) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7653), (7936) imply: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | (7942) ~ (e1 = e0) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7931) gives: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | (7943) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7943) gives: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7944) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7944) implies: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7945) op(e0, e3) = e0 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7938), (7945), (function-axioms) are % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219. % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7946) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7946) implies: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7947) all_56_31 = e2 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7930), (7947) imply: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7948) op(e0, e0) = e2 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7949) all_54_7 = e3 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7624), (7949) are inconsistent by % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #338. % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7950) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7950) gives: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7951) all_54_7 = e2 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (7951) imply: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7952) all_52_13 = e2 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7952) implies: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7953) all_52_13 = e2 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (7953) imply: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7954) ~ (all_4_2 = e2) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7954) implies: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7955) ~ (all_4_2 = e2) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (7930), (7948), (7955), (function-axioms) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #427. % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7956) all_54_7 = e1 | all_54_7 = e0 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7656), (7940), (7956) are inconsistent by % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #313. % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | (7957) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7957) gives: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7958) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7958) implies: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7959) ~ (all_56_15 = e2) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7960) op(e0, e2) = all_56_15 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7961) all_54_7 = e3 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7624), (7961) are inconsistent by % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #338. % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7962) ~ (all_54_7 = e3) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7963) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7963) gives: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7964) all_54_7 = e2 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (7964) imply: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7965) all_52_13 = e2 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7965) implies: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7966) all_52_13 = e2 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (7966) imply: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7967) ~ (all_4_2 = e2) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7967) implies: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7968) ~ (all_4_2 = e2) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7624), (7966) imply: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7969) ~ (e3 = e2) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7970) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7970) gives: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7971) all_57_12 = e2 & op(e0, e3) = e2 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7971) implies: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7972) all_57_12 = e2 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237), % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7906), (7972), (function-axioms) are inconsistent % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #290. % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7973) all_57_13 = e2 & op(e0, e2) = e2 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7973) implies: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7974) op(e0, e2) = e2 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7959), (7960), (7974), (function-axioms) are % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609. % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7975) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7975) gives: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7976) all_57_14 = e2 & op(e0, e1) = e2 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7001), (7976), (function-axioms) are % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7977) all_57_15 = e2 & op(e0, e0) = e2 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7977) implies: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7978) op(e0, e0) = e2 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (7930), (7968), (7978), (function-axioms) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #427. % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7979) all_54_7 = e1 | all_54_7 = e0 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7656), (7940), (7979) are inconsistent by % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #313. % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7980) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7980) implies: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7981) all_56_31 = e1 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7930), (7981) imply: % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (7982) op(e0, e0) = e1 % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (7982), (function-axioms) are % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354. % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | (7983) all_57_10 = e1 & op(e2, e0) = e1 % 134.25/19.43 | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | ALPHA: (7983) implies: % 134.25/19.43 | | | | | | | | | | | | | | | | (7984) op(e2, e0) = e1 % 134.25/19.43 | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7656), (7984), (function-axioms) are % 134.25/19.43 | | | | | | | | | | | | | | | | inconsistent by sub-proof #180. % 134.25/19.43 | | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | (7985) all_54_6 = e0 % 134.25/19.43 | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | | REF_CLOSE: (7627), (7635), (7985) are inconsistent by % 134.25/19.43 | | | | | | | | | | | | | | sub-proof #75. % 134.25/19.43 | | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | | % 134.25/19.43 | | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | (7986) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 134.25/19.43 | | | | | | | | | | e3 & op(e0, e2) = e3) % 134.25/19.43 | | | | | | | | | | % 134.25/19.43 | | | | | | | | | | REF_CLOSE: (158), (162), (7621), (7622), (7986), % 134.25/19.43 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.43 | | | | | | | | | | #555. % 134.25/19.43 | | | | | | | | | | % 134.25/19.43 | | | | | | | | | End of split % 134.25/19.43 | | | | | | | | | % 134.25/19.43 | | | | | | | | Case 2: % 134.25/19.43 | | | | | | | | | % 134.25/19.43 | | | | | | | | | (7987) ~ (all_6_1 = e3) & op(e2, e2) = all_6_1 & % 134.25/19.43 | | | | | | | | | $i(all_6_1) % 134.25/19.43 | | | | | | | | | % 134.25/19.43 | | | | | | | | | REF_CLOSE: (7625), (7987), (function-axioms) are inconsistent % 134.25/19.43 | | | | | | | | | by sub-proof #74. % 134.25/19.43 | | | | | | | | | % 134.25/19.43 | | | | | | | | End of split % 134.25/19.43 | | | | | | | | % 134.25/19.43 | | | | | | | End of split % 134.25/19.43 | | | | | | | % 134.25/19.43 | | | | | | Case 2: % 134.25/19.43 | | | | | | | % 134.25/19.43 | | | | | | | (7988) all_10_2 = e0 % 134.25/19.43 | | | | | | | % 134.25/19.43 | | | | | | | COMBINE_EQS: (319), (7988) imply: % 134.25/19.43 | | | | | | | (7989) all_24_2 = e0 % 134.25/19.43 | | | | | | | % 134.25/19.43 | | | | | | | REDUCE: (336), (7988) imply: % 134.25/19.43 | | | | | | | (7990) ~ (all_52_1 = e0) % 134.25/19.43 | | | | | | | % 134.25/19.43 | | | | | | | REDUCE: (338), (7988) imply: % 134.25/19.43 | | | | | | | (7991) ~ (all_52_2 = e0) % 134.25/19.43 | | | | | | | % 134.25/19.43 | | | | | | | REDUCE: (340), (7988) imply: % 134.25/19.43 | | | | | | | (7992) ~ (all_52_3 = e0) % 134.25/19.43 | | | | | | | % 134.25/19.43 | | | | | | | REDUCE: (342), (7988) imply: % 134.25/19.43 | | | | | | | (7993) ~ (all_52_4 = e0) % 134.25/19.43 | | | | | | | % 134.25/19.43 | | | | | | | REDUCE: (344), (7988) imply: % 134.25/19.43 | | | | | | | (7994) ~ (all_52_8 = e0) % 134.25/19.43 | | | | | | | % 134.25/19.43 | | | | | | | REDUCE: (346), (7988) imply: % 134.25/19.43 | | | | | | | (7995) ~ (all_52_12 = e0) % 134.25/19.43 | | | | | | | % 134.25/19.44 | | | | | | | REDUCE: (45), (7988) imply: % 134.25/19.44 | | | | | | | (7996) op(e3, e3) = e0 % 134.25/19.44 | | | | | | | % 134.25/19.44 | | | | | | | BETA: splitting (52) gives: % 134.25/19.44 | | | | | | | % 134.25/19.44 | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | % 134.25/19.44 | | | | | | | | (7997) ~ (all_14_2 = e3) % 134.25/19.44 | | | | | | | | % 134.25/19.44 | | | | | | | | REDUCE: (329), (7997) imply: % 134.25/19.44 | | | | | | | | (7998) ~ (all_8_2 = e3) % 134.25/19.44 | | | | | | | | % 134.25/19.44 | | | | | | | | BETA: splitting (58) gives: % 134.25/19.44 | | | | | | | | % 134.25/19.44 | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | % 134.25/19.44 | | | | | | | | | (7999) ~ (all_18_2 = e2) % 134.25/19.44 | | | | | | | | | % 134.25/19.44 | | | | | | | | | REDUCE: (6996), (7999) imply: % 134.25/19.44 | | | | | | | | | (8000) $false % 134.25/19.44 | | | | | | | | | % 134.25/19.44 | | | | | | | | | CLOSE: (8000) is inconsistent. % 134.25/19.44 | | | | | | | | | % 134.25/19.44 | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | % 134.25/19.44 | | | | | | | | | (8001) ( ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 & % 134.25/19.44 | | | | | | | | | $i(all_18_0)) | ( ~ (all_18_1 = e0) & op(e2, e2) = % 134.25/19.44 | | | | | | | | | all_18_1 & $i(all_18_1)) % 134.25/19.44 | | | | | | | | | % 134.25/19.44 | | | | | | | | | BETA: splitting (61) gives: % 134.25/19.44 | | | | | | | | | % 134.25/19.44 | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | (8002) ~ (all_20_2 = e2) % 134.25/19.44 | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | REDUCE: (318), (8002) imply: % 134.25/19.44 | | | | | | | | | | (8003) ~ (all_4_2 = e2) % 134.25/19.44 | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | BETA: splitting (76) gives: % 134.25/19.44 | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | (8004) ~ (all_30_2 = e0) % 134.25/19.44 | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | REDUCE: (309), (8004) imply: % 134.25/19.44 | | | | | | | | | | | (8005) ~ (all_8_2 = e0) % 134.25/19.44 | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | BETA: splitting (199) gives: % 134.25/19.44 | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | (8006) all_54_5 = e3 % 134.25/19.44 | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | REF_CLOSE: (267), (7998), (8006) are inconsistent by % 134.25/19.44 | | | | | | | | | | | | sub-proof #554. % 134.25/19.44 | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | (8007) ~ (all_54_5 = e3) % 134.25/19.44 | | | | | | | | | | | | (8008) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 134.25/19.44 | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | BETA: splitting (8008) gives: % 134.25/19.44 | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | (8009) all_54_5 = e2 % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | COMBINE_EQS: (267), (8009) imply: % 134.25/19.44 | | | | | | | | | | | | | (8010) all_8_2 = e2 % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | SIMP: (8010) implies: % 134.25/19.44 | | | | | | | | | | | | | (8011) all_8_2 = e2 % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | REDUCE: (347), (8011) imply: % 134.25/19.44 | | | | | | | | | | | | | (8012) ~ (all_52_1 = e2) % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | REDUCE: (350), (8011) imply: % 134.25/19.44 | | | | | | | | | | | | | (8013) ~ (all_52_4 = e2) % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | REDUCE: (358), (8011) imply: % 134.25/19.44 | | | | | | | | | | | | | (8014) ~ (all_52_13 = e2) % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | REDUCE: (7998), (8011) imply: % 134.25/19.44 | | | | | | | | | | | | | (8015) ~ (e3 = e2) % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | BETA: splitting (235) gives: % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | (8016) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 134.25/19.44 | | | | | | | | | | | | | | & op(e2, e3) = e2) % 134.25/19.44 | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | BETA: splitting (8016) gives: % 134.25/19.44 | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | (8017) all_57_0 = e2 & op(e3, e3) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | ALPHA: (8017) implies: % 134.25/19.44 | | | | | | | | | | | | | | | (8018) op(e3, e3) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | REF_CLOSE: (5), (7996), (8018), (function-axioms) are % 134.25/19.44 | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 134.25/19.44 | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | (8019) all_57_2 = e2 & op(e2, e3) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | ALPHA: (8019) implies: % 134.25/19.44 | | | | | | | | | | | | | | | (8020) op(e2, e3) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | REF_CLOSE: (167), (8012), (8020), (function-axioms) are % 134.25/19.44 | | | | | | | | | | | | | | | inconsistent by sub-proof #779. % 134.25/19.44 | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | End of split % 134.25/19.44 | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | (8021) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 134.25/19.44 | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 134.25/19.44 | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | BETA: splitting (8021) gives: % 134.25/19.44 | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | (8022) all_57_6 = e2 & op(e1, e3) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | REF_CLOSE: (163), (6997), (8022), (function-axioms) are % 134.25/19.44 | | | | | | | | | | | | | | | inconsistent by sub-proof #341. % 134.25/19.44 | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | (8023) all_57_12 = e2 & op(e0, e3) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | ALPHA: (8023) implies: % 134.25/19.44 | | | | | | | | | | | | | | | (8024) all_57_12 = e2 % 134.25/19.44 | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 134.25/19.44 | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | (8025) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 134.25/19.44 | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 134.25/19.44 | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | BETA: splitting (8025) gives: % 134.25/19.44 | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | (8026) all_57_0 = e2 & op(e3, e3) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | ALPHA: (8026) implies: % 134.25/19.44 | | | | | | | | | | | | | | | | | (8027) op(e3, e3) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237), % 134.25/19.44 | | | | | | | | | | | | | | | | | (8024), (8027), (function-axioms) are inconsistent % 134.25/19.44 | | | | | | | | | | | | | | | | | by sub-proof #290. % 134.25/19.44 | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | (8028) all_57_1 = e2 & op(e3, e2) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (8013), (8028), (function-axioms) are % 134.25/19.44 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #396. % 134.25/19.44 | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | End of split % 134.25/19.44 | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | (8029) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 134.25/19.44 | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 134.25/19.44 | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | BETA: splitting (8029) gives: % 134.25/19.44 | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | (8030) all_57_4 = e2 & op(e3, e1) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6999), (8030), (function-axioms) are % 134.25/19.44 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442. % 134.25/19.44 | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | (8031) all_57_9 = e2 & op(e3, e0) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | ALPHA: (8031) implies: % 134.25/19.44 | | | | | | | | | | | | | | | | | (8032) op(e3, e0) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 134.25/19.44 | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | (8033) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 134.25/19.44 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 134.25/19.44 | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | BETA: splitting (8033) gives: % 134.25/19.44 | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | (8034) all_57_2 = e2 & op(e2, e3) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | ALPHA: (8034) implies: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | (8035) op(e2, e3) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (8012), (8035), (function-axioms) are % 134.25/19.44 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #779. % 134.25/19.44 | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | (8036) all_57_3 = e2 & op(e2, e2) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | ALPHA: (8036) implies: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | (8037) all_57_3 = e2 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | (8038) op(e2, e2) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (8039) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8039) gives: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (8040) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8040) gives: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (8041) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8041) implies: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (8042) op(e3, e3) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237), % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (8024), (8042), (function-axioms) are inconsistent % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #290. % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (8043) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8043) implies: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (8044) op(e3, e3) = e1 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7996), (8044), (function-axioms) are % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (8045) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (168), (7998), (8032), (8045), % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | #110. % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (8046) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8046) gives: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (8047) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (8047), % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | #108. % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (8048) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8048) gives: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (8049) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8049) implies: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (8050) op(e2, e0) = e2 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8014), (8050), (function-axioms) are % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (8051) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8051) gives: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (8052) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8052) implies: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (8053) ~ (all_56_11 = e2) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (8054) op(e2, e2) = all_56_11 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8038), (8053), (8054), (function-axioms) are % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #531. % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (8055) op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8055) implies: % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (8056) op(e0, e0) = all_56_31 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (8057) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (159), (164), (165), (167), (225), % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (371), (7000), (7007), (7992), (8012), (8014), % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | (8037), (8038), (8056), (8057), (function-axioms) % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #101. % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.44 | | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.44 | | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | End of split % 134.25/19.44 | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | (8058) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 134.25/19.44 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 134.25/19.44 | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (7000), (8014), (8058), % 134.25/19.44 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.44 | | | | | | | | | | | | | | | | | | #625. % 134.25/19.44 | | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | | End of split % 134.25/19.44 | | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | | End of split % 134.25/19.44 | | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | | End of split % 134.25/19.44 | | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | | End of split % 134.25/19.44 | | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | End of split % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | (8059) all_54_5 = e1 | all_54_5 = e0 % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | REF_CLOSE: (267), (7008), (8005), (8059) are inconsistent by % 134.25/19.44 | | | | | | | | | | | | | sub-proof #624. % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | End of split % 134.25/19.44 | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | End of split % 134.25/19.44 | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | (8060) all_30_2 = e0 % 134.25/19.44 | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | COMBINE_EQS: (309), (8060) imply: % 134.25/19.44 | | | | | | | | | | | (8061) all_8_2 = e0 % 134.25/19.44 | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | SIMP: (8061) implies: % 134.25/19.44 | | | | | | | | | | | (8062) all_8_2 = e0 % 134.25/19.44 | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | COMBINE_EQS: (301), (8062) imply: % 134.25/19.44 | | | | | | | | | | | (8063) all_42_2 = e0 % 134.25/19.44 | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | REDUCE: (352), (8062) imply: % 134.25/19.44 | | | | | | | | | | | (8064) ~ (all_52_6 = e0) % 134.25/19.44 | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | REDUCE: (356), (8062) imply: % 134.25/19.44 | | | | | | | | | | | (8065) ~ (all_52_9 = e0) % 134.25/19.44 | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | REDUCE: (42), (8062) imply: % 134.25/19.44 | | | | | | | | | | | (8066) op(e2, e2) = e0 % 134.25/19.44 | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | BETA: splitting (215) gives: % 134.25/19.44 | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | (8067) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 % 134.25/19.44 | | | | | | | | | | | | & op(e1, e2) = e0) % 134.25/19.44 | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | BETA: splitting (8067) gives: % 134.25/19.44 | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | (8068) all_57_6 = e0 & op(e1, e3) = e0 % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | REF_CLOSE: (163), (7991), (8068), (function-axioms) are % 134.25/19.44 | | | | | | | | | | | | | inconsistent by sub-proof #73. % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | (8069) all_57_7 = e0 & op(e1, e2) = e0 % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | | REF_CLOSE: (162), (8064), (8069), (function-axioms) are % 134.25/19.44 | | | | | | | | | | | | | inconsistent by sub-proof #505. % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | End of split % 134.25/19.44 | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | Case 2: % 134.25/19.44 | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | (8070) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = % 134.25/19.44 | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 134.25/19.44 | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | BETA: splitting (8070) gives: % 134.25/19.44 | | | | | | | | | | | | % 134.25/19.44 | | | | | | | | | | | | Case 1: % 134.25/19.44 | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | (8071) all_57_8 = e0 & op(e1, e1) = e0 % 134.25/19.45 | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | REF_CLOSE: (5), (7006), (8071) are inconsistent by sub-proof % 134.25/19.45 | | | | | | | | | | | | | #573. % 134.25/19.45 | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | (8072) all_57_11 = e0 & op(e1, e0) = e0 % 134.25/19.45 | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | ALPHA: (8072) implies: % 134.25/19.45 | | | | | | | | | | | | | (8073) op(e1, e0) = e0 % 134.25/19.45 | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | BETA: splitting (219) gives: % 134.25/19.45 | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | (8074) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 134.25/19.45 | | | | | | | | | | | | | | & op(e2, e1) = e0) % 134.25/19.45 | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | BETA: splitting (8074) gives: % 134.25/19.45 | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | (8075) all_57_4 = e0 & op(e3, e1) = e0 % 134.25/19.45 | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | REF_CLOSE: (169), (7994), (8075), (function-axioms) are % 134.25/19.45 | | | | | | | | | | | | | | | inconsistent by sub-proof #224. % 134.25/19.45 | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | (8076) all_57_5 = e0 & op(e2, e1) = e0 % 134.25/19.45 | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | REF_CLOSE: (165), (8065), (8076), (function-axioms) are % 134.25/19.45 | | | | | | | | | | | | | | | inconsistent by sub-proof #455. % 134.25/19.45 | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | End of split % 134.25/19.45 | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | (8077) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 134.25/19.45 | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 134.25/19.45 | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | BETA: splitting (8077) gives: % 134.25/19.45 | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | (8078) all_57_8 = e0 & op(e1, e1) = e0 % 134.25/19.45 | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | REF_CLOSE: (5), (7006), (8078) are inconsistent by sub-proof % 134.25/19.45 | | | | | | | | | | | | | | | #83. % 134.25/19.45 | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | (8079) all_57_14 = e0 & op(e0, e1) = e0 % 134.25/19.45 | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | ALPHA: (8079) implies: % 134.25/19.45 | | | | | | | | | | | | | | | (8080) all_57_14 = e0 % 134.25/19.45 | | | | | | | | | | | | | | | (8081) op(e0, e1) = e0 % 134.25/19.45 | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | BETA: splitting (8001) gives: % 134.25/19.45 | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | (8082) ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 & % 134.25/19.45 | | | | | | | | | | | | | | | | $i(all_18_0) % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | ALPHA: (8082) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | (8083) ~ (all_18_0 = e3) % 134.25/19.45 | | | | | | | | | | | | | | | | (8084) op(e2, e1) = all_18_0 % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11, % 134.25/19.45 | | | | | | | | | | | | | | | | e0, e1, e0, simplifying with (157), (8081) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | (8085) all_52_11 = e0 % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 134.25/19.45 | | | | | | | | | | | | | | | | e0, e0, e1, simplifying with (160), (8073) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | (8086) all_52_14 = e0 % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, % 134.25/19.45 | | | | | | | | | | | | | | | | all_18_0, e1, e2, simplifying with (165), (8084) % 134.25/19.45 | | | | | | | | | | | | | | | | gives: % 134.25/19.45 | | | | | | | | | | | | | | | | (8087) all_52_9 = all_18_0 % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (8087) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | (8088) all_54_6 = all_18_0 % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | REDUCE: (125), (8085) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | (8089) ~ (all_52_7 = e0) % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | REDUCE: (123), (8087) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | (8090) ~ (all_52_8 = all_18_0) % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | REDUCE: (117), (8087) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | (8091) ~ (all_52_13 = all_18_0) % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | SIMP: (8091) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | (8092) ~ (all_52_13 = all_18_0) % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | REDUCE: (7000), (8087) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | (8093) ~ (all_18_0 = e2) % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | REDUCE: (8065), (8087) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | (8094) ~ (all_18_0 = e0) % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | REDUCE: (110), (8086) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | (8095) ~ (all_52_13 = e0) % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | REDUCE: (370), (8086) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | (8096) ~ (all_4_2 = e0) % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | SIMP: (8096) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | (8097) ~ (all_4_2 = e0) % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | REDUCE: (7002), (8086) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | (8098) ~ (e2 = e0) % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | (8099) all_54_6 = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | COMBINE_EQS: (8088), (8099) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | (8100) all_18_0 = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | REDUCE: (8083), (8100) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | (8101) $false % 134.25/19.45 | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | CLOSE: (8101) is inconsistent. % 134.25/19.45 | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | (8102) ~ (all_54_6 = e3) % 134.25/19.45 | | | | | | | | | | | | | | | | | (8103) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 134.25/19.45 | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | BETA: splitting (8103) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | (8104) all_54_6 = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8088), (8104) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | (8105) all_18_0 = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | REDUCE: (8093), (8105) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | (8106) $false % 134.25/19.45 | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | CLOSE: (8106) is inconsistent. % 134.25/19.45 | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | (8107) ~ (all_54_6 = e2) % 134.25/19.45 | | | | | | | | | | | | | | | | | | (8108) all_54_6 = e1 | all_54_6 = e0 % 134.25/19.45 | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | BETA: splitting (8108) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | (8109) all_54_6 = e1 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8088), (8109) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | (8110) all_18_0 = e1 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | REDUCE: (8090), (8110) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | (8111) ~ (all_52_8 = e1) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | REDUCE: (8093), (8110) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | (8112) ~ (e2 = e1) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | (8113) all_54_2 = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (8113) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | (8114) all_52_8 = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | SIMP: (8114) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | (8115) all_52_8 = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (8115) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | (8116) ~ (all_52_4 = e3) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (8115) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | (8117) ~ (all_52_12 = e3) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | SIMP: (8117) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | (8118) ~ (all_52_12 = e3) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | (8119) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (7996), (8116), (8119), % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | #197. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | (8120) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8120) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | (8121) all_57_4 = e3 & op(e3, e1) = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8121) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | (8122) all_57_4 = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | (8123) op(e3, e1) = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | (8124) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8124) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | (8125) all_57_4 = e1 & op(e3, e1) = e1 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8122), (8125) are inconsistent by sub-proof % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | #382. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | (8126) all_57_5 = e1 & op(e2, e1) = e1 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8126) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | (8127) all_57_5 = e1 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | (8128) all_54_15 = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (8128) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | (8129) all_4_2 = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8129) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | (8130) all_4_2 = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (8130) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | (8131) ~ (all_52_7 = e3) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (8130) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | (8132) ~ (all_52_13 = e3) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (8130) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | (8133) op(e0, e0) = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (8134) ~ (all_42_2 = e0) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8063), (8134) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (8135) $false % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8135) is inconsistent. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | (8136) ( ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_42_0)) | ( ~ (all_42_1 = e3) & op(e0, e0) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_42_1 & $i(all_42_1)) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8136) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8137) ~ (all_42_0 = e1) & op(e0, e2) = all_42_0 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_42_0) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8137) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8138) ~ (all_42_0 = e1) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8139) op(e0, e2) = all_42_0 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8140) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8140) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8141) all_57_2 = e3 & op(e2, e3) = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8141) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8142) all_57_2 = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8143) op(e2, e3) = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8144) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8144) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8145) all_57_0 = e2 & op(e3, e3) = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8145) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8146) op(e3, e3) = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7996), (8146), (function-axioms) are % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8147) all_57_2 = e2 & op(e2, e3) = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8142), (8147) are inconsistent by sub-proof % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #454. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8148) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8148) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8149) all_57_6 = e2 & op(e1, e3) = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6997), (8149), (function-axioms) are % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #341. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8150) all_57_12 = e2 & op(e0, e3) = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8150) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8151) all_57_12 = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8152) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8152) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8153) all_57_2 = e2 & op(e2, e3) = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8142), (8153) are inconsistent by sub-proof % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #454. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8154) all_57_3 = e2 & op(e2, e2) = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8154) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8155) all_57_3 = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (162), (170), (227), (7993), (8064), % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8089), (8155), (function-axioms) are inconsistent % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #503. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8156) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8156) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8157) all_57_5 = e2 & op(e2, e1) = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8157) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8158) op(e2, e1) = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7000), (8158), (function-axioms) are % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8159) all_57_10 = e2 & op(e2, e0) = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8159) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8160) all_57_10 = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8161) all_54_6 = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8088), (8161) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8162) all_18_0 = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8083), (8162) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8163) $false % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8163) is inconsistent. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8103) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8164) all_54_6 = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8088), (8164) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8165) all_18_0 = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8093), (8165) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8166) $false % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8166) is inconsistent. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8108) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8092), (8110) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8167) ~ (all_52_13 = e1) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8083), (8110) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8168) ~ (e3 = e1) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8169) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8169) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8170) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8170) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8171) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8171) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8172) op(e3, e3) = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237), % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8151), (8172), (function-axioms) are inconsistent % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #290. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8173) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8173) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8174) op(e3, e3) = e1 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (168), (169), (170), (232), (7993), % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7995), (8123), (8174), (function-axioms) are % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #599. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8175) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (8066), (8118), (8175), % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #622. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8176) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8176) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8177) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8177) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8178) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8178) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8179) ~ (all_56_9 = e2) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8180) op(e3, e2) = all_56_9 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8181) all_54_7 = e3 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8132), (8181) are inconsistent by % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #338. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8182) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8182) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8183) all_54_7 = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (8183) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8184) all_52_13 = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8184) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8185) all_52_13 = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (8185) imply: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8186) ~ (all_52_12 = e2) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8187) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8187) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8188) all_57_0 = e2 & op(e3, e3) = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8188) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8189) all_57_0 = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (231), (233), (8142), % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8151), (8189) are inconsistent by sub-proof #133. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8190) all_57_1 = e2 & op(e3, e2) = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8190) implies: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8191) op(e3, e2) = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8179), (8180), (8191), (function-axioms) are % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #199. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8192) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8192) gives: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8193) all_57_4 = e2 & op(e3, e1) = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6999), (8193), (function-axioms) are % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8194) all_57_9 = e2 & op(e3, e0) = e2 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8186), (8194), (function-axioms) are % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8195) all_54_7 = e1 | all_54_7 = e0 % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8095), (8167), (8195) are inconsistent by % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #313. % 134.25/19.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8196) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8196) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8197) op(e2, e1) = e2 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7000), (8197), (function-axioms) are % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8198) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8198) gives: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8199) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8199) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8200) op(e0, e2) = all_56_15 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (113), (133), (158), (170), (197), % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201), (223), (224), (228), (230), (259), (269), % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7995), (8066), (8095), (8116), (8118), (8131), % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8132), (8138), (8139), (8142), (8160), (8167), % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8200), (function-axioms) are inconsistent by % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #72. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8201) ~ (all_54_2 = e3) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (8201) imply: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8202) ~ (all_52_8 = e3) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (8123), (8202), (function-axioms) are % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #705. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8203) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8203) gives: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8204) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8204) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8205) ~ (all_56_3 = e3) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8206) op(e2, e3) = all_56_3 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8143), (8205), (8206), (function-axioms) are % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #347. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8207) op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8207) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8208) op(e0, e0) = all_56_31 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8209) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8209) gives: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8210) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8210) gives: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8211) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8211) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8212) op(e0, e3) = e0 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7992), (8212), (function-axioms) are % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8213) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8213) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8214) op(e0, e2) = e0 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8089), (8214), (function-axioms) are % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8215) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8215) gives: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8216) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8216) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8217) op(e0, e2) = all_56_15 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (113), (133), (158), (170), (197), % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201), (223), (224), (228), (230), (259), (269), % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7995), (8066), (8095), (8116), (8118), (8131), % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8132), (8138), (8139), (8142), (8160), (8167), % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8217), (function-axioms) are inconsistent by % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #72. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8218) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8218) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8219) all_56_31 = e1 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8208), (8219) imply: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8220) op(e0, e0) = e1 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8133), (8220), (function-axioms) are % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8221) ~ (all_54_2 = e3) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (8221) imply: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8222) ~ (all_52_8 = e3) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (8123), (8222), (function-axioms) are % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #705. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8223) all_54_6 = e0 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8088), (8223) imply: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8224) all_18_0 = e0 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8094), (8224) imply: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8225) $false % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8225) is inconsistent. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8226) all_57_3 = e3 & op(e2, e2) = e3 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8226) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8227) op(e2, e2) = e3 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8066), (8227), (function-axioms) are % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8228) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8228) gives: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8229) all_57_5 = e3 & op(e2, e1) = e3 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8229) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8230) all_57_5 = e3 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8127), (8230) are inconsistent by sub-proof % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #88. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8231) all_57_10 = e3 & op(e2, e0) = e3 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8132), (8231), (function-axioms) are % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8232) ~ (all_42_1 = e3) & op(e0, e0) = all_42_1 & % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_42_1) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8133), (8232), (function-axioms) are inconsistent % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #602. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | (8233) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (8003), (8097), (8233) are % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #746. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | (8234) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8234) gives: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | (8235) all_57_8 = e1 & op(e1, e1) = e1 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7006), (8235) are inconsistent by sub-proof % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | #574. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | (8236) all_57_14 = e1 & op(e0, e1) = e1 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8236) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | (8237) all_57_14 = e1 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8080), (8237) are inconsistent by sub-proof % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | #221. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | (8238) all_57_9 = e3 & op(e3, e0) = e3 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8238) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | (8239) op(e3, e0) = e3 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8118), (8239), (function-axioms) are % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #733. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | (8240) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (6999), (7994), (8111), (8240) are % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #71. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | (8241) all_54_6 = e0 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8088), (8241) imply: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | (8242) all_18_0 = e0 % 134.25/19.46 | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | REDUCE: (8094), (8242) imply: % 134.25/19.46 | | | | | | | | | | | | | | | | | | | (8243) $false % 134.25/19.46 | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | | CLOSE: (8243) is inconsistent. % 134.25/19.46 | | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | (8244) ~ (all_18_1 = e0) & op(e2, e2) = all_18_1 & % 134.25/19.46 | | | | | | | | | | | | | | | | $i(all_18_1) % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | ALPHA: (8244) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | (8245) ~ (all_18_1 = e0) % 134.25/19.46 | | | | | | | | | | | | | | | | (8246) op(e2, e2) = all_18_1 % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_18_1, % 134.25/19.46 | | | | | | | | | | | | | | | | e2, e2, simplifying with (8066), (8246) gives: % 134.25/19.46 | | | | | | | | | | | | | | | | (8247) all_18_1 = e0 % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | REDUCE: (8245), (8247) imply: % 134.25/19.46 | | | | | | | | | | | | | | | | (8248) $false % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | CLOSE: (8248) is inconsistent. % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | End of split % 134.25/19.46 | | | | | | | | | | % 134.25/19.46 | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | (8249) all_20_2 = e2 % 134.25/19.46 | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | COMBINE_EQS: (318), (8249) imply: % 134.25/19.46 | | | | | | | | | | (8250) all_4_2 = e2 % 134.25/19.46 | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | REDUCE: (349), (8250) imply: % 134.25/19.46 | | | | | | | | | | (8251) ~ (all_52_3 = e2) % 134.25/19.46 | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | REDUCE: (368), (8250) imply: % 134.25/19.46 | | | | | | | | | | (8252) ~ (all_52_12 = e2) % 134.25/19.46 | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | REDUCE: (36), (8250) imply: % 134.25/19.46 | | | | | | | | | | (8253) op(e0, e0) = e2 % 134.25/19.46 | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | BETA: splitting (67) gives: % 134.25/19.46 | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | Case 1: % 134.25/19.46 | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | (8254) ~ (all_24_2 = e0) % 134.25/19.46 | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | REDUCE: (7989), (8254) imply: % 134.25/19.46 | | | | | | | | | | | (8255) $false % 134.25/19.46 | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | CLOSE: (8255) is inconsistent. % 134.25/19.46 | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | (8256) ( ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 & % 134.25/19.46 | | | | | | | | | | | $i(all_24_0)) | ( ~ (all_24_1 = e2) & op(e0, e0) % 134.25/19.46 | | | | | | | | | | | = all_24_1 & $i(all_24_1)) % 134.25/19.46 | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | BETA: splitting (8256) gives: % 134.25/19.46 | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | Case 1: % 134.25/19.46 | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | (8257) ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 & % 134.25/19.46 | | | | | | | | | | | | $i(all_24_0) % 134.25/19.46 | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | ALPHA: (8257) implies: % 134.25/19.46 | | | | | | | | | | | | (8258) ~ (all_24_0 = e1) % 134.25/19.46 | | | | | | | | | | | | (8259) op(e0, e3) = all_24_0 % 134.25/19.46 | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | BETA: splitting (235) gives: % 134.25/19.46 | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | Case 1: % 134.25/19.46 | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | (8260) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 134.25/19.46 | | | | | | | | | | | | | & op(e2, e3) = e2) % 134.25/19.46 | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | BETA: splitting (8260) gives: % 134.25/19.46 | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | Case 1: % 134.25/19.46 | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | (8261) all_57_0 = e2 & op(e3, e3) = e2 % 134.25/19.46 | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | ALPHA: (8261) implies: % 134.25/19.46 | | | | | | | | | | | | | | (8262) op(e3, e3) = e2 % 134.25/19.46 | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | REF_CLOSE: (5), (7996), (8262), (function-axioms) are % 134.25/19.46 | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 134.25/19.46 | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | (8263) all_57_2 = e2 & op(e2, e3) = e2 % 134.25/19.46 | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | ALPHA: (8263) implies: % 134.25/19.46 | | | | | | | | | | | | | | (8264) all_57_2 = e2 % 134.25/19.46 | | | | | | | | | | | | | | (8265) op(e2, e3) = e2 % 134.25/19.46 | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | BETA: splitting (236) gives: % 134.25/19.46 | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | Case 1: % 134.25/19.46 | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | (8266) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 134.25/19.46 | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 134.25/19.46 | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | BETA: splitting (8266) gives: % 134.25/19.46 | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | Case 1: % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | (8267) all_57_0 = e2 & op(e3, e3) = e2 % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | ALPHA: (8267) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | (8268) op(e3, e3) = e2 % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7996), (8268), (function-axioms) are % 134.25/19.46 | | | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | Case 2: % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | (8269) all_57_1 = e2 & op(e3, e2) = e2 % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | ALPHA: (8269) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | (8270) all_57_1 = e2 % 134.25/19.46 | | | | | | | | | | | | | | | | (8271) op(e3, e2) = e2 % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, % 134.25/19.46 | | | | | | | | | | | | | | | | all_24_0, e3, e0, simplifying with (159), (8259) % 134.25/19.46 | | | | | | | | | | | | | | | | gives: % 134.25/19.46 | | | | | | | | | | | | | | | | (8272) all_52_3 = all_24_0 % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2, % 134.25/19.46 | | | | | | | | | | | | | | | | e3, e2, simplifying with (167), (8265) gives: % 134.25/19.46 | | | | | | | | | | | | | | | | (8273) all_52_1 = e2 % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2, % 134.25/19.46 | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (8271) gives: % 134.25/19.46 | | | | | | | | | | | | | | | | (8274) all_52_4 = e2 % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (8272) imply: % 134.25/19.46 | | | | | | | | | | | | | | | | (8275) all_54_12 = all_24_0 % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | REDUCE: (146), (8273) imply: % 134.25/19.46 | | | | | | | | | | | | | | | | (8276) ~ (all_52_9 = e2) % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | REDUCE: (145), (8273) imply: % 134.25/19.46 | | | | | | | | | | | | | | | | (8277) ~ (all_52_13 = e2) % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | SIMP: (8277) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | (8278) ~ (all_52_13 = e2) % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | REDUCE: (144), (8272) imply: % 134.25/19.46 | | | | | | | | | | | | | | | | (8279) ~ (all_52_2 = all_24_0) % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | REDUCE: (140), (8272) imply: % 134.25/19.46 | | | | | | | | | | | | | | | | (8280) ~ (all_52_7 = all_24_0) % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | SIMP: (8280) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | (8281) ~ (all_52_7 = all_24_0) % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | REDUCE: (139), (8272) imply: % 134.25/19.46 | | | | | | | | | | | | | | | | (8282) ~ (all_52_11 = all_24_0) % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | SIMP: (8282) implies: % 134.25/19.46 | | | | | | | | | | | | | | | | (8283) ~ (all_52_11 = all_24_0) % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | REDUCE: (8251), (8272) imply: % 134.25/19.46 | | | | | | | | | | | | | | | | (8284) ~ (all_24_0 = e2) % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | REDUCE: (7992), (8272) imply: % 134.25/19.46 | | | | | | | | | | | | | | | | (8285) ~ (all_24_0 = e0) % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | BETA: splitting (192) gives: % 134.25/19.46 | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | Case 1: % 134.25/19.46 | | | | | | | | | | | | | | | | | % 134.25/19.46 | | | | | | | | | | | | | | | | | (8286) all_54_12 = e3 % 134.25/19.47 | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | COMBINE_EQS: (8275), (8286) imply: % 134.25/19.47 | | | | | | | | | | | | | | | | | (8287) all_24_0 = e3 % 134.25/19.47 | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | SIMP: (8287) implies: % 134.25/19.47 | | | | | | | | | | | | | | | | | (8288) all_24_0 = e3 % 134.25/19.47 | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | REDUCE: (8279), (8288) imply: % 134.25/19.47 | | | | | | | | | | | | | | | | | (8289) ~ (all_52_2 = e3) % 134.25/19.47 | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | REDUCE: (8281), (8288) imply: % 134.25/19.47 | | | | | | | | | | | | | | | | | (8290) ~ (all_52_7 = e3) % 134.25/19.47 | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | REDUCE: (8283), (8288) imply: % 134.25/19.47 | | | | | | | | | | | | | | | | | (8291) ~ (all_52_11 = e3) % 134.25/19.47 | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | (8292) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 134.25/19.47 | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 134.25/19.47 | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (7996), (8264), (8292), % 134.25/19.47 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.47 | | | | | | | | | | | | | | | | | | #70. % 134.25/19.47 | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | (8293) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 134.25/19.47 | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | BETA: splitting (8293) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | (8294) all_57_6 = e3 & op(e1, e3) = e3 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (8289), (8294), (function-axioms) are % 134.25/19.47 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #761. % 134.25/19.47 | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | (8295) all_57_12 = e3 & op(e0, e3) = e3 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | ALPHA: (8295) implies: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | (8296) all_57_12 = e3 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | (8297) op(e0, e3) = e3 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | (8298) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7996), (8265), (8298), % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | #69. % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | (8299) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8299) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | (8300) all_57_6 = e1 & op(e1, e3) = e1 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8300) implies: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | (8301) all_57_6 = e1 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | (8302) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8302) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8303) all_57_1 = e3 & op(e3, e2) = e3 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8303) implies: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8304) all_57_1 = e3 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8270), (8304) imply: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8305) e3 = e2 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8305) implies: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8306) e3 = e2 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8296), (8306) imply: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8307) all_57_12 = e2 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (208), (209), % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (211), (8253), (8291), (8307), (function-axioms) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #458. % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8308) all_57_3 = e3 & op(e2, e2) = e3 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8308) implies: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8309) op(e2, e2) = e3 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (7998), (8309), (function-axioms) are % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228. % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | (8310) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8310) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8311) all_57_7 = e3 & op(e1, e2) = e3 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8311) implies: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8312) all_57_7 = e3 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8313) op(e1, e2) = e3 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (8314) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8314) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (8315) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8315) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (8316) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8316) implies: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (8317) op(e3, e3) = e2 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (231), (8264), (8296), (8301), % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (8317), (function-axioms) are inconsistent by % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #491. % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (8318) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8318) implies: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (8319) op(e3, e3) = e1 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7996), (8319), (function-axioms) are % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (8320) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (7998), (8297), (8320), (function-axioms) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #68. % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (8321) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8321) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (8322) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (8322), % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | #108. % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (8323) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8323) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (8324) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8324) implies: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (8325) op(e2, e0) = e2 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8278), (8325), (function-axioms) are % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (8326) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8326) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8327) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8327) implies: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8328) ~ (all_56_11 = e2) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8329) op(e1, e2) = e1 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8330) op(e2, e2) = all_56_11 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8331) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8331) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8332) all_57_1 = e0 & op(e3, e2) = e0 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (7993), (8332), (function-axioms) are % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #693. % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8333) all_57_3 = e0 & op(e2, e2) = e0 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8333) implies: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8334) op(e2, e2) = e0 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8001) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e3, e2, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (8313), (8329) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8335) e3 = e1 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8296), (8335) imply: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8336) all_57_12 = e1 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (211), (8253), (8290), % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8291), (8336), (function-axioms) are inconsistent % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #123. % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8337) ~ (all_18_1 = e0) & op(e2, e2) = all_18_1 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_18_1) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8334), (8337), (function-axioms) are inconsistent % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #103. % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8338) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8338) gives: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8339) all_57_7 = e0 & op(e1, e2) = e0 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8312), (8339) are inconsistent by sub-proof % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #147. % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8340) all_57_13 = e0 & op(e0, e2) = e0 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8340) implies: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8341) op(e0, e2) = e0 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (158), (199), (267), (354), (7008), (7998), % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8328), (8330), (8341), (function-axioms) are % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #227. % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8342) op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8342) implies: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8343) op(e0, e0) = all_56_31 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8344) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (157), (158), % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (199), (208), (209), (211), (267), (354), (7008), % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7998), (8253), (8291), (8296), (8297), (8343), % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8344), (function-axioms) are inconsistent by % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #208. % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | (8345) all_57_13 = e3 & op(e0, e2) = e3 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8290), (8345), (function-axioms) are % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #556. % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | (8346) all_57_12 = e1 & op(e0, e3) = e1 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8346) implies: % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | (8347) all_57_12 = e1 % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (211), (8253), (8290), % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | (8291), (8347), (function-axioms) are inconsistent % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | by sub-proof #123. % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | (8348) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 134.25/19.47 | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | | REF_CLOSE: (8258), (8275), (8284), (8285), (8348) are % 134.25/19.47 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #205. % 134.25/19.47 | | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | (8349) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 134.25/19.47 | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 134.25/19.47 | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | BETA: splitting (8349) gives: % 134.25/19.47 | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | Case 1: % 134.25/19.47 | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | (8350) all_57_4 = e2 & op(e3, e1) = e2 % 134.25/19.47 | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6999), (8350), (function-axioms) are % 134.25/19.47 | | | | | | | | | | | | | | | | inconsistent by sub-proof #442. % 134.25/19.47 | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | (8351) all_57_9 = e2 & op(e3, e0) = e2 % 134.25/19.47 | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8252), (8351), (function-axioms) are % 134.25/19.47 | | | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 134.25/19.47 | | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | | End of split % 134.25/19.47 | | | | | | | | | | | | | % 134.25/19.47 | | | | | | | | | | | | Case 2: % 134.25/19.47 | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | (8352) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 134.25/19.48 | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 134.25/19.48 | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | BETA: splitting (8352) gives: % 134.25/19.48 | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | (8353) all_57_6 = e2 & op(e1, e3) = e2 % 134.25/19.48 | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | REF_CLOSE: (163), (6997), (8353), (function-axioms) are % 134.25/19.48 | | | | | | | | | | | | | | inconsistent by sub-proof #341. % 134.25/19.48 | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | (8354) all_57_12 = e2 & op(e0, e3) = e2 % 134.25/19.48 | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | REF_CLOSE: (159), (8251), (8354), (function-axioms) are % 134.25/19.48 | | | | | | | | | | | | | | inconsistent by sub-proof #97. % 134.25/19.48 | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | End of split % 134.25/19.48 | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | End of split % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | (8355) ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 & % 134.25/19.48 | | | | | | | | | | | | $i(all_24_1) % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | REF_CLOSE: (8253), (8355), (function-axioms) are inconsistent % 134.25/19.48 | | | | | | | | | | | | by sub-proof #204. % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | End of split % 134.25/19.48 | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | End of split % 134.25/19.48 | | | | | | | | | | % 134.25/19.48 | | | | | | | | | End of split % 134.25/19.48 | | | | | | | | | % 134.25/19.48 | | | | | | | | End of split % 134.25/19.48 | | | | | | | | % 134.25/19.48 | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | % 134.25/19.48 | | | | | | | | (8356) all_14_2 = e3 % 134.25/19.48 | | | | | | | | (8357) ( ~ (all_14_0 = e1) & op(e3, e2) = all_14_0 & % 134.25/19.48 | | | | | | | | $i(all_14_0)) | ( ~ (all_14_1 = e0) & op(e3, e3) = % 134.25/19.48 | | | | | | | | all_14_1 & $i(all_14_1)) % 134.25/19.48 | | | | | | | | % 134.25/19.48 | | | | | | | | COMBINE_EQS: (329), (8356) imply: % 134.25/19.48 | | | | | | | | (8358) all_8_2 = e3 % 134.25/19.48 | | | | | | | | % 134.25/19.48 | | | | | | | | SIMP: (8358) implies: % 134.25/19.48 | | | | | | | | (8359) all_8_2 = e3 % 134.25/19.48 | | | | | | | | % 134.25/19.48 | | | | | | | | REDUCE: (347), (8359) imply: % 134.25/19.48 | | | | | | | | (8360) ~ (all_52_1 = e3) % 134.25/19.48 | | | | | | | | % 134.25/19.48 | | | | | | | | REDUCE: (350), (8359) imply: % 134.25/19.48 | | | | | | | | (8361) ~ (all_52_4 = e3) % 134.25/19.48 | | | | | | | | % 134.25/19.48 | | | | | | | | REDUCE: (352), (8359) imply: % 134.25/19.48 | | | | | | | | (8362) ~ (all_52_6 = e3) % 134.25/19.48 | | | | | | | | % 134.25/19.48 | | | | | | | | REDUCE: (354), (8359) imply: % 134.25/19.48 | | | | | | | | (8363) ~ (all_52_7 = e3) % 134.25/19.48 | | | | | | | | % 134.25/19.48 | | | | | | | | REDUCE: (356), (8359) imply: % 134.25/19.48 | | | | | | | | (8364) ~ (all_52_9 = e3) % 134.25/19.48 | | | | | | | | % 134.25/19.48 | | | | | | | | REDUCE: (358), (8359) imply: % 134.25/19.48 | | | | | | | | (8365) ~ (all_52_13 = e3) % 134.25/19.48 | | | | | | | | % 134.25/19.48 | | | | | | | | BETA: splitting (230) gives: % 134.25/19.48 | | | | | | | | % 134.25/19.48 | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | % 134.25/19.48 | | | | | | | | | (8366) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & % 134.25/19.48 | | | | | | | | | op(e2, e2) = e3) % 134.25/19.48 | | | | | | | | | % 134.25/19.48 | | | | | | | | | BETA: splitting (8366) gives: % 134.25/19.48 | | | | | | | | | % 134.25/19.48 | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | (8367) all_57_1 = e3 & op(e3, e2) = e3 % 134.25/19.48 | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | ALPHA: (8367) implies: % 134.25/19.48 | | | | | | | | | | (8368) op(e3, e2) = e3 % 134.25/19.48 | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | REF_CLOSE: (170), (8361), (8368), (function-axioms) are % 134.25/19.48 | | | | | | | | | | inconsistent by sub-proof #738. % 134.25/19.48 | | | | | | | | | | % 134.25/19.48 | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | (8369) all_57_3 = e3 & op(e2, e2) = e3 % 134.25/19.48 | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | ALPHA: (8369) implies: % 134.25/19.48 | | | | | | | | | | (8370) all_57_3 = e3 % 134.25/19.48 | | | | | | | | | | (8371) op(e2, e2) = e3 % 134.25/19.48 | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | BETA: splitting (6995) gives: % 134.25/19.48 | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | (8372) ~ (all_6_0 = e0) & op(e2, e1) = all_6_0 & % 134.25/19.48 | | | | | | | | | | | $i(all_6_0) % 134.25/19.48 | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | ALPHA: (8372) implies: % 134.25/19.48 | | | | | | | | | | | (8373) ~ (all_6_0 = e0) % 134.25/19.48 | | | | | | | | | | | (8374) op(e2, e1) = all_6_0 % 134.25/19.48 | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | BETA: splitting (8357) gives: % 134.25/19.48 | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | (8375) ~ (all_14_0 = e1) & op(e3, e2) = all_14_0 & % 134.25/19.48 | | | | | | | | | | | | $i(all_14_0) % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | ALPHA: (8375) implies: % 134.25/19.48 | | | | | | | | | | | | (8376) ~ (all_14_0 = e1) % 134.25/19.48 | | | | | | | | | | | | (8377) op(e3, e2) = all_14_0 % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, % 134.25/19.48 | | | | | | | | | | | | all_6_0, e1, e2, simplifying with (165), (8374) % 134.25/19.48 | | | | | | | | | | | | gives: % 134.25/19.48 | | | | | | | | | | | | (8378) all_52_9 = all_6_0 % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 134.25/19.48 | | | | | | | | | | | | all_14_0, e2, e3, simplifying with (170), (8377) % 134.25/19.48 | | | | | | | | | | | | gives: % 134.25/19.48 | | | | | | | | | | | | (8379) all_52_4 = all_14_0 % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | COMBINE_EQS: (260), (8378) imply: % 134.25/19.48 | | | | | | | | | | | | (8380) all_54_6 = all_6_0 % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | COMBINE_EQS: (271), (8379) imply: % 134.25/19.48 | | | | | | | | | | | | (8381) all_54_1 = all_14_0 % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | REDUCE: (146), (8378) imply: % 134.25/19.48 | | | | | | | | | | | | (8382) ~ (all_52_1 = all_6_0) % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | REDUCE: (136), (8379) imply: % 134.25/19.48 | | | | | | | | | | | | (8383) ~ (all_52_6 = all_14_0) % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | SIMP: (8383) implies: % 134.25/19.48 | | | | | | | | | | | | (8384) ~ (all_52_6 = all_14_0) % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | REDUCE: (134), (8379) imply: % 134.25/19.48 | | | | | | | | | | | | (8385) ~ (all_52_8 = all_14_0) % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | SIMP: (8385) implies: % 134.25/19.48 | | | | | | | | | | | | (8386) ~ (all_52_8 = all_14_0) % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | REDUCE: (133), (8379) imply: % 134.25/19.48 | | | | | | | | | | | | (8387) ~ (all_52_12 = all_14_0) % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | SIMP: (8387) implies: % 134.25/19.48 | | | | | | | | | | | | (8388) ~ (all_52_12 = all_14_0) % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | REDUCE: (8361), (8379) imply: % 134.25/19.48 | | | | | | | | | | | | (8389) ~ (all_14_0 = e3) % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | REDUCE: (7993), (8379) imply: % 134.25/19.48 | | | | | | | | | | | | (8390) ~ (all_14_0 = e0) % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | REDUCE: (123), (8378) imply: % 134.25/19.48 | | | | | | | | | | | | (8391) ~ (all_52_8 = all_6_0) % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | REDUCE: (117), (8378) imply: % 134.25/19.48 | | | | | | | | | | | | (8392) ~ (all_52_13 = all_6_0) % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | SIMP: (8392) implies: % 134.25/19.48 | | | | | | | | | | | | (8393) ~ (all_52_13 = all_6_0) % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | REDUCE: (8364), (8378) imply: % 134.25/19.48 | | | | | | | | | | | | (8394) ~ (all_6_0 = e3) % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | REDUCE: (7000), (8378) imply: % 134.25/19.48 | | | | | | | | | | | | (8395) ~ (all_6_0 = e2) % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | BETA: splitting (203) gives: % 134.25/19.48 | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | (8396) all_54_1 = e3 % 134.25/19.48 | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | COMBINE_EQS: (8381), (8396) imply: % 134.25/19.48 | | | | | | | | | | | | | (8397) all_14_0 = e3 % 134.25/19.48 | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | REDUCE: (8389), (8397) imply: % 134.25/19.48 | | | | | | | | | | | | | (8398) $false % 134.25/19.48 | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | CLOSE: (8398) is inconsistent. % 134.25/19.48 | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | (8399) ~ (all_54_1 = e3) % 134.25/19.48 | | | | | | | | | | | | | (8400) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 134.25/19.48 | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | BETA: splitting (219) gives: % 134.25/19.48 | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | (8401) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 % 134.25/19.48 | | | | | | | | | | | | | | & op(e2, e1) = e0) % 134.25/19.48 | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | BETA: splitting (8401) gives: % 134.25/19.48 | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | (8402) all_57_4 = e0 & op(e3, e1) = e0 % 134.25/19.48 | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | REF_CLOSE: (169), (7994), (8402), (function-axioms) are % 134.25/19.48 | | | | | | | | | | | | | | | inconsistent by sub-proof #224. % 134.25/19.48 | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | (8403) all_57_5 = e0 & op(e2, e1) = e0 % 134.25/19.48 | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | ALPHA: (8403) implies: % 134.25/19.48 | | | | | | | | | | | | | | | (8404) all_57_5 = e0 % 134.25/19.48 | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 134.25/19.48 | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | (8405) all_54_6 = e3 % 134.25/19.48 | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | REF_CLOSE: (8380), (8394), (8405) are inconsistent by % 134.25/19.48 | | | | | | | | | | | | | | | | sub-proof #79. % 134.25/19.48 | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | (8406) ~ (all_54_6 = e3) % 134.25/19.48 | | | | | | | | | | | | | | | | (8407) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | BETA: splitting (8407) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | (8408) all_54_6 = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | REF_CLOSE: (8380), (8395), (8408) are inconsistent by % 134.25/19.48 | | | | | | | | | | | | | | | | | sub-proof #78. % 134.25/19.48 | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | (8409) all_54_6 = e1 | all_54_6 = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | BETA: splitting (8409) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | (8410) all_54_6 = e1 % 134.25/19.48 | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8380), (8410) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | (8411) all_6_0 = e1 % 134.25/19.48 | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | SIMP: (8411) implies: % 134.25/19.48 | | | | | | | | | | | | | | | | | | (8412) all_6_0 = e1 % 134.25/19.48 | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | REDUCE: (8382), (8412) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | (8413) ~ (all_52_1 = e1) % 134.25/19.48 | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | REDUCE: (8393), (8412) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | (8414) ~ (all_52_13 = e1) % 134.25/19.48 | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | REDUCE: (8394), (8412) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | (8415) ~ (e3 = e1) % 134.25/19.48 | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | (8416) all_54_4 = e3 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (8416) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | (8417) all_52_1 = e3 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | REDUCE: (8360), (8417) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | (8418) $false % 134.25/19.48 | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | CLOSE: (8418) is inconsistent. % 134.25/19.48 | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | (8419) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | BETA: splitting (8419) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (8420) all_54_4 = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (8420) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (8421) all_52_1 = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (8421) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (8422) ~ (all_52_13 = e2) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | SIMP: (8422) implies: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (8423) ~ (all_52_13 = e2) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (8421) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (8424) op(e2, e3) = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | (8425) all_54_7 = e3 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8365), (8425) are inconsistent by % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | sub-proof #338. % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | (8426) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8426) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | (8427) all_54_7 = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8423), (8427) are inconsistent by % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | sub-proof #337. % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | (8428) all_54_7 = e1 | all_54_7 = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8428) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | (8429) all_54_7 = e1 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8414), (8429) are inconsistent by % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #314. % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | (8430) all_54_7 = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (8430) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | (8431) all_52_13 = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8431) implies: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | (8432) all_52_13 = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8414), (8432) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | (8433) ~ (e1 = e0) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (8432) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | (8434) op(e2, e0) = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | (8435) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (8371), (8424), (8435), % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | #292. % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | (8436) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8436) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | (8437) all_57_5 = e1 & op(e2, e1) = e1 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8404), (8437) are inconsistent by sub-proof % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | #365. % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | (8438) all_57_10 = e1 & op(e2, e0) = e1 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8438) implies: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | (8439) op(e2, e0) = e1 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8434), (8439), (function-axioms) are % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #695. % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (8440) all_54_4 = e1 | all_54_4 = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7990), (8413), (8440) are inconsistent by % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | sub-proof #153. % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.48 | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | End of split % 134.25/19.48 | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | (8441) all_54_6 = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8373), (8380), (8441) are inconsistent by % 134.25/19.48 | | | | | | | | | | | | | | | | | | sub-proof #75. % 134.25/19.48 | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | End of split % 134.25/19.48 | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | End of split % 134.25/19.48 | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | End of split % 134.25/19.48 | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | End of split % 134.25/19.48 | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | (8442) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = % 134.25/19.48 | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 134.25/19.48 | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | BETA: splitting (8442) gives: % 134.25/19.48 | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | (8443) all_57_8 = e0 & op(e1, e1) = e0 % 134.25/19.48 | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | REF_CLOSE: (5), (7006), (8443) are inconsistent by sub-proof % 134.25/19.48 | | | | | | | | | | | | | | | #83. % 134.25/19.48 | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | (8444) all_57_14 = e0 & op(e0, e1) = e0 % 134.25/19.48 | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | ALPHA: (8444) implies: % 134.25/19.48 | | | | | | | | | | | | | | | (8445) all_57_14 = e0 % 134.25/19.48 | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 134.25/19.48 | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | (8446) all_54_6 = e3 % 134.25/19.48 | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | REF_CLOSE: (8380), (8394), (8446) are inconsistent by % 134.25/19.48 | | | | | | | | | | | | | | | | sub-proof #79. % 134.25/19.48 | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | (8447) ~ (all_54_6 = e3) % 134.25/19.48 | | | | | | | | | | | | | | | | (8448) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | BETA: splitting (8448) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | (8449) all_54_6 = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | REF_CLOSE: (8380), (8395), (8449) are inconsistent by % 134.25/19.48 | | | | | | | | | | | | | | | | | sub-proof #78. % 134.25/19.48 | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | (8450) ~ (all_54_6 = e2) % 134.25/19.48 | | | | | | | | | | | | | | | | | (8451) all_54_6 = e1 | all_54_6 = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | (8452) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 134.25/19.48 | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 134.25/19.48 | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | BETA: splitting (8452) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | (8453) all_57_4 = e3 & op(e3, e1) = e3 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | ALPHA: (8453) implies: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | (8454) all_57_4 = e3 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (8455) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (167), (7990), (8371), (8455), % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | #203. % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | (8456) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8456) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | (8457) all_57_5 = e0 & op(e2, e1) = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8457) implies: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | (8458) all_57_5 = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (220), (7006), (8445), (8454), % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | (8458) are inconsistent by sub-proof #84. % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | (8459) all_57_10 = e0 & op(e2, e0) = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8459) implies: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | (8460) op(e2, e0) = e0 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | (8461) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8461) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | (8462) all_57_2 = e2 & op(e2, e3) = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8462) implies: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | (8463) all_57_2 = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8400) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | (8464) all_54_1 = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8381), (8464) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | (8465) all_14_0 = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8388), (8465) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | (8466) ~ (all_52_12 = e2) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8389), (8465) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | (8467) ~ (e3 = e2) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | (8468) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8468) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (8469) all_57_1 = e2 & op(e3, e2) = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8469) implies: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (8470) all_57_1 = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (8471) op(e3, e2) = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8451) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8472) all_54_6 = e1 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8380), (8472) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8473) all_6_0 = e1 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8473) implies: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8474) all_6_0 = e1 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8391), (8474) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8475) ~ (all_52_8 = e1) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8394), (8474) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8476) ~ (e3 = e1) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8395), (8474) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8477) ~ (e2 = e1) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8478) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (8460), (8466), (8478), % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #200. % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8479) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8479) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8480) all_57_11 = e2 & op(e1, e0) = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8480) implies: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8481) all_57_11 = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (215), (216), % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (7006), (8362), (8481), (function-axioms) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #571. % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8482) all_57_15 = e2 & op(e0, e0) = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8482) implies: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8483) op(e0, e0) = e2 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8484) all_54_2 = e3 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (8484) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8485) all_52_8 = e3 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8485) implies: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8486) all_52_8 = e3 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (8486) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8487) ~ (all_52_11 = e3) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8487) implies: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8488) ~ (all_52_11 = e3) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (8486) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8489) ~ (all_52_12 = e3) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8489) implies: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8490) ~ (all_52_12 = e3) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (8486) imply: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8491) op(e3, e1) = e3 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8492) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (168), (169), (170), (232), (7993), % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7995), (8470), (8491), (8492), (function-axioms) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #202. % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8493) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8493) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8494) all_57_4 = e1 & op(e3, e1) = e1 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8454), (8494) are inconsistent by sub-proof % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #382. % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8495) all_57_9 = e1 & op(e3, e0) = e1 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8495) implies: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8496) all_57_9 = e1 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8497) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8497) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8498) all_57_12 = e3 & op(e0, e3) = e3 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8498) implies: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8499) all_57_12 = e3 % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8500) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8500) gives: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8501) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (231), (232), % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (236), (238), (7993), (8463), (8496), % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8499), (8501), (function-axioms) are inconsistent % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #116. % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8502) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8471), (8490), (8502), (function-axioms) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #198. % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8503) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8503) gives: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8504) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (8504), % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #108. % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8505) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8505) gives: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8506) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8506) implies: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8507) op(e2, e2) = e0 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8371), (8507), (function-axioms) are % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8508) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (91), (157), (190), (246), (332), % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364), (7001), (8460), (8483), (8508), % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #67. % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8509) all_57_13 = e3 & op(e0, e2) = e3 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8363), (8509), (function-axioms) are % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #556. % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8510) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (8483), (8488), (8510), % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #459. % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8511) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (6999), (7994), (8475), (8511) are % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #71. % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8512) all_54_6 = e0 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8373), (8380), (8512) are inconsistent by % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #75. % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (8513) all_57_3 = e2 & op(e2, e2) = e2 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8513) implies: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (8514) all_57_3 = e2 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8370), (8514) are inconsistent by sub-proof % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | #762. % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | (8515) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8515) gives: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (8516) all_57_7 = e2 & op(e1, e2) = e2 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (6998), (8516), (function-axioms) are % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515. % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (8517) all_57_13 = e2 & op(e0, e2) = e2 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (168), (169), (227), % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (236), (6999), (7996), (8370), (8466), % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (8517), (function-axioms) are inconsistent by % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #193. % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | (8518) all_54_1 = e1 | all_54_1 = e0 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8376), (8381), (8390), (8518) are inconsistent by % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #192. % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | (8519) all_57_3 = e2 & op(e2, e2) = e2 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8370), (8519) are inconsistent by sub-proof % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | #375. % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | (8520) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8520) gives: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | (8521) all_57_5 = e2 & op(e2, e1) = e2 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8521) implies: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | (8522) op(e2, e1) = e2 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7000), (8522), (function-axioms) are % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770. % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | (8523) all_57_10 = e2 & op(e2, e0) = e2 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8523) implies: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | (8524) op(e2, e0) = e2 % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8460), (8524), (function-axioms) are % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #451. % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | | End of split % 134.25/19.49 | | | | | | | | | | | | | | | | | | | % 134.25/19.49 | | | | | | | | | | | | | | | | | | Case 2: % 134.25/19.49 | | | | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | | | | (8525) all_57_5 = e3 & op(e2, e1) = e3 % 134.53/19.49 | | | | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (8364), (8525), (function-axioms) are % 134.53/19.49 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 134.53/19.49 | | | | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.49 | | | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.49 | | | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | | | (8526) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 134.53/19.49 | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 134.53/19.49 | | | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | | | BETA: splitting (8526) gives: % 134.53/19.49 | | | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.49 | | | | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | | | | (8527) all_57_8 = e3 & op(e1, e1) = e3 % 134.53/19.49 | | | | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | | | | ALPHA: (8527) implies: % 134.53/19.49 | | | | | | | | | | | | | | | | | | | (8528) op(e1, e1) = e3 % 134.53/19.49 | | | | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7007), (8528), (function-axioms) are % 134.53/19.49 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109. % 134.53/19.49 | | | | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.49 | | | | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | | | | (8529) all_57_14 = e3 & op(e0, e1) = e3 % 134.53/19.49 | | | | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | | | | ALPHA: (8529) implies: % 134.53/19.49 | | | | | | | | | | | | | | | | | | | (8530) all_57_14 = e3 % 134.53/19.49 | | | | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8445), (8530) are inconsistent by sub-proof % 134.53/19.49 | | | | | | | | | | | | | | | | | | | #400. % 134.53/19.49 | | | | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.49 | | | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | | End of split % 134.53/19.49 | | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | End of split % 134.53/19.49 | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | End of split % 134.53/19.49 | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | End of split % 134.53/19.49 | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | End of split % 134.53/19.49 | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | End of split % 134.53/19.49 | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | Case 2: % 134.53/19.49 | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | (8531) ~ (all_14_1 = e0) & op(e3, e3) = all_14_1 & % 134.53/19.49 | | | | | | | | | | | | $i(all_14_1) % 134.53/19.49 | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | REF_CLOSE: (7996), (8531), (function-axioms) are inconsistent % 134.53/19.49 | | | | | | | | | | | | by sub-proof #191. % 134.53/19.49 | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | End of split % 134.53/19.49 | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | Case 2: % 134.53/19.49 | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | (8532) ~ (all_6_1 = e3) & op(e2, e2) = all_6_1 & % 134.53/19.49 | | | | | | | | | | | $i(all_6_1) % 134.53/19.49 | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | REF_CLOSE: (8371), (8532), (function-axioms) are inconsistent % 134.53/19.49 | | | | | | | | | | | by sub-proof #74. % 134.53/19.49 | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | End of split % 134.53/19.49 | | | | | | | | | | % 134.53/19.49 | | | | | | | | | End of split % 134.53/19.49 | | | | | | | | | % 134.53/19.49 | | | | | | | | Case 2: % 134.53/19.49 | | | | | | | | | % 134.53/19.49 | | | | | | | | | (8533) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 % 134.53/19.49 | | | | | | | | | & op(e0, e2) = e3) % 134.53/19.49 | | | | | | | | | % 134.53/19.49 | | | | | | | | | REF_CLOSE: (158), (162), (8362), (8363), (8533), % 134.53/19.49 | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.49 | | | | | | | | | #555. % 134.53/19.49 | | | | | | | | | % 134.53/19.49 | | | | | | | | End of split % 134.53/19.49 | | | | | | | | % 134.53/19.49 | | | | | | | End of split % 134.53/19.49 | | | | | | | % 134.53/19.49 | | | | | | End of split % 134.53/19.49 | | | | | | % 134.53/19.49 | | | | | Case 2: % 134.53/19.49 | | | | | | % 134.53/19.49 | | | | | | (8534) all_8_2 = e1 % 134.53/19.49 | | | | | | % 134.53/19.49 | | | | | | REDUCE: (347), (8534) imply: % 134.53/19.49 | | | | | | (8535) ~ (all_52_1 = e1) % 134.53/19.49 | | | | | | % 134.53/19.49 | | | | | | REDUCE: (350), (8534) imply: % 134.53/19.49 | | | | | | (8536) ~ (all_52_4 = e1) % 134.53/19.49 | | | | | | % 134.53/19.49 | | | | | | REDUCE: (352), (8534) imply: % 134.53/19.49 | | | | | | (8537) ~ (all_52_6 = e1) % 134.53/19.49 | | | | | | % 134.53/19.49 | | | | | | REDUCE: (354), (8534) imply: % 134.53/19.49 | | | | | | (8538) ~ (all_52_7 = e1) % 134.53/19.49 | | | | | | % 134.53/19.49 | | | | | | REDUCE: (356), (8534) imply: % 134.53/19.49 | | | | | | (8539) ~ (all_52_9 = e1) % 134.53/19.49 | | | | | | % 134.53/19.49 | | | | | | REDUCE: (358), (8534) imply: % 134.53/19.49 | | | | | | (8540) ~ (all_52_13 = e1) % 134.53/19.49 | | | | | | % 134.53/19.49 | | | | | | BETA: splitting (224) gives: % 134.53/19.49 | | | | | | % 134.53/19.49 | | | | | | Case 1: % 134.53/19.49 | | | | | | | % 134.53/19.49 | | | | | | | (8541) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & % 134.53/19.49 | | | | | | | op(e2, e2) = e1) % 134.53/19.49 | | | | | | | % 134.53/19.49 | | | | | | | BETA: splitting (8541) gives: % 134.53/19.49 | | | | | | | % 134.53/19.49 | | | | | | | Case 1: % 134.53/19.49 | | | | | | | | % 134.53/19.49 | | | | | | | | (8542) all_57_2 = e1 & op(e2, e3) = e1 % 134.53/19.49 | | | | | | | | % 134.53/19.49 | | | | | | | | REF_CLOSE: (167), (8535), (8542), (function-axioms) are % 134.53/19.49 | | | | | | | | inconsistent by sub-proof #676. % 134.53/19.49 | | | | | | | | % 134.53/19.49 | | | | | | | Case 2: % 134.53/19.49 | | | | | | | | % 134.53/19.49 | | | | | | | | (8543) all_57_3 = e1 & op(e2, e2) = e1 % 134.53/19.49 | | | | | | | | % 134.53/19.49 | | | | | | | | ALPHA: (8543) implies: % 134.53/19.49 | | | | | | | | (8544) all_57_3 = e1 % 134.53/19.49 | | | | | | | | (8545) op(e2, e2) = e1 % 134.53/19.49 | | | | | | | | % 134.53/19.49 | | | | | | | | BETA: splitting (46) gives: % 134.53/19.49 | | | | | | | | % 134.53/19.49 | | | | | | | | Case 1: % 134.53/19.49 | | | | | | | | | % 134.53/19.49 | | | | | | | | | (8546) ~ (all_10_2 = e0) % 134.53/19.49 | | | | | | | | | % 134.53/19.49 | | | | | | | | | BETA: splitting (55) gives: % 134.53/19.49 | | | | | | | | | % 134.53/19.49 | | | | | | | | | Case 1: % 134.53/19.49 | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | (8547) ~ (all_16_2 = e2) % 134.53/19.49 | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | REDUCE: (327), (8547) imply: % 134.53/19.49 | | | | | | | | | | (8548) ~ (all_10_2 = e2) % 134.53/19.49 | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | BETA: splitting (58) gives: % 134.53/19.49 | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | Case 1: % 134.53/19.49 | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | (8549) ~ (all_18_2 = e2) % 134.53/19.49 | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | REDUCE: (6996), (8549) imply: % 134.53/19.49 | | | | | | | | | | | (8550) $false % 134.53/19.49 | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | CLOSE: (8550) is inconsistent. % 134.53/19.49 | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | Case 2: % 134.53/19.49 | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | (8551) ( ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 & % 134.53/19.49 | | | | | | | | | | | $i(all_18_0)) | ( ~ (all_18_1 = e0) & op(e2, e2) % 134.53/19.49 | | | | | | | | | | | = all_18_1 & $i(all_18_1)) % 134.53/19.49 | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | BETA: splitting (61) gives: % 134.53/19.49 | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | Case 1: % 134.53/19.49 | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | (8552) ~ (all_20_2 = e2) % 134.53/19.49 | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | REDUCE: (318), (8552) imply: % 134.53/19.49 | | | | | | | | | | | | (8553) ~ (all_4_2 = e2) % 134.53/19.49 | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | BETA: splitting (79) gives: % 134.53/19.49 | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | Case 1: % 134.53/19.49 | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | (8554) ~ (all_32_2 = e1) % 134.53/19.49 | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | REDUCE: (312), (8554) imply: % 134.53/19.49 | | | | | | | | | | | | | (8555) ~ (all_10_2 = e1) % 134.53/19.49 | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | BETA: splitting (206) gives: % 134.53/19.49 | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | Case 1: % 134.53/19.49 | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | (8556) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.49 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.49 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.49 | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.49 | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.49 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.49 | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.49 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.49 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.49 | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.49 | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.49 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.53/19.49 | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.49 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.49 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.49 | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.49 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.49 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.49 | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.49 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.49 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.49 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.49 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.49 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.49 | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | BETA: splitting (8556) gives: % 134.53/19.49 | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | Case 1: % 134.53/19.49 | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | (8557) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.49 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.49 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.49 | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.49 | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.49 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.49 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.49 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.49 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.49 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.49 | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.49 | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.49 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.49 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 134.53/19.49 | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | REF_CLOSE: (45), (204), (278), (8546), (8548), (8555), % 134.53/19.49 | | | | | | | | | | | | | | | (8557), (function-axioms) are inconsistent by % 134.53/19.49 | | | | | | | | | | | | | | | sub-proof #66. % 134.53/19.49 | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | Case 2: % 134.53/19.49 | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | (8558) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.49 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.49 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.49 | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.49 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.49 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.49 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.49 | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.49 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.49 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.49 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.49 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.49 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.49 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.49 | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | BETA: splitting (8558) gives: % 134.53/19.49 | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | Case 1: % 134.53/19.49 | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | (8559) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.49 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.49 | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 134.53/19.49 | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.49 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.49 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.49 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.49 | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | ALPHA: (8559) implies: % 134.53/19.49 | | | | | | | | | | | | | | | | (8560) op(e3, e3) = e0 % 134.53/19.49 | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | REF_CLOSE: (45), (204), (278), (8546), (8548), (8555), % 134.53/19.49 | | | | | | | | | | | | | | | | (8560), (function-axioms) are inconsistent by % 134.53/19.49 | | | | | | | | | | | | | | | | sub-proof #772. % 134.53/19.49 | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | Case 2: % 134.53/19.49 | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | (8561) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.49 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 134.53/19.49 | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.49 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.49 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 134.53/19.49 | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.49 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 134.53/19.49 | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | ALPHA: (8561) implies: % 134.53/19.49 | | | | | | | | | | | | | | | | (8562) op(e2, e2) = e3 % 134.53/19.49 | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8545), (8562), (function-axioms) are % 134.53/19.49 | | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 134.53/19.49 | | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | | End of split % 134.53/19.49 | | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | End of split % 134.53/19.49 | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | Case 2: % 134.53/19.49 | | | | | | | | | | | | | | % 134.53/19.49 | | | | | | | | | | | | | | (8563) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.49 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.49 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.49 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.49 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.49 | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.49 | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.49 | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.49 | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.49 | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.49 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.49 | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.53/19.49 | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.53/19.49 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.49 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.53/19.49 | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.49 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.53/19.49 | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.53/19.49 | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.49 | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.49 | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.49 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.53/19.49 | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.53/19.49 | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.53/19.49 | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.53/19.49 | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.53/19.49 | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.53/19.49 | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.49 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.53/19.49 | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.49 | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.53/19.49 | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.53/19.49 | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.53/19.49 | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.49 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.49 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.49 | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.53/19.49 | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.53/19.49 | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.53/19.49 | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.49 | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.53/19.49 | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.53/19.49 | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.49 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.49 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.49 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.49 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.49 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.49 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.49 | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.49 | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | BETA: splitting (8563) gives: % 134.53/19.50 | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | Case 1: % 134.53/19.50 | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | (8564) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.50 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.50 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.50 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.50 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.50 | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.50 | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.50 | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.50 | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.50 | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.50 | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (8564), % 134.53/19.50 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.50 | | | | | | | | | | | | | | | #108. % 134.53/19.50 | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | Case 2: % 134.53/19.50 | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | (8565) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.50 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.50 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.53/19.50 | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.50 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.50 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.50 | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.50 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.50 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.50 | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.50 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.50 | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.50 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.50 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.50 | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.50 | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.50 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.50 | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.50 | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.50 | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.50 | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.50 | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.50 | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.50 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.50 | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.50 | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.50 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.50 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.50 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.50 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.50 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.50 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.50 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.50 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.50 | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.50 | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | BETA: splitting (8565) gives: % 134.53/19.50 | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | Case 1: % 134.53/19.50 | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | (8566) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.50 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.50 | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.53/19.50 | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.50 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.50 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.50 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.50 | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | ALPHA: (8566) implies: % 134.53/19.50 | | | | | | | | | | | | | | | | (8567) op(e2, e2) = e0 % 134.53/19.50 | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8545), (8567), (function-axioms) are % 134.53/19.50 | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 134.53/19.50 | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | Case 2: % 134.53/19.50 | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | (8568) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.50 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.50 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.50 | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.50 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.50 | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.50 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.50 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.50 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.50 | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.50 | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.50 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.50 | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.50 | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.50 | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.50 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.50 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.50 | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.50 | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.50 | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.50 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.50 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.50 | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.50 | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.50 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.50 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.50 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.50 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.50 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.50 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.50 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.50 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.50 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.50 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.50 | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.50 | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | BETA: splitting (8568) gives: % 134.53/19.50 | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | Case 1: % 134.53/19.50 | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | (8569) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.53/19.50 | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.50 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.50 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 134.53/19.50 | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.53/19.50 | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | ALPHA: (8569) implies: % 134.53/19.50 | | | | | | | | | | | | | | | | | (8570) op(e1, e2) = e1 % 134.53/19.50 | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (8537), (8570), (function-axioms) are % 134.53/19.50 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #65. % 134.53/19.50 | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | Case 2: % 134.53/19.50 | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | (8571) op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.50 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 134.53/19.50 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.50 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 134.53/19.50 | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.50 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 134.53/19.50 | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.50 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.50 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.50 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.50 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.50 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.50 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 134.53/19.50 | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 134.53/19.50 | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 134.53/19.50 | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.53/19.50 | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_29))) % 134.53/19.50 | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | ALPHA: (8571) implies: % 134.53/19.50 | | | | | | | | | | | | | | | | | (8572) op(e0, e0) = all_56_31 % 134.53/19.50 | | | | | | | | | | | | | | | | | (8573) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.50 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.50 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.50 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.53/19.50 | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.53/19.50 | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.53/19.50 | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.53/19.50 | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.53/19.50 | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.53/19.50 | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.50 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 134.53/19.50 | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.50 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.53/19.50 | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.53/19.50 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.50 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.53/19.50 | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.53/19.50 | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.53/19.50 | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.50 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.50 | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 134.53/19.50 | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8574) all_54_0 = e3 % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (8574) imply: % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8575) all_10_2 = e3 % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | SIMP: (8575) implies: % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8576) all_10_2 = e3 % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | REDUCE: (45), (8576) imply: % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8577) op(e3, e3) = e3 % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 134.53/19.50 | | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (36), (8572) % 134.53/19.50 | | | | | | | | | | | | | | | | | | gives: % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8578) all_56_31 = all_4_2 % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | BETA: splitting (8573) gives: % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.50 | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | (8579) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.53/19.50 | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8553), (8577), (8578), (8579), (function-axioms) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #764. % 134.53/19.50 | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.50 | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | (8580) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.50 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (371), (7007), (8578), (8580), % 134.53/19.50 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.50 | | | | | | | | | | | | | | | | | | | #86. % 134.53/19.50 | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8581) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (8546), (8548), (8555), (8581) are % 134.53/19.50 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #777. % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | End of split % 134.53/19.50 | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | End of split % 134.53/19.50 | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | End of split % 134.53/19.50 | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | End of split % 134.53/19.50 | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | End of split % 134.53/19.50 | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | Case 2: % 134.53/19.50 | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | (8582) all_32_2 = e1 % 134.53/19.50 | | | | | | | | | | | | | (8583) ( ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 & % 134.53/19.50 | | | | | | | | | | | | | $i(all_32_0)) | ( ~ (all_32_1 = e2) & op(e1, e1) % 134.53/19.50 | | | | | | | | | | | | | = all_32_1 & $i(all_32_1)) % 134.53/19.50 | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | COMBINE_EQS: (312), (8582) imply: % 134.53/19.50 | | | | | | | | | | | | | (8584) all_10_2 = e1 % 134.53/19.50 | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | SIMP: (8584) implies: % 134.53/19.50 | | | | | | | | | | | | | (8585) all_10_2 = e1 % 134.53/19.50 | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | REDUCE: (338), (8585) imply: % 134.53/19.50 | | | | | | | | | | | | | (8586) ~ (all_52_2 = e1) % 134.53/19.50 | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | REDUCE: (346), (8585) imply: % 134.53/19.50 | | | | | | | | | | | | | (8587) ~ (all_52_12 = e1) % 134.53/19.50 | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | REDUCE: (8548), (8585) imply: % 134.53/19.50 | | | | | | | | | | | | | (8588) ~ (e2 = e1) % 134.53/19.50 | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | REDUCE: (45), (8585) imply: % 134.53/19.50 | | | | | | | | | | | | | (8589) op(e3, e3) = e1 % 134.53/19.50 | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | BETA: splitting (8583) gives: % 134.53/19.50 | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | Case 1: % 134.53/19.50 | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | (8590) ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 & % 134.53/19.50 | | | | | | | | | | | | | | $i(all_32_0) % 134.53/19.50 | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | ALPHA: (8590) implies: % 134.53/19.50 | | | | | | | | | | | | | | (8591) ~ (all_32_0 = e0) % 134.53/19.50 | | | | | | | | | | | | | | (8592) op(e1, e3) = all_32_0 % 134.53/19.50 | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | BETA: splitting (209) gives: % 134.53/19.50 | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | Case 1: % 134.53/19.50 | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | (8593) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 134.53/19.50 | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 134.53/19.50 | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (231), (235), % 134.53/19.50 | | | | | | | | | | | | | | | (237), (8538), (8589), (8593), (function-axioms) % 134.53/19.50 | | | | | | | | | | | | | | | are inconsistent by sub-proof #177. % 134.53/19.50 | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | Case 2: % 134.53/19.50 | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | (8594) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 134.53/19.50 | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 134.53/19.50 | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | BETA: splitting (8594) gives: % 134.53/19.50 | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | Case 1: % 134.53/19.50 | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | (8595) all_57_14 = e1 & op(e0, e1) = e1 % 134.53/19.50 | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | ALPHA: (8595) implies: % 134.53/19.50 | | | | | | | | | | | | | | | | (8596) op(e0, e1) = e1 % 134.53/19.50 | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 134.53/19.50 | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | Case 1: % 134.53/19.50 | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | (8597) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = % 134.53/19.50 | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 134.53/19.50 | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (8540), (8587), (8597), % 134.53/19.50 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.50 | | | | | | | | | | | | | | | | | #179. % 134.53/19.50 | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | Case 2: % 134.53/19.50 | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | (8598) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = % 134.53/19.50 | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 134.53/19.50 | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | BETA: splitting (8598) gives: % 134.53/19.50 | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8599) all_57_11 = e1 & op(e1, e0) = e1 % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | ALPHA: (8599) implies: % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8600) op(e1, e0) = e1 % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11, % 134.53/19.50 | | | | | | | | | | | | | | | | | | e1, e1, e0, simplifying with (157), (8596) gives: % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8601) all_52_11 = e1 % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 134.53/19.50 | | | | | | | | | | | | | | | | | | e1, e0, e1, simplifying with (160), (8600) gives: % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8602) all_52_14 = e1 % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 134.53/19.50 | | | | | | | | | | | | | | | | | | all_32_0, e3, e1, simplifying with (163), (8592) % 134.53/19.50 | | | | | | | | | | | | | | | | | | gives: % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8603) all_52_2 = all_32_0 % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (8603) imply: % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8604) all_54_8 = all_32_0 % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | REDUCE: (144), (8603) imply: % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8605) ~ (all_52_3 = all_32_0) % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | SIMP: (8605) implies: % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8606) ~ (all_52_3 = all_32_0) % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | REDUCE: (143), (8603) imply: % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8607) ~ (all_52_6 = all_32_0) % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | SIMP: (8607) implies: % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8608) ~ (all_52_6 = all_32_0) % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | REDUCE: (6997), (8603) imply: % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8609) ~ (all_32_0 = e2) % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | REDUCE: (8586), (8603) imply: % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8610) ~ (all_32_0 = e1) % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | REDUCE: (139), (8601) imply: % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8611) ~ (all_52_3 = e1) % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | REDUCE: (370), (8602) imply: % 134.53/19.50 | | | | | | | | | | | | | | | | | | (8612) ~ (all_4_2 = e1) % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 134.53/19.50 | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.50 | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | (8613) all_54_8 = e3 % 134.53/19.50 | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8604), (8613) imply: % 134.53/19.50 | | | | | | | | | | | | | | | | | | | (8614) all_32_0 = e3 % 134.53/19.50 | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | REDUCE: (8606), (8614) imply: % 134.53/19.50 | | | | | | | | | | | | | | | | | | | (8615) ~ (all_52_3 = e3) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | REDUCE: (8608), (8614) imply: % 134.53/19.50 | | | | | | | | | | | | | | | | | | | (8616) ~ (all_52_6 = e3) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | REDUCE: (8592), (8614) imply: % 134.53/19.50 | | | | | | | | | | | | | | | | | | | (8617) op(e1, e3) = e3 % 134.53/19.50 | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 134.53/19.50 | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (8618) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (8545), (8589), (8617), (8618), % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | #174. % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (8619) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8619) gives: % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | (8620) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (8620), % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | #108. % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.50 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | (8621) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8621) gives: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | (8622) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8622) implies: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | (8623) op(e2, e2) = e0 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8545), (8623), (function-axioms) are % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | (8624) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8624) gives: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (8625) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8625) implies: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (8626) op(e1, e2) = e1 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (8537), (8626), (function-axioms) are % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #65. % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (8627) op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8627) implies: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (8628) op(e0, e0) = all_56_31 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (8629) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | (8630) all_54_9 = e3 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (8616), (8630) are inconsistent by % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #64. % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | (8631) ~ (all_54_9 = e3) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | (8632) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8632) gives: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | (8633) all_54_9 = e2 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (6998), (8633) are inconsistent by % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #582. % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | (8634) ~ (all_54_9 = e2) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | (8635) all_54_9 = e1 | all_54_9 = e0 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8635) gives: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (8636) all_54_9 = e1 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (8537), (8636) are inconsistent by % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #169. % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (8637) all_54_9 = e0 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (8637) imply: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (8638) all_52_6 = e0 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8638) implies: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (8639) all_52_6 = e0 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (8639) imply: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (8640) ~ (all_52_7 = e0) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8640) implies: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (8641) ~ (all_52_7 = e0) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6998), (8639) imply: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (8642) ~ (e2 = e0) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8629) gives: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8643) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8643) gives: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8644) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8644) implies: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8645) all_56_31 = e3 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8646) ~ (all_56_25 = e0) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8647) ~ (all_56_9 = e2) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8648) op(e0, e3) = e0 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8649) op(e3, e0) = all_56_25 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8650) op(e3, e2) = all_56_9 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8651) op(e3, e3) = all_56_1 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8628), (8645) imply: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8652) op(e0, e0) = e3 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e3, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (36), (8652) gives: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8653) all_4_2 = e3 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (8648) gives: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8654) all_52_3 = e0 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_25, e0, e3, simplifying with (168), (8649) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8655) all_56_25 = all_52_12 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_9, e2, e3, simplifying with (170), (8650) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8656) all_56_9 = all_52_4 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_56_1, % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (8589), (8651) gives: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8657) all_56_1 = e1 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (8653) imply: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8658) all_34_2 = e3 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8647), (8656) imply: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8659) ~ (all_52_4 = e2) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (8653) imply: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8660) ~ (all_52_7 = e3) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8661) ~ (all_34_2 = e3) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8658), (8661) imply: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8662) $false % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8662) is inconsistent. % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8663) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_34_1 & $i(all_34_1)) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8664) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (159), (168), (170), (232), (236), % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8545), (8589), (8611), (8615), (8646), (8648), % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8649), (8650), (8651), (8659), (8663), (8664), % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #173. % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8665) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (8616), (8660), (8665), % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #555. % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8666) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8666) implies: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8667) op(e0, e2) = e0 % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8641), (8667), (function-axioms) are % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8668) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8668) gives: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8669) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8669) implies: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8670) op(e1, e1) = e0 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7007), (8670), (function-axioms) are % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #98. % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8671) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8671) implies: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8672) ~ (all_56_5 = e3) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8673) op(e1, e3) = all_56_5 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8617), (8672), (8673), (function-axioms) are % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #724. % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8674) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8591), (8604), (8609), (8610), (8674) are % 134.53/19.54 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #96. % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.54 | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | (8675) all_57_15 = e1 & op(e0, e0) = e1 % 134.53/19.54 | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | ALPHA: (8675) implies: % 134.53/19.54 | | | | | | | | | | | | | | | | | | (8676) op(e0, e0) = e1 % 134.53/19.54 | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (8676), (function-axioms) are % 134.53/19.54 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354. % 134.53/19.54 | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | Case 2: % 134.53/19.54 | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | (8677) all_57_15 = e1 & op(e0, e0) = e1 % 134.53/19.54 | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | ALPHA: (8677) implies: % 134.53/19.54 | | | | | | | | | | | | | | | | (8678) op(e0, e0) = e1 % 134.53/19.54 | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (8678), (function-axioms) are % 134.53/19.54 | | | | | | | | | | | | | | | | inconsistent by sub-proof #354. % 134.53/19.54 | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | Case 2: % 134.53/19.54 | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | (8679) ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 & % 134.53/19.54 | | | | | | | | | | | | | | $i(all_32_1) % 134.53/19.54 | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | REF_CLOSE: (7007), (8679), (function-axioms) are inconsistent % 134.53/19.54 | | | | | | | | | | | | | | by sub-proof #95. % 134.53/19.54 | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | Case 2: % 134.53/19.54 | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | (8680) all_20_2 = e2 % 134.53/19.54 | | | | | | | | | | | | (8681) ( ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 & % 134.53/19.54 | | | | | | | | | | | | $i(all_20_0)) | ( ~ (all_20_1 = e1) & op(e2, e2) % 134.53/19.54 | | | | | | | | | | | | = all_20_1 & $i(all_20_1)) % 134.53/19.54 | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | COMBINE_EQS: (318), (8680) imply: % 134.53/19.54 | | | | | | | | | | | | (8682) all_4_2 = e2 % 134.53/19.54 | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | REDUCE: (368), (8682) imply: % 134.53/19.54 | | | | | | | | | | | | (8683) ~ (all_52_12 = e2) % 134.53/19.54 | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | REDUCE: (369), (8682) imply: % 134.53/19.54 | | | | | | | | | | | | (8684) ~ (all_52_13 = e2) % 134.53/19.54 | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | BETA: splitting (8681) gives: % 134.53/19.54 | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | Case 1: % 134.53/19.54 | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | (8685) ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 & % 134.53/19.54 | | | | | | | | | | | | | $i(all_20_0) % 134.53/19.54 | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | ALPHA: (8685) implies: % 134.53/19.54 | | | | | | | | | | | | | (8686) ~ (all_20_0 = e3) % 134.53/19.54 | | | | | | | | | | | | | (8687) op(e2, e0) = all_20_0 % 134.53/19.54 | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | BETA: splitting (236) gives: % 134.53/19.54 | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | Case 1: % 134.53/19.54 | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | (8688) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 134.53/19.54 | | | | | | | | | | | | | | & op(e3, e2) = e2) % 134.53/19.54 | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | BETA: splitting (8688) gives: % 134.53/19.54 | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | Case 1: % 134.53/19.54 | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | (8689) all_57_0 = e2 & op(e3, e3) = e2 % 134.53/19.54 | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | ALPHA: (8689) implies: % 134.53/19.54 | | | | | | | | | | | | | | | (8690) op(e3, e3) = e2 % 134.53/19.54 | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | REF_CLOSE: (45), (8548), (8690), (function-axioms) are % 134.53/19.54 | | | | | | | | | | | | | | | inconsistent by sub-proof #536. % 134.53/19.54 | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | Case 2: % 134.53/19.54 | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | (8691) all_57_1 = e2 & op(e3, e2) = e2 % 134.53/19.54 | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | ALPHA: (8691) implies: % 134.53/19.54 | | | | | | | | | | | | | | | (8692) op(e3, e2) = e2 % 134.53/19.54 | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 134.53/19.54 | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | Case 1: % 134.53/19.54 | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | (8693) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 134.53/19.54 | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 134.53/19.54 | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | BETA: splitting (8693) gives: % 134.53/19.54 | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | Case 1: % 134.53/19.54 | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | (8694) all_57_2 = e2 & op(e2, e3) = e2 % 134.53/19.54 | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 134.53/19.54 | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.54 | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | (8695) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 134.53/19.54 | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (8683), (8684), (8695), % 134.53/19.54 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.54 | | | | | | | | | | | | | | | | | | #440. % 134.53/19.54 | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.54 | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | (8696) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 134.53/19.54 | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | BETA: splitting (8696) gives: % 134.53/19.54 | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8697) all_57_11 = e2 & op(e1, e0) = e2 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (7002), (8697), (function-axioms) are % 134.53/19.54 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #514. % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8698) all_57_15 = e2 & op(e0, e0) = e2 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | ALPHA: (8698) implies: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8699) op(e0, e0) = e2 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | ALPHA: (8694) implies: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8700) all_57_2 = e2 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8701) op(e2, e3) = e2 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 134.53/19.54 | | | | | | | | | | | | | | | | | | | all_20_0, e0, e2, simplifying with (164), (8687) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | gives: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8702) all_52_13 = all_20_0 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2, % 134.53/19.54 | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (167), (8701) gives: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8703) all_52_1 = e2 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2, % 134.53/19.54 | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (8692) gives: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8704) all_52_4 = e2 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (8702) imply: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8705) all_54_7 = all_20_0 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | REDUCE: (146), (8703) imply: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8706) ~ (all_52_9 = e2) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | REDUCE: (134), (8704) imply: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8707) ~ (all_52_8 = e2) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | REDUCE: (342), (8704) imply: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8708) ~ (all_10_2 = e2) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | REDUCE: (117), (8702) imply: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8709) ~ (all_52_9 = all_20_0) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | REDUCE: (8684), (8702) imply: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8710) ~ (all_20_0 = e2) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | REDUCE: (8540), (8702) imply: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | (8711) ~ (all_20_0 = e1) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | (8712) all_54_7 = e3 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8686), (8705), (8712) are inconsistent by % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | sub-proof #119. % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | (8713) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8713) gives: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | (8714) all_54_7 = e2 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8705), (8710), (8714) are inconsistent by % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | sub-proof #63. % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | (8715) ~ (all_54_7 = e2) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | (8716) all_54_7 = e1 | all_54_7 = e0 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8716) gives: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | (8717) all_54_7 = e1 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8705), (8711), (8717) are inconsistent by % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | sub-proof #62. % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | (8718) all_54_7 = e0 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8705), (8718) imply: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | (8719) all_20_0 = e0 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | SIMP: (8719) implies: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | (8720) all_20_0 = e0 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8709), (8720) imply: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | (8721) ~ (all_52_9 = e0) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8710), (8720) imply: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | (8722) ~ (e2 = e0) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8711), (8720) imply: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | (8723) ~ (e1 = e0) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8687), (8720) imply: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | (8724) op(e2, e0) = e0 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | (8725) all_54_6 = e3 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (8725) imply: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | (8726) all_52_9 = e3 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8726) implies: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | (8727) all_52_9 = e3 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (8727) imply: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | (8728) ~ (all_52_8 = e3) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (8727) imply: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | (8729) op(e2, e1) = e3 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (8730) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8730) gives: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (8731) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (169), (8548), (8728), (8731), % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | #469. % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (8732) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8732) gives: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (8733) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8733) implies: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (8734) op(e3, e3) = e0 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (8546), (8734), (function-axioms) are % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #534. % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (8735) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8735) implies: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (8736) op(e2, e2) = e3 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8545), (8736), (function-axioms) are % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (8737) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8737) gives: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (8738) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8738) gives: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (8739) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8739) implies: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (8740) op(e1, e1) = e3 % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7007), (8740), (function-axioms) are % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109. % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (8741) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8729), (8741), (function-axioms) are % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #114. % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (8742) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8742) gives: % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (8743) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8743) implies: % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (8744) op(e2, e2) = e0 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (79), (117), % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (123), (164), (165), (169), (198), (206), (224), % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (226), (231), (237), (260), (312), (6999), (7000), % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (7007), (8546), (8548), (8551), (8681), (8692), % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (8699), (8700), (8701), (8721), (8744), % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | #90. % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (8745) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (91), (157), (190), (246), (332), % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (364), (7001), (8699), (8724), (8745), % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | #67. % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | (8746) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (7000), (8539), (8721), (8746) are % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #478. % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | (8747) all_57_3 = e2 & op(e2, e2) = e2 % 134.53/19.55 | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | ALPHA: (8747) implies: % 134.53/19.55 | | | | | | | | | | | | | | | | | (8748) all_57_3 = e2 % 134.53/19.55 | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8544), (8748) are inconsistent by sub-proof % 134.53/19.55 | | | | | | | | | | | | | | | | | #728. % 134.53/19.55 | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | (8749) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 134.53/19.55 | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (7000), (8684), (8749), % 134.53/19.55 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.55 | | | | | | | | | | | | | | | | #625. % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | (8750) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 134.53/19.55 | | | | | | | | | | | | | | & op(e3, e0) = e2) % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | BETA: splitting (8750) gives: % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | Case 1: % 134.53/19.55 | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | (8751) all_57_4 = e2 & op(e3, e1) = e2 % 134.53/19.55 | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | REF_CLOSE: (169), (6999), (8751), (function-axioms) are % 134.53/19.55 | | | | | | | | | | | | | | | inconsistent by sub-proof #442. % 134.53/19.55 | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | (8752) all_57_9 = e2 & op(e3, e0) = e2 % 134.53/19.55 | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | REF_CLOSE: (168), (8683), (8752), (function-axioms) are % 134.53/19.55 | | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 134.53/19.55 | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | (8753) ~ (all_20_1 = e1) & op(e2, e2) = all_20_1 & % 134.53/19.55 | | | | | | | | | | | | | $i(all_20_1) % 134.53/19.55 | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | REF_CLOSE: (8545), (8753), (function-axioms) are inconsistent % 134.53/19.55 | | | | | | | | | | | | | by sub-proof #113. % 134.53/19.55 | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | % 134.53/19.55 | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | (8754) all_16_2 = e2 % 134.53/19.55 | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | COMBINE_EQS: (327), (8754) imply: % 134.53/19.55 | | | | | | | | | | (8755) all_10_2 = e2 % 134.53/19.55 | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | SIMP: (8755) implies: % 134.53/19.55 | | | | | | | | | | (8756) all_10_2 = e2 % 134.53/19.55 | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | COMBINE_EQS: (299), (8756) imply: % 134.53/19.55 | | | | | | | | | | (8757) all_38_2 = e2 % 134.53/19.55 | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | REDUCE: (336), (8756) imply: % 134.53/19.55 | | | | | | | | | | (8758) ~ (all_52_1 = e2) % 134.53/19.55 | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | REDUCE: (342), (8756) imply: % 134.53/19.55 | | | | | | | | | | (8759) ~ (all_52_4 = e2) % 134.53/19.55 | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | REDUCE: (45), (8756) imply: % 134.53/19.55 | | | | | | | | | | (8760) op(e3, e3) = e2 % 134.53/19.55 | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | BETA: splitting (225) gives: % 134.53/19.55 | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | Case 1: % 134.53/19.55 | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | (8761) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 134.53/19.55 | | | | | | | | | | | & op(e2, e2) = e2) % 134.53/19.55 | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | REF_CLOSE: (6), (167), (8544), (8758), (8761), % 134.53/19.55 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.55 | | | | | | | | | | | #127. % 134.53/19.55 | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | (8762) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 134.53/19.55 | | | | | | | | | | | e2 & op(e2, e0) = e2) % 134.53/19.55 | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | BETA: splitting (8762) gives: % 134.53/19.55 | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | Case 1: % 134.53/19.55 | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | (8763) all_57_5 = e2 & op(e2, e1) = e2 % 134.53/19.55 | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | ALPHA: (8763) implies: % 134.53/19.55 | | | | | | | | | | | | (8764) op(e2, e1) = e2 % 134.53/19.55 | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | REF_CLOSE: (165), (7000), (8764), (function-axioms) are % 134.53/19.55 | | | | | | | | | | | | inconsistent by sub-proof #770. % 134.53/19.55 | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | (8765) all_57_10 = e2 & op(e2, e0) = e2 % 134.53/19.55 | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | ALPHA: (8765) implies: % 134.53/19.55 | | | | | | | | | | | | (8766) op(e2, e0) = e2 % 134.53/19.55 | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | BETA: splitting (229) gives: % 134.53/19.55 | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | Case 1: % 134.53/19.55 | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | (8767) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 134.53/19.55 | | | | | | | | | | | | | & op(e2, e2) = e2) % 134.53/19.55 | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | BETA: splitting (8767) gives: % 134.53/19.55 | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | Case 1: % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | (8768) all_57_1 = e2 & op(e3, e2) = e2 % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | REF_CLOSE: (170), (8759), (8768), (function-axioms) are % 134.53/19.55 | | | | | | | | | | | | | | inconsistent by sub-proof #396. % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | (8769) all_57_3 = e2 & op(e2, e2) = e2 % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | ALPHA: (8769) implies: % 134.53/19.55 | | | | | | | | | | | | | | (8770) all_57_3 = e2 % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | REF_CLOSE: (6), (8544), (8770) are inconsistent by sub-proof % 134.53/19.55 | | | | | | | | | | | | | | #728. % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | (8771) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 134.53/19.55 | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 134.53/19.55 | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | BETA: splitting (8771) gives: % 134.53/19.55 | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | Case 1: % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | (8772) all_57_7 = e2 & op(e1, e2) = e2 % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | REF_CLOSE: (162), (6998), (8772), (function-axioms) are % 134.53/19.55 | | | | | | | | | | | | | | inconsistent by sub-proof #515. % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | (8773) all_57_13 = e2 & op(e0, e2) = e2 % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | ALPHA: (8773) implies: % 134.53/19.55 | | | | | | | | | | | | | | (8774) op(e0, e2) = e2 % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | BETA: splitting (88) gives: % 134.53/19.55 | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | Case 1: % 134.53/19.55 | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | (8775) ~ (all_38_2 = e2) % 134.53/19.55 | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | REDUCE: (8757), (8775) imply: % 134.53/19.55 | | | | | | | | | | | | | | | (8776) $false % 134.53/19.55 | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | CLOSE: (8776) is inconsistent. % 134.53/19.55 | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | (8777) ( ~ (all_38_0 = e0) & op(e2, e3) = all_38_0 & % 134.53/19.55 | | | | | | | | | | | | | | | $i(all_38_0)) | ( ~ (all_38_1 = e1) & op(e2, e2) % 134.53/19.55 | | | | | | | | | | | | | | | = all_38_1 & $i(all_38_1)) % 134.53/19.55 | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | BETA: splitting (8777) gives: % 134.53/19.55 | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | Case 1: % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | (8778) ~ (all_38_0 = e0) & op(e2, e3) = all_38_0 & % 134.53/19.55 | | | | | | | | | | | | | | | | $i(all_38_0) % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | ALPHA: (8778) implies: % 134.53/19.55 | | | | | | | | | | | | | | | | (8779) ~ (all_38_0 = e0) % 134.53/19.55 | | | | | | | | | | | | | | | | (8780) op(e2, e3) = all_38_0 % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2, % 134.53/19.55 | | | | | | | | | | | | | | | | e2, e0, simplifying with (158), (8774) gives: % 134.53/19.55 | | | | | | | | | | | | | | | | (8781) all_52_7 = e2 % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 134.53/19.55 | | | | | | | | | | | | | | | | e2, e0, e2, simplifying with (164), (8766) gives: % 134.53/19.55 | | | | | | | | | | | | | | | | (8782) all_52_13 = e2 % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, % 134.53/19.55 | | | | | | | | | | | | | | | | all_38_0, e3, e2, simplifying with (167), (8780) % 134.53/19.55 | | | | | | | | | | | | | | | | gives: % 134.53/19.55 | | | | | | | | | | | | | | | | (8783) all_52_1 = all_38_0 % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (8783) imply: % 134.53/19.55 | | | | | | | | | | | | | | | | (8784) all_54_4 = all_38_0 % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | REDUCE: (146), (8783) imply: % 134.53/19.55 | | | | | | | | | | | | | | | | (8785) ~ (all_52_9 = all_38_0) % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | SIMP: (8785) implies: % 134.53/19.55 | | | | | | | | | | | | | | | | (8786) ~ (all_52_9 = all_38_0) % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | REDUCE: (8758), (8783) imply: % 134.53/19.55 | | | | | | | | | | | | | | | | (8787) ~ (all_38_0 = e2) % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | REDUCE: (8535), (8783) imply: % 134.53/19.55 | | | | | | | | | | | | | | | | (8788) ~ (all_38_0 = e1) % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | REDUCE: (369), (8782) imply: % 134.53/19.55 | | | | | | | | | | | | | | | | (8789) ~ (all_4_2 = e2) % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | SIMP: (8789) implies: % 134.53/19.55 | | | | | | | | | | | | | | | | (8790) ~ (all_4_2 = e2) % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 134.53/19.55 | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | Case 1: % 134.53/19.55 | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | (8791) all_54_4 = e3 % 134.53/19.55 | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | COMBINE_EQS: (8784), (8791) imply: % 134.53/19.55 | | | | | | | | | | | | | | | | | (8792) all_38_0 = e3 % 134.53/19.55 | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | SIMP: (8792) implies: % 134.53/19.55 | | | | | | | | | | | | | | | | | (8793) all_38_0 = e3 % 134.53/19.55 | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | REDUCE: (8786), (8793) imply: % 134.53/19.55 | | | | | | | | | | | | | | | | | (8794) ~ (all_52_9 = e3) % 134.53/19.55 | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | REDUCE: (8780), (8793) imply: % 134.53/19.55 | | | | | | | | | | | | | | | | | (8795) op(e2, e3) = e3 % 134.53/19.55 | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 134.53/19.55 | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.55 | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | (8796) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.55 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.55 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.55 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.55 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.55 | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | BETA: splitting (8796) gives: % 134.53/19.55 | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.55 | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | (8797) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8760), (8795), (8797), (function-axioms) are % 134.53/19.55 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #335. % 134.53/19.55 | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | (8798) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8545), (8774), (8798), (function-axioms) are % 134.53/19.55 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #157. % 134.53/19.55 | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.55 | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | (8799) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.55 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.55 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.55 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.55 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.53/19.55 | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.53/19.55 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.53/19.55 | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.53/19.55 | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.53/19.55 | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.53/19.55 | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.55 | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.53/19.55 | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.55 | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.53/19.55 | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.55 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.55 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.55 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.55 | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.55 | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | BETA: splitting (8799) gives: % 134.53/19.55 | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.55 | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | (8800) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.55 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.55 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (8800), % 134.53/19.55 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.55 | | | | | | | | | | | | | | | | | | | #108. % 134.53/19.55 | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | (8801) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.55 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.55 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | BETA: splitting (8801) gives: % 134.53/19.55 | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | (8802) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | ALPHA: (8802) implies: % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | (8803) op(e2, e2) = e0 % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8545), (8803), (function-axioms) are % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | % 134.53/19.55 | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.55 | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | (8804) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8804) gives: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (8805) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8805) implies: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (8806) ~ (all_56_3 = e3) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (8807) op(e2, e3) = all_56_3 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8795), (8806), (8807), (function-axioms) are % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #347. % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (8808) op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8808) implies: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (8809) op(e0, e0) = all_56_31 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (8810) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8810) gives: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | (8811) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8811) gives: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8812) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8812) implies: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8813) all_56_31 = e3 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8814) op(e3, e2) = all_56_9 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8815) op(e3, e3) = all_56_1 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8809), (8813) imply: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8816) op(e0, e0) = e3 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e3, % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (36), (8816) gives: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8817) all_4_2 = e3 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | all_56_9, e2, e3, simplifying with (170), (8814) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | gives: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8818) all_56_9 = all_52_4 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_1, % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (8760), (8815) gives: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8819) all_56_1 = e2 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (8817) imply: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8820) all_44_2 = e3 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (8817) imply: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8821) ~ (all_52_11 = e3) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | (8822) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8822) gives: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (8823) all_57_4 = e3 & op(e3, e1) = e3 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8823) implies: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (8824) all_57_4 = e3 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (8825) ~ (all_44_2 = e3) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8820), (8825) imply: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (8826) $false % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8826) is inconsistent. % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (8827) ( ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_44_0)) | ( ~ (all_44_1 = e2) & op(e3, e3) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_44_1 & $i(all_44_1)) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (170), (234), (8536), (8760), (8824), % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (8827), (function-axioms) are inconsistent by % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #134. % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (8828) all_57_5 = e3 & op(e2, e1) = e3 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (8794), (8828), (function-axioms) are % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | (8829) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8829) gives: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (8830) all_57_8 = e3 & op(e1, e1) = e3 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8830) implies: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (8831) op(e1, e1) = e3 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7007), (8831), (function-axioms) are % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109. % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (8832) all_57_14 = e3 & op(e0, e1) = e3 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (8821), (8832), (function-axioms) are % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #652. % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8833) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8833) implies: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8834) ~ (all_56_3 = e3) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8835) op(e2, e3) = all_56_3 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8795), (8834), (8835), (function-axioms) are % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #347. % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | (8836) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8836) gives: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8837) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8837) implies: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8838) op(e1, e1) = e0 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7007), (8838), (function-axioms) are % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #98. % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8839) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8839) implies: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8840) all_56_31 = e1 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8809), (8840) imply: % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | (8841) op(e0, e0) = e1 % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (8841), (function-axioms) are % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #354. % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | Case 2: % 134.53/19.56 | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | (8842) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 134.53/19.56 | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | | REF_CLOSE: (8779), (8784), (8787), (8788), (8842) are % 134.53/19.56 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #126. % 134.53/19.56 | | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | Case 2: % 134.53/19.56 | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | (8843) ~ (all_38_1 = e1) & op(e2, e2) = all_38_1 & % 134.53/19.56 | | | | | | | | | | | | | | | | $i(all_38_1) % 134.53/19.56 | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | | REF_CLOSE: (8545), (8843), (function-axioms) are inconsistent % 134.53/19.56 | | | | | | | | | | | | | | | | by sub-proof #125. % 134.53/19.56 | | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | % 134.53/19.56 | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | % 134.53/19.56 | | | | | | | | Case 2: % 134.53/19.56 | | | | | | | | | % 134.53/19.56 | | | | | | | | | (8844) all_10_2 = e0 % 134.53/19.56 | | | | | | | | | % 134.53/19.56 | | | | | | | | | COMBINE_EQS: (319), (8844) imply: % 134.53/19.56 | | | | | | | | | (8845) all_24_2 = e0 % 134.53/19.56 | | | | | | | | | % 134.53/19.56 | | | | | | | | | REDUCE: (340), (8844) imply: % 134.53/19.56 | | | | | | | | | (8846) ~ (all_52_3 = e0) % 134.53/19.56 | | | | | | | | | % 134.53/19.56 | | | | | | | | | REDUCE: (342), (8844) imply: % 134.53/19.56 | | | | | | | | | (8847) ~ (all_52_4 = e0) % 134.53/19.56 | | | | | | | | | % 134.53/19.56 | | | | | | | | | REDUCE: (45), (8844) imply: % 134.53/19.56 | | | | | | | | | (8848) op(e3, e3) = e0 % 134.53/19.56 | | | | | | | | | % 134.53/19.56 | | | | | | | | | BETA: splitting (61) gives: % 134.53/19.56 | | | | | | | | | % 134.53/19.56 | | | | | | | | | Case 1: % 134.53/19.56 | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | (8849) ~ (all_20_2 = e2) % 134.53/19.56 | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | REDUCE: (318), (8849) imply: % 134.53/19.56 | | | | | | | | | | (8850) ~ (all_4_2 = e2) % 134.53/19.56 | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | BETA: splitting (206) gives: % 134.53/19.56 | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | Case 1: % 134.53/19.56 | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | (8851) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.56 | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.56 | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.56 | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.56 | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.56 | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.56 | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.56 | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.56 | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.56 | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.56 | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.56 | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.56 | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.56 | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.53/19.56 | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.56 | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.56 | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.56 | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.56 | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.56 | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.56 | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.56 | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.56 | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.56 | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.56 | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.56 | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.56 | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.56 | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.56 | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | BETA: splitting (8851) gives: % 134.53/19.56 | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | Case 1: % 134.53/19.56 | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | (8852) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.56 | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.56 | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.56 | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.56 | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.56 | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.56 | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.56 | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.56 | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.56 | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.56 | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.56 | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.56 | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.56 | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 134.53/19.56 | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | REF_CLOSE: (4), (5), (8848), (8852), (function-axioms) are % 134.53/19.56 | | | | | | | | | | | | inconsistent by sub-proof #229. % 134.53/19.56 | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | Case 2: % 134.53/19.56 | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | (8853) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.56 | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.56 | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.56 | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.56 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.56 | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.56 | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.56 | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.56 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.56 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.56 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.56 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.56 | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.56 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.56 | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | BETA: splitting (8853) gives: % 134.53/19.56 | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | Case 1: % 134.53/19.56 | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | (8854) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.56 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.56 | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 134.53/19.56 | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.56 | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.56 | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.56 | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.56 | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | ALPHA: (8854) implies: % 134.53/19.56 | | | | | | | | | | | | | (8855) ~ (all_56_31 = e0) % 134.53/19.56 | | | | | | | | | | | | | (8856) op(e0, e0) = all_56_31 % 134.53/19.56 | | | | | | | | | | | | | (8857) op(e3, e0) = e3 % 134.53/19.56 | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 134.53/19.56 | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (36), (8856) % 134.53/19.56 | | | | | | | | | | | | | gives: % 134.53/19.56 | | | | | | | | | | | | | (8858) all_56_31 = all_4_2 % 134.53/19.56 | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 134.53/19.56 | | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (8857) gives: % 134.53/19.56 | | | | | | | | | | | | | (8859) all_52_12 = e3 % 134.53/19.56 | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | REDUCE: (8855), (8858) imply: % 134.53/19.56 | | | | | | | | | | | | | (8860) ~ (all_4_2 = e0) % 134.53/19.56 | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | REDUCE: (368), (8859) imply: % 134.53/19.56 | | | | | | | | | | | | | (8861) ~ (all_4_2 = e3) % 134.53/19.56 | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | SIMP: (8861) implies: % 134.53/19.56 | | | | | | | | | | | | | (8862) ~ (all_4_2 = e3) % 134.53/19.56 | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | BETA: splitting (189) gives: % 134.53/19.56 | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | Case 1: % 134.53/19.56 | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | (8863) all_54_15 = e3 % 134.53/19.56 | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | COMBINE_EQS: (245), (8863) imply: % 134.53/19.56 | | | | | | | | | | | | | | (8864) all_4_2 = e3 % 134.53/19.56 | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | REDUCE: (8862), (8864) imply: % 134.53/19.56 | | | | | | | | | | | | | | (8865) $false % 134.53/19.56 | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | CLOSE: (8865) is inconsistent. % 134.53/19.56 | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | Case 2: % 134.53/19.56 | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | (8866) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 134.53/19.56 | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | | REF_CLOSE: (245), (371), (8850), (8860), (8866) are % 134.53/19.56 | | | | | | | | | | | | | | inconsistent by sub-proof #746. % 134.53/19.56 | | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | Case 2: % 134.53/19.56 | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | (8867) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.56 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 134.53/19.56 | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.56 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.56 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 134.53/19.56 | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.56 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 134.53/19.56 | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | ALPHA: (8867) implies: % 134.53/19.56 | | | | | | | | | | | | | (8868) op(e2, e2) = e3 % 134.53/19.56 | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | | REF_CLOSE: (8), (8545), (8868), (function-axioms) are % 134.53/19.56 | | | | | | | | | | | | | inconsistent by sub-proof #325. % 134.53/19.56 | | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | | End of split % 134.53/19.56 | | | | | | | | | | | % 134.53/19.56 | | | | | | | | | | Case 2: % 134.53/19.56 | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | (8869) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.57 | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.57 | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.57 | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.57 | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.57 | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.57 | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.57 | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.57 | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.57 | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.57 | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.57 | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.57 | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.57 | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.53/19.57 | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.53/19.57 | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.57 | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.53/19.57 | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.57 | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.53/19.57 | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.57 | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.53/19.57 | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.57 | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.57 | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.57 | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.53/19.57 | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.53/19.57 | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.57 | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.53/19.57 | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.53/19.57 | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.53/19.57 | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.53/19.57 | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.57 | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.53/19.57 | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.57 | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.57 | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.53/19.57 | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.53/19.57 | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.53/19.57 | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.57 | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.57 | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.57 | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.57 | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.53/19.57 | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.53/19.57 | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.53/19.57 | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.57 | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.53/19.57 | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.53/19.57 | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.57 | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.57 | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.57 | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.57 | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.57 | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.57 | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.57 | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.57 | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.57 | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | BETA: splitting (8869) gives: % 134.53/19.57 | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | (8870) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.57 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.57 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.57 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.57 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.57 | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.57 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.57 | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.57 | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.57 | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.57 | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.57 | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.57 | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.57 | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.57 | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (8870), % 134.53/19.57 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.57 | | | | | | | | | | | | #108. % 134.53/19.57 | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | Case 2: % 134.53/19.57 | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | (8871) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.57 | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.57 | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.53/19.57 | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.57 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.57 | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.57 | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.57 | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.57 | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.57 | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.57 | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.57 | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.57 | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.57 | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.57 | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.57 | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.57 | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.57 | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.57 | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.57 | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.57 | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.57 | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.57 | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.57 | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.57 | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.57 | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.57 | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.57 | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.57 | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.57 | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.57 | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.57 | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.57 | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.57 | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.57 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.57 | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.57 | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.57 | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.57 | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.57 | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.57 | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.57 | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.57 | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.57 | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.57 | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | BETA: splitting (8871) gives: % 134.53/19.57 | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | (8872) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.57 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.57 | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.53/19.57 | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.57 | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.57 | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.57 | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.57 | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | ALPHA: (8872) implies: % 134.53/19.57 | | | | | | | | | | | | | (8873) op(e2, e2) = e0 % 134.53/19.57 | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | REF_CLOSE: (4), (8545), (8873), (function-axioms) are % 134.53/19.57 | | | | | | | | | | | | | inconsistent by sub-proof #675. % 134.53/19.57 | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | Case 2: % 134.53/19.57 | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | (8874) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.57 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.57 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.57 | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.57 | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.57 | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.57 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.57 | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.57 | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.57 | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.57 | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.57 | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.57 | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.57 | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.57 | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.57 | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.57 | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.57 | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.57 | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.57 | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.57 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.57 | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.57 | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.57 | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.57 | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.57 | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.57 | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.57 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.57 | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.57 | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.57 | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.57 | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.57 | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.57 | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.57 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.57 | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.57 | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.57 | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | BETA: splitting (8874) gives: % 134.53/19.57 | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | (8875) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.57 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.53/19.57 | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.57 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.57 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 134.53/19.57 | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | ALPHA: (8875) implies: % 134.53/19.57 | | | | | | | | | | | | | | (8876) op(e1, e2) = e1 % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | REF_CLOSE: (162), (8537), (8876), (function-axioms) are % 134.53/19.57 | | | | | | | | | | | | | | inconsistent by sub-proof #65. % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | Case 2: % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | (8877) op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.57 | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.57 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 134.53/19.57 | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.57 | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 134.53/19.57 | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.57 | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 134.53/19.57 | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.57 | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.57 | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.57 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.57 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.57 | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.57 | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.57 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.57 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.57 | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.57 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 134.53/19.57 | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 134.53/19.57 | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 134.53/19.57 | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 134.53/19.57 | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 134.53/19.57 | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.53/19.57 | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_29))) % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | ALPHA: (8877) implies: % 134.53/19.57 | | | | | | | | | | | | | | (8878) op(e0, e0) = all_56_31 % 134.53/19.57 | | | | | | | | | | | | | | (8879) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.57 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.57 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.57 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.57 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.53/19.57 | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.53/19.57 | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.53/19.57 | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.53/19.57 | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.53/19.57 | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.53/19.57 | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.57 | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.57 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.57 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 134.53/19.57 | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.57 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.53/19.57 | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.53/19.57 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.57 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.53/19.57 | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.53/19.57 | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.53/19.57 | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.57 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 134.53/19.57 | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (36), (8878) % 134.53/19.57 | | | | | | | | | | | | | | gives: % 134.53/19.57 | | | | | | | | | | | | | | (8880) all_56_31 = all_4_2 % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | BETA: splitting (8879) gives: % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | (8881) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.57 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.57 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.57 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.57 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.57 | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.57 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.53/19.57 | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.53/19.57 | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.53/19.57 | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.53/19.57 | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.53/19.57 | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.53/19.57 | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 134.53/19.57 | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | BETA: splitting (8881) gives: % 134.53/19.57 | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | (8882) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 134.53/19.57 | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.57 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.57 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.57 | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.57 | | | | | | | | | | | | | | | | $i(all_56_25) % 134.53/19.57 | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | ALPHA: (8882) implies: % 134.53/19.57 | | | | | | | | | | | | | | | | (8883) op(e0, e3) = e0 % 134.53/19.57 | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8846), (8883), (function-axioms) are % 134.53/19.57 | | | | | | | | | | | | | | | | inconsistent by sub-proof #219. % 134.53/19.57 | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | Case 2: % 134.53/19.57 | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | (8884) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 134.53/19.57 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.53/19.57 | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.57 | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.57 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.57 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 134.53/19.57 | | | | | | | | | | | | | | | | $i(all_56_27) % 134.53/19.57 | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | REF_CLOSE: (8850), (8880), (8884) are inconsistent by % 134.53/19.57 | | | | | | | | | | | | | | | | sub-proof #765. % 134.53/19.57 | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | End of split % 134.53/19.57 | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | Case 2: % 134.53/19.57 | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | (8885) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 134.53/19.57 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.57 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.57 | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.57 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.57 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.53/19.57 | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.53/19.57 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.57 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.53/19.57 | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.53/19.57 | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.53/19.57 | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.57 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.57 | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | REF_CLOSE: (5), (371), (7007), (8880), (8885), % 134.53/19.57 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.57 | | | | | | | | | | | | | | | #86. % 134.53/19.57 | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | End of split % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | End of split % 134.53/19.57 | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | End of split % 134.53/19.57 | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | End of split % 134.53/19.57 | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | End of split % 134.53/19.57 | | | | | | | | | | % 134.53/19.57 | | | | | | | | | Case 2: % 134.53/19.57 | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | (8886) all_20_2 = e2 % 134.53/19.57 | | | | | | | | | | (8887) ( ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 & % 134.53/19.57 | | | | | | | | | | $i(all_20_0)) | ( ~ (all_20_1 = e1) & op(e2, e2) % 134.53/19.57 | | | | | | | | | | = all_20_1 & $i(all_20_1)) % 134.53/19.57 | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | COMBINE_EQS: (318), (8886) imply: % 134.53/19.57 | | | | | | | | | | (8888) all_4_2 = e2 % 134.53/19.57 | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | SIMP: (8888) implies: % 134.53/19.57 | | | | | | | | | | (8889) all_4_2 = e2 % 134.53/19.57 | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | REDUCE: (349), (8889) imply: % 134.53/19.57 | | | | | | | | | | (8890) ~ (all_52_3 = e2) % 134.53/19.57 | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | REDUCE: (368), (8889) imply: % 134.53/19.57 | | | | | | | | | | (8891) ~ (all_52_12 = e2) % 134.53/19.57 | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | REDUCE: (369), (8889) imply: % 134.53/19.57 | | | | | | | | | | (8892) ~ (all_52_13 = e2) % 134.53/19.57 | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | REDUCE: (36), (8889) imply: % 134.53/19.57 | | | | | | | | | | (8893) op(e0, e0) = e2 % 134.53/19.57 | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | BETA: splitting (67) gives: % 134.53/19.57 | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | (8894) ~ (all_24_2 = e0) % 134.53/19.57 | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | REDUCE: (8845), (8894) imply: % 134.53/19.57 | | | | | | | | | | | (8895) $false % 134.53/19.57 | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | CLOSE: (8895) is inconsistent. % 134.53/19.57 | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | Case 2: % 134.53/19.57 | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | (8896) ( ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 & % 134.53/19.57 | | | | | | | | | | | $i(all_24_0)) | ( ~ (all_24_1 = e2) & op(e0, e0) % 134.53/19.57 | | | | | | | | | | | = all_24_1 & $i(all_24_1)) % 134.53/19.57 | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | BETA: splitting (8896) gives: % 134.53/19.57 | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | (8897) ~ (all_24_0 = e1) & op(e0, e3) = all_24_0 & % 134.53/19.57 | | | | | | | | | | | | $i(all_24_0) % 134.53/19.57 | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | ALPHA: (8897) implies: % 134.53/19.57 | | | | | | | | | | | | (8898) ~ (all_24_0 = e1) % 134.53/19.57 | | | | | | | | | | | | (8899) op(e0, e3) = all_24_0 % 134.53/19.57 | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | BETA: splitting (236) gives: % 134.53/19.57 | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | (8900) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 134.53/19.57 | | | | | | | | | | | | | & op(e3, e2) = e2) % 134.53/19.57 | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | BETA: splitting (8900) gives: % 134.53/19.57 | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | (8901) all_57_0 = e2 & op(e3, e3) = e2 % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | ALPHA: (8901) implies: % 134.53/19.57 | | | | | | | | | | | | | | (8902) op(e3, e3) = e2 % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | REF_CLOSE: (5), (8848), (8902), (function-axioms) are % 134.53/19.57 | | | | | | | | | | | | | | inconsistent by sub-proof #495. % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | Case 2: % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | (8903) all_57_1 = e2 & op(e3, e2) = e2 % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | ALPHA: (8903) implies: % 134.53/19.57 | | | | | | | | | | | | | | (8904) op(e3, e2) = e2 % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | BETA: splitting (225) gives: % 134.53/19.57 | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | (8905) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 134.53/19.57 | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 134.53/19.57 | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | BETA: splitting (8905) gives: % 134.53/19.57 | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | (8906) all_57_2 = e2 & op(e2, e3) = e2 % 134.53/19.57 | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | ALPHA: (8906) implies: % 134.53/19.57 | | | | | | | | | | | | | | | | (8907) all_57_2 = e2 % 134.53/19.57 | | | | | | | | | | | | | | | | (8908) op(e2, e3) = e2 % 134.53/19.57 | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | BETA: splitting (8887) gives: % 134.53/19.57 | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | (8909) ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 & % 134.53/19.57 | | | | | | | | | | | | | | | | | $i(all_20_0) % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | ALPHA: (8909) implies: % 134.53/19.57 | | | | | | | | | | | | | | | | | (8910) ~ (all_20_0 = e3) % 134.53/19.57 | | | | | | | | | | | | | | | | | (8911) op(e2, e0) = all_20_0 % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, % 134.53/19.57 | | | | | | | | | | | | | | | | | all_24_0, e3, e0, simplifying with (159), (8899) % 134.53/19.57 | | | | | | | | | | | | | | | | | gives: % 134.53/19.57 | | | | | | | | | | | | | | | | | (8912) all_52_3 = all_24_0 % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 134.53/19.57 | | | | | | | | | | | | | | | | | all_20_0, e0, e2, simplifying with (164), (8911) % 134.53/19.57 | | | | | | | | | | | | | | | | | gives: % 134.53/19.57 | | | | | | | | | | | | | | | | | (8913) all_52_13 = all_20_0 % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2, % 134.53/19.57 | | | | | | | | | | | | | | | | | e3, e2, simplifying with (167), (8908) gives: % 134.53/19.57 | | | | | | | | | | | | | | | | | (8914) all_52_1 = e2 % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2, % 134.53/19.57 | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (8904) gives: % 134.53/19.57 | | | | | | | | | | | | | | | | | (8915) all_52_4 = e2 % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (8912) imply: % 134.53/19.57 | | | | | | | | | | | | | | | | | (8916) all_54_12 = all_24_0 % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (8913) imply: % 134.53/19.57 | | | | | | | | | | | | | | | | | (8917) all_54_7 = all_20_0 % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | REDUCE: (146), (8914) imply: % 134.53/19.57 | | | | | | | | | | | | | | | | | (8918) ~ (all_52_9 = e2) % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | REDUCE: (140), (8912) imply: % 134.53/19.57 | | | | | | | | | | | | | | | | | (8919) ~ (all_52_7 = all_24_0) % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | SIMP: (8919) implies: % 134.53/19.57 | | | | | | | | | | | | | | | | | (8920) ~ (all_52_7 = all_24_0) % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | REDUCE: (139), (8912) imply: % 134.53/19.57 | | | | | | | | | | | | | | | | | (8921) ~ (all_52_11 = all_24_0) % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | SIMP: (8921) implies: % 134.53/19.57 | | | | | | | | | | | | | | | | | (8922) ~ (all_52_11 = all_24_0) % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | REDUCE: (8890), (8912) imply: % 134.53/19.57 | | | | | | | | | | | | | | | | | (8923) ~ (all_24_0 = e2) % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | REDUCE: (8846), (8912) imply: % 134.53/19.57 | | | | | | | | | | | | | | | | | (8924) ~ (all_24_0 = e0) % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | REDUCE: (8892), (8913) imply: % 134.53/19.57 | | | | | | | | | | | | | | | | | (8925) ~ (all_20_0 = e2) % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | REDUCE: (8540), (8913) imply: % 134.53/19.57 | | | | | | | | | | | | | | | | | (8926) ~ (all_20_0 = e1) % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 134.53/19.57 | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | (8927) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 134.53/19.57 | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 134.53/19.57 | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (8535), (8848), (8927), % 134.53/19.57 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.57 | | | | | | | | | | | | | | | | | | #118. % 134.53/19.57 | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.57 | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | (8928) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 134.53/19.57 | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 134.53/19.57 | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | BETA: splitting (8928) gives: % 134.53/19.57 | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | (8929) all_57_6 = e1 & op(e1, e3) = e1 % 134.53/19.57 | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | ALPHA: (8929) implies: % 134.53/19.57 | | | | | | | | | | | | | | | | | | | (8930) all_57_6 = e1 % 134.53/19.57 | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 134.53/19.57 | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | (8931) all_54_7 = e3 % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8910), (8917), (8931) are inconsistent by % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | sub-proof #119. % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | (8932) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives: % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | (8933) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (8848), (8907), (8933), % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | #70. % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | (8934) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8934) gives: % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | (8935) all_57_6 = e3 & op(e1, e3) = e3 % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8930), (8935) are inconsistent by sub-proof % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | #61. % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | (8936) all_57_12 = e3 & op(e0, e3) = e3 % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8936) implies: % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | (8937) all_57_12 = e3 % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | (8938) op(e0, e3) = e3 % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8932) gives: % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | (8939) all_54_7 = e2 % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8917), (8925), (8939) are inconsistent by % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #63. % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | (8940) all_54_7 = e1 | all_54_7 = e0 % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.57 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (8941) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8941) gives: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (8942) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8942) gives: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (8943) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8943) implies: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (8944) op(e3, e3) = e2 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (231), (233), (8907), % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (8937), (8944), (function-axioms) are inconsistent % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #489. % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (8945) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8945) implies: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (8946) op(e3, e3) = e1 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8848), (8946), (function-axioms) are % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (8947) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8545), (8938), (8947), (function-axioms) are % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #115. % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (8948) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8948) gives: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (8949) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (165), (7000), (7007), (8949), % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | #108. % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (8950) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8950) gives: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (8951) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8951) implies: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (8952) op(e2, e2) = e0 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8545), (8952), (function-axioms) are % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (8953) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8953) gives: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8954) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8954) implies: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8955) op(e1, e2) = e1 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (8537), (8955), (function-axioms) are % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #65. % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8956) op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8956) implies: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8957) op(e0, e0) = all_56_31 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8958) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8940) gives: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8959) all_54_7 = e1 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8917), (8926), (8959) are inconsistent by % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #62. % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8960) all_54_7 = e0 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8917), (8960) imply: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8961) all_20_0 = e0 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8961) implies: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8962) all_20_0 = e0 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8911), (8962) imply: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8963) op(e2, e0) = e0 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (39), (91), (157), (190), (246), (332), % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364), (7001), (8893), (8957), (8958), (8963), % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #273. % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | (8964) all_57_12 = e1 & op(e0, e3) = e1 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | ALPHA: (8964) implies: % 134.53/19.58 | | | | | | | | | | | | | | | | | | | (8965) all_57_12 = e1 % 134.53/19.58 | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (192), (211), (8893), (8898), % 134.53/19.58 | | | | | | | | | | | | | | | | | | | (8916), (8920), (8922), (8923), (8924), (8965), % 134.53/19.58 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.58 | | | | | | | | | | | | | | | | | | | #120. % 134.53/19.58 | | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | Case 2: % 134.53/19.58 | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | (8966) ~ (all_20_1 = e1) & op(e2, e2) = all_20_1 & % 134.53/19.58 | | | | | | | | | | | | | | | | | $i(all_20_1) % 134.53/19.58 | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | | REF_CLOSE: (8545), (8966), (function-axioms) are inconsistent % 134.53/19.58 | | | | | | | | | | | | | | | | | by sub-proof #113. % 134.53/19.58 | | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | Case 2: % 134.53/19.58 | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | (8967) all_57_3 = e2 & op(e2, e2) = e2 % 134.53/19.58 | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | ALPHA: (8967) implies: % 134.53/19.58 | | | | | | | | | | | | | | | | (8968) all_57_3 = e2 % 134.53/19.58 | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8544), (8968) are inconsistent by sub-proof % 134.53/19.58 | | | | | | | | | | | | | | | | #728. % 134.53/19.58 | | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | Case 2: % 134.53/19.58 | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | (8969) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 134.53/19.58 | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 134.53/19.58 | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (7000), (8892), (8969), % 134.53/19.58 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.58 | | | | | | | | | | | | | | | #625. % 134.53/19.58 | | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | Case 2: % 134.53/19.58 | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | (8970) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 134.53/19.58 | | | | | | | | | | | | | & op(e3, e0) = e2) % 134.53/19.58 | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | BETA: splitting (8970) gives: % 134.53/19.58 | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | Case 1: % 134.53/19.58 | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | (8971) all_57_4 = e2 & op(e3, e1) = e2 % 134.53/19.58 | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | REF_CLOSE: (169), (6999), (8971), (function-axioms) are % 134.53/19.58 | | | | | | | | | | | | | | inconsistent by sub-proof #442. % 134.53/19.58 | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | Case 2: % 134.53/19.58 | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | (8972) all_57_9 = e2 & op(e3, e0) = e2 % 134.53/19.58 | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | | REF_CLOSE: (168), (8891), (8972), (function-axioms) are % 134.53/19.58 | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 134.53/19.58 | | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | Case 2: % 134.53/19.58 | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | (8973) ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 & % 134.53/19.58 | | | | | | | | | | | | $i(all_24_1) % 134.53/19.58 | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | | REF_CLOSE: (8893), (8973), (function-axioms) are inconsistent % 134.53/19.58 | | | | | | | | | | | | by sub-proof #204. % 134.53/19.58 | | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | | % 134.53/19.58 | | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | | % 134.53/19.58 | | | | | | | | | End of split % 134.53/19.58 | | | | | | | | | % 134.53/19.58 | | | | | | | | End of split % 134.53/19.58 | | | | | | | | % 134.53/19.58 | | | | | | | End of split % 134.53/19.58 | | | | | | | % 134.53/19.58 | | | | | | Case 2: % 134.53/19.58 | | | | | | | % 134.53/19.58 | | | | | | | (8974) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & % 134.53/19.58 | | | | | | | op(e2, e0) = e1) % 134.53/19.58 | | | | | | | % 134.53/19.58 | | | | | | | REF_CLOSE: (164), (165), (8539), (8540), (8974), (function-axioms) % 134.53/19.58 | | | | | | | are inconsistent by sub-proof #112. % 134.53/19.58 | | | | | | | % 134.53/19.58 | | | | | | End of split % 134.53/19.58 | | | | | | % 134.53/19.58 | | | | | End of split % 134.53/19.58 | | | | | % 134.53/19.58 | | | | Case 2: % 134.53/19.58 | | | | | % 134.53/19.58 | | | | | (8975) all_57_14 = e2 & op(e0, e1) = e2 % 134.53/19.58 | | | | | % 134.53/19.58 | | | | | REF_CLOSE: (157), (7001), (8975), (function-axioms) are inconsistent % 134.53/19.58 | | | | | by sub-proof #512. % 134.53/19.58 | | | | | % 134.53/19.58 | | | | End of split % 134.53/19.58 | | | | % 134.53/19.58 | | | End of split % 134.53/19.58 | | | % 134.53/19.58 | | End of split % 134.53/19.58 | | % 134.53/19.58 | Case 2: % 134.53/19.58 | | % 134.53/19.58 | | (8976) all_4_2 = e1 % 134.53/19.58 | | (8977) ( ~ (all_4_0 = e3) & op(e1, e0) = all_4_0 & $i(all_4_0)) | ( ~ % 134.53/19.58 | | (all_4_1 = e2) & op(e1, e1) = all_4_1 & $i(all_4_1)) % 134.53/19.58 | | % 134.53/19.58 | | COMBINE_EQS: (330), (8976) imply: % 134.53/19.58 | | (8978) all_12_2 = e1 % 134.53/19.58 | | % 134.53/19.58 | | REDUCE: (349), (8976) imply: % 134.53/19.58 | | (8979) ~ (all_52_3 = e1) % 134.53/19.58 | | % 134.53/19.58 | | REDUCE: (360), (8976) imply: % 134.53/19.58 | | (8980) ~ (all_52_7 = e1) % 134.53/19.58 | | % 134.53/19.58 | | REDUCE: (367), (8976) imply: % 134.53/19.58 | | (8981) ~ (all_52_11 = e1) % 134.53/19.58 | | % 134.53/19.58 | | REDUCE: (368), (8976) imply: % 134.53/19.58 | | (8982) ~ (all_52_12 = e1) % 134.53/19.58 | | % 134.53/19.58 | | REDUCE: (369), (8976) imply: % 134.53/19.58 | | (8983) ~ (all_52_13 = e1) % 134.53/19.58 | | % 134.53/19.58 | | REDUCE: (370), (8976) imply: % 134.53/19.58 | | (8984) ~ (all_52_14 = e1) % 134.53/19.58 | | % 134.53/19.58 | | BETA: splitting (212) gives: % 134.53/19.58 | | % 134.53/19.58 | | Case 1: % 134.53/19.58 | | | % 134.53/19.58 | | | (8985) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) % 134.53/19.58 | | | = e1) % 134.53/19.58 | | | % 134.53/19.58 | | | REF_CLOSE: (164), (168), (8982), (8983), (8985), (function-axioms) are % 134.53/19.58 | | | inconsistent by sub-proof #179. % 134.53/19.58 | | | % 134.53/19.58 | | Case 2: % 134.53/19.58 | | | % 134.53/19.58 | | | (8986) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, % 134.53/19.58 | | | e0) = e1) % 134.53/19.58 | | | % 134.53/19.58 | | | BETA: splitting (8986) gives: % 134.53/19.58 | | | % 134.53/19.58 | | | Case 1: % 134.53/19.58 | | | | % 134.53/19.58 | | | | (8987) all_57_11 = e1 & op(e1, e0) = e1 % 134.53/19.58 | | | | % 134.53/19.58 | | | | ALPHA: (8987) implies: % 134.53/19.58 | | | | (8988) op(e1, e0) = e1 % 134.53/19.58 | | | | % 134.53/19.58 | | | | REF_CLOSE: (160), (8984), (8988), (function-axioms) are inconsistent by % 134.53/19.58 | | | | sub-proof #327. % 134.53/19.58 | | | | % 134.53/19.58 | | | Case 2: % 134.53/19.58 | | | | % 134.53/19.58 | | | | (8989) all_57_15 = e1 & op(e0, e0) = e1 % 134.53/19.58 | | | | % 134.53/19.58 | | | | ALPHA: (8989) implies: % 134.53/19.59 | | | | (8990) all_57_15 = e1 % 134.53/19.59 | | | | (8991) op(e0, e0) = e1 % 134.53/19.59 | | | | % 134.53/19.59 | | | | BETA: splitting (40) gives: % 134.53/19.59 | | | | % 134.53/19.59 | | | | Case 1: % 134.53/19.59 | | | | | % 134.53/19.59 | | | | | (8992) ~ (all_6_2 = e2) % 134.53/19.59 | | | | | % 134.53/19.59 | | | | | BETA: splitting (43) gives: % 134.53/19.59 | | | | | % 134.53/19.59 | | | | | Case 1: % 134.53/19.59 | | | | | | % 134.53/19.59 | | | | | | (8993) ~ (all_8_2 = e1) % 134.53/19.59 | | | | | | % 134.53/19.59 | | | | | | BETA: splitting (46) gives: % 134.53/19.59 | | | | | | % 134.53/19.59 | | | | | | Case 1: % 134.53/19.59 | | | | | | | % 134.53/19.59 | | | | | | | (8994) ~ (all_10_2 = e0) % 134.53/19.59 | | | | | | | % 134.53/19.59 | | | | | | | BETA: splitting (49) gives: % 134.53/19.59 | | | | | | | % 134.53/19.59 | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | % 134.53/19.59 | | | | | | | | (8995) ~ (all_12_2 = e1) % 134.53/19.59 | | | | | | | | % 134.53/19.59 | | | | | | | | REDUCE: (8978), (8995) imply: % 134.53/19.59 | | | | | | | | (8996) $false % 134.53/19.59 | | | | | | | | % 134.53/19.59 | | | | | | | | CLOSE: (8996) is inconsistent. % 134.53/19.59 | | | | | | | | % 134.53/19.59 | | | | | | | Case 2: % 134.53/19.59 | | | | | | | | % 134.53/19.59 | | | | | | | | (8997) ( ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 & % 134.53/19.59 | | | | | | | | $i(all_12_0)) | ( ~ (all_12_1 = e3) & op(e1, e1) = % 134.53/19.59 | | | | | | | | all_12_1 & $i(all_12_1)) % 134.53/19.59 | | | | | | | | % 134.53/19.59 | | | | | | | | BETA: splitting (52) gives: % 134.53/19.59 | | | | | | | | % 134.53/19.59 | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | % 134.53/19.59 | | | | | | | | | (8998) ~ (all_14_2 = e3) % 134.53/19.59 | | | | | | | | | % 134.53/19.59 | | | | | | | | | REDUCE: (329), (8998) imply: % 134.53/19.59 | | | | | | | | | (8999) ~ (all_8_2 = e3) % 134.53/19.59 | | | | | | | | | % 134.53/19.59 | | | | | | | | | BETA: splitting (55) gives: % 134.53/19.59 | | | | | | | | | % 134.53/19.59 | | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | (9000) ~ (all_16_2 = e2) % 134.53/19.59 | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | REDUCE: (327), (9000) imply: % 134.53/19.59 | | | | | | | | | | (9001) ~ (all_10_2 = e2) % 134.53/19.59 | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | BETA: splitting (73) gives: % 134.53/19.59 | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | (9002) ~ (all_28_2 = e3) % 134.53/19.59 | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | REDUCE: (316), (9002) imply: % 134.53/19.59 | | | | | | | | | | | (9003) ~ (all_6_2 = e3) % 134.53/19.59 | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | BETA: splitting (76) gives: % 134.53/19.59 | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | (9004) ~ (all_30_2 = e0) % 134.53/19.59 | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | REDUCE: (309), (9004) imply: % 134.53/19.59 | | | | | | | | | | | | (9005) ~ (all_8_2 = e0) % 134.53/19.59 | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | BETA: splitting (199) gives: % 134.53/19.59 | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | (9006) all_54_5 = e3 % 134.53/19.59 | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | REF_CLOSE: (267), (8999), (9006) are inconsistent by % 134.53/19.59 | | | | | | | | | | | | | sub-proof #554. % 134.53/19.59 | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | Case 2: % 134.53/19.59 | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | (9007) ~ (all_54_5 = e3) % 134.53/19.59 | | | | | | | | | | | | | (9008) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 134.53/19.59 | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | BETA: splitting (9008) gives: % 134.53/19.59 | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | (9009) all_54_5 = e2 % 134.53/19.59 | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | COMBINE_EQS: (267), (9009) imply: % 134.53/19.59 | | | | | | | | | | | | | | (9010) all_8_2 = e2 % 134.53/19.59 | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | SIMP: (9010) implies: % 134.53/19.59 | | | | | | | | | | | | | | (9011) all_8_2 = e2 % 134.53/19.59 | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | REDUCE: (347), (9011) imply: % 134.53/19.59 | | | | | | | | | | | | | | (9012) ~ (all_52_1 = e2) % 134.53/19.59 | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | REDUCE: (350), (9011) imply: % 134.53/19.59 | | | | | | | | | | | | | | (9013) ~ (all_52_4 = e2) % 134.53/19.59 | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | REDUCE: (356), (9011) imply: % 134.53/19.59 | | | | | | | | | | | | | | (9014) ~ (all_52_9 = e2) % 134.53/19.59 | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | REDUCE: (8999), (9011) imply: % 134.53/19.59 | | | | | | | | | | | | | | (9015) ~ (e3 = e2) % 134.53/19.59 | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | BETA: splitting (225) gives: % 134.53/19.59 | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | (9016) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 % 134.53/19.59 | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 134.53/19.59 | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | BETA: splitting (9016) gives: % 134.53/19.59 | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | (9017) all_57_2 = e2 & op(e2, e3) = e2 % 134.53/19.59 | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | ALPHA: (9017) implies: % 134.53/19.59 | | | | | | | | | | | | | | | | (9018) op(e2, e3) = e2 % 134.53/19.59 | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | REF_CLOSE: (167), (9012), (9018), (function-axioms) are % 134.53/19.59 | | | | | | | | | | | | | | | | inconsistent by sub-proof #779. % 134.53/19.59 | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | Case 2: % 134.53/19.59 | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | (9019) all_57_3 = e2 & op(e2, e2) = e2 % 134.53/19.59 | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | ALPHA: (9019) implies: % 134.53/19.59 | | | | | | | | | | | | | | | | (9020) all_57_3 = e2 % 134.53/19.59 | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 134.53/19.59 | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | (9021) ~ (all_32_2 = e1) % 134.53/19.59 | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | REDUCE: (312), (9021) imply: % 134.53/19.59 | | | | | | | | | | | | | | | | | (9022) ~ (all_10_2 = e1) % 134.53/19.59 | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 134.53/19.59 | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | (9023) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.59 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.59 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.59 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.59 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.59 | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | BETA: splitting (9023) gives: % 134.53/19.59 | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | (9024) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (204), (278), (8994), (9001), (9022), % 134.53/19.59 | | | | | | | | | | | | | | | | | | | (9024), (function-axioms) are inconsistent by % 134.53/19.59 | | | | | | | | | | | | | | | | | | | sub-proof #66. % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | (9025) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (9025) gives: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9026) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (9026) implies: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9027) op(e3, e3) = e0 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (204), (278), (8994), (9001), (9022), % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9027), (function-axioms) are inconsistent by % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | sub-proof #772. % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9028) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (9028) implies: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9029) op(e2, e2) = e3 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (8999), (9029), (function-axioms) are % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228. % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.59 | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.59 | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | (9030) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.59 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.59 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.59 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.59 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.53/19.59 | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.53/19.59 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.53/19.59 | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.53/19.59 | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.53/19.59 | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.59 | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.53/19.59 | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.59 | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.53/19.59 | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.59 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.59 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.59 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.59 | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.59 | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | BETA: splitting (9030) gives: % 134.53/19.59 | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | (9031) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (165), (9003), (9014), (9031), % 134.53/19.59 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.59 | | | | | | | | | | | | | | | | | | | #769. % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | (9032) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (9032) gives: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9033) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (9033) implies: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9034) op(e2, e0) = e2 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (267), (358), (8993), (9005), (9008), % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9034), (function-axioms) are inconsistent by % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | sub-proof #60. % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (9035) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9035) gives: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (9036) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9036) implies: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (9037) op(e1, e1) = e2 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (9037), (function-axioms) are % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (9038) op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9038) implies: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (9039) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (9040) all_54_0 = e3 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (9040) imply: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (9041) all_10_2 = e3 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | SIMP: (9041) implies: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (9042) all_10_2 = e3 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (9042) imply: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (9043) op(e3, e3) = e3 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (42), (157), (158), (160), (194), (199), % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (267), (334), (354), (364), (8984), (8992), % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (8993), (8999), (9003), (9039), (9043), % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | #58. % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | (9044) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (8994), (9001), (9022), (9044) are % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #777. % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.59 | | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.59 | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | End of split % 134.53/19.59 | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | Case 2: % 134.53/19.59 | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | (9045) all_32_2 = e1 % 134.53/19.59 | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | COMBINE_EQS: (312), (9045) imply: % 134.53/19.59 | | | | | | | | | | | | | | | | | (9046) all_10_2 = e1 % 134.53/19.59 | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | SIMP: (9046) implies: % 134.53/19.59 | | | | | | | | | | | | | | | | | (9047) all_10_2 = e1 % 134.53/19.59 | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (9047) imply: % 134.53/19.59 | | | | | | | | | | | | | | | | | (9048) all_50_2 = e1 % 134.53/19.59 | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | REDUCE: (336), (9047) imply: % 134.53/19.59 | | | | | | | | | | | | | | | | | (9049) ~ (all_52_1 = e1) % 134.53/19.59 | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | REDUCE: (342), (9047) imply: % 134.53/19.59 | | | | | | | | | | | | | | | | | (9050) ~ (all_52_4 = e1) % 134.53/19.59 | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | REDUCE: (45), (9047) imply: % 134.53/19.59 | | | | | | | | | | | | | | | | | (9051) op(e3, e3) = e1 % 134.53/19.59 | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 134.53/19.59 | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | (9052) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 134.53/19.59 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 134.53/19.59 | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | BETA: splitting (9052) gives: % 134.53/19.59 | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | (9053) all_57_2 = e1 & op(e2, e3) = e1 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (9049), (9053), (function-axioms) are % 134.53/19.59 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #676. % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | (9054) all_57_3 = e1 & op(e2, e2) = e1 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | ALPHA: (9054) implies: % 134.53/19.59 | | | | | | | | | | | | | | | | | | | (9055) op(e2, e2) = e1 % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (8993), (9055), (function-axioms) are % 134.53/19.59 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #57. % 134.53/19.59 | | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.59 | | | | | | | | | | | | | | | | | | % 134.53/19.59 | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.59 | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | (9056) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | BETA: splitting (9056) gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | (9057) all_57_5 = e1 & op(e2, e1) = e1 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | ALPHA: (9057) implies: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | (9058) op(e2, e1) = e1 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | (9059) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9059) gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9060) all_57_1 = e1 & op(e3, e2) = e1 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (9050), (9060), (function-axioms) are % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #684. % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9061) all_57_3 = e1 & op(e2, e2) = e1 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9061) implies: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9062) op(e2, e2) = e1 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (8993), (9062), (function-axioms) are % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #57. % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | (9063) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9063) gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9064) all_57_7 = e1 & op(e1, e2) = e1 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9064) implies: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9065) op(e1, e2) = e1 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (162), (9065) gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9066) all_52_6 = e1 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (9058) gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9067) all_52_9 = e1 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (9066) imply: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9068) ~ (all_52_2 = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (9066) imply: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9069) ~ (all_52_14 = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (9067) imply: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9070) ~ (all_52_8 = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (9067) imply: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9071) ~ (all_6_2 = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | SIMP: (9071) implies: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9072) ~ (all_6_2 = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9014), (9067) imply: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | (9073) ~ (e2 = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | (9074) all_54_10 = e3 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (9003), (9074) are inconsistent by % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | sub-proof #742. % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | (9075) ~ (all_54_10 = e3) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | (9076) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9076) gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | (9077) all_54_10 = e2 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (8992), (9077) are inconsistent by % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #741. % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | (9078) ~ (all_54_10 = e2) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | (9079) all_54_10 = e1 | all_54_10 = e0 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9079) gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | (9080) all_54_10 = e1 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (9072), (9080) are inconsistent by % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #736. % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | (9081) all_54_10 = e0 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (9081) imply: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | (9082) all_6_2 = e0 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9082) implies: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | (9083) all_6_2 = e0 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (9083) imply: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | (9084) ~ (all_52_11 = e0) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9003), (9083) imply: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | (9085) ~ (e3 = e0) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9072), (9083) imply: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | (9086) ~ (e1 = e0) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (9083) imply: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | (9087) op(e1, e1) = e0 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (9088) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9088) gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (9089) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9089) gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9090) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9090) implies: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9091) op(e3, e3) = e2 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9051), (9091), (function-axioms) are % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743. % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9092) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9092) implies: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9093) ~ (all_56_13 = e2) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9094) ~ (all_56_5 = e3) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9095) op(e1, e2) = all_56_13 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9096) op(e1, e3) = all_56_5 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9097) op(e3, e1) = e3 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e2, e1, simplifying with (9065), (9095) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9098) all_56_13 = e1 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5, e3, e1, simplifying with (163), (9096) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9099) all_56_5 = all_52_2 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (9097) gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9100) all_52_8 = e3 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (9100) imply: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9101) ~ (all_52_4 = e3) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (9100) imply: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9102) ~ (all_52_12 = e3) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9102) implies: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9103) ~ (all_52_12 = e3) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (39), (106), (163), (168), (170), % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (194), (203), (216), (217), (218), (228), (230), % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (271), (334), (8992), (9003), (9013), % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9020), (9048), (9050), (9051), (9068), (9072), % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9094), (9096), (9101), (9103), (function-axioms) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #718. % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (9104) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9104) gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9105) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9105) implies: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9106) op(e3, e3) = e0 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9051), (9106), (function-axioms) are % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9107) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9107) implies: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9108) op(e2, e2) = e3 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (8999), (9108), (function-axioms) are % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228. % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (9109) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9109) gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (9110) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (165), (9014), (9087), (9110), % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | #143. % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (9111) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9111) gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9112) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9112) implies: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9113) op(e2, e0) = e2 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (267), (358), (8993), (9005), (9008), % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9113), (function-axioms) are inconsistent by % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #60. % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9114) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9114) gives: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9115) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9115) implies: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9116) ~ (all_56_19 = e1) % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9117) op(e2, e1) = all_56_19 % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9058), (9116), (9117), (function-axioms) are % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106. % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9118) op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9118) implies: % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9119) op(e0, e0) = all_56_31 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9120) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (160), (8984), (8991), (9058), (9084), % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9119), (9120), (function-axioms) are inconsistent % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #55. % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (9121) all_57_13 = e1 & op(e0, e2) = e1 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8980), (9121), (function-axioms) are % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #178. % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.61 | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | (9122) all_57_10 = e1 & op(e2, e0) = e1 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | ALPHA: (9122) implies: % 134.53/19.61 | | | | | | | | | | | | | | | | | | | (9123) op(e2, e0) = e1 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8983), (9123), (function-axioms) are % 134.53/19.61 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180. % 134.53/19.61 | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | Case 2: % 134.53/19.61 | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | (9124) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = % 134.53/19.61 | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 134.53/19.61 | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | BETA: splitting (9124) gives: % 134.53/19.61 | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | Case 1: % 134.53/19.61 | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | (9125) all_57_5 = e2 & op(e2, e1) = e2 % 134.53/19.61 | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | ALPHA: (9125) implies: % 134.53/19.61 | | | | | | | | | | | | | | | | (9126) op(e2, e1) = e2 % 134.53/19.61 | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9014), (9126), (function-axioms) are % 134.53/19.61 | | | | | | | | | | | | | | | | inconsistent by sub-proof #770. % 134.53/19.61 | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | Case 2: % 134.53/19.61 | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | (9127) all_57_10 = e2 & op(e2, e0) = e2 % 134.53/19.61 | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | ALPHA: (9127) implies: % 134.53/19.61 | | | | | | | | | | | | | | | | (9128) op(e2, e0) = e2 % 134.53/19.61 | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | REF_CLOSE: (164), (267), (358), (8993), (9005), (9008), % 134.53/19.61 | | | | | | | | | | | | | | | | (9128), (function-axioms) are inconsistent by % 134.53/19.61 | | | | | | | | | | | | | | | | sub-proof #60. % 134.53/19.61 | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | Case 2: % 134.53/19.61 | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | (9129) all_54_5 = e1 | all_54_5 = e0 % 134.53/19.61 | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | REF_CLOSE: (267), (8993), (9005), (9129) are inconsistent by % 134.53/19.61 | | | | | | | | | | | | | | sub-proof #624. % 134.53/19.61 | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | Case 2: % 134.53/19.61 | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | (9130) all_30_2 = e0 % 134.53/19.61 | | | | | | | | | | | | (9131) ( ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 & % 134.53/19.61 | | | | | | | | | | | | $i(all_30_0)) | ( ~ (all_30_1 = e1) & op(e0, e0) % 134.53/19.61 | | | | | | | | | | | | = all_30_1 & $i(all_30_1)) % 134.53/19.61 | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | COMBINE_EQS: (309), (9130) imply: % 134.53/19.61 | | | | | | | | | | | | (9132) all_8_2 = e0 % 134.53/19.61 | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | SIMP: (9132) implies: % 134.53/19.61 | | | | | | | | | | | | (9133) all_8_2 = e0 % 134.53/19.61 | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | REDUCE: (350), (9133) imply: % 134.53/19.61 | | | | | | | | | | | | (9134) ~ (all_52_4 = e0) % 134.53/19.61 | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | REDUCE: (352), (9133) imply: % 134.53/19.61 | | | | | | | | | | | | (9135) ~ (all_52_6 = e0) % 134.53/19.61 | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | REDUCE: (354), (9133) imply: % 134.53/19.61 | | | | | | | | | | | | (9136) ~ (all_52_7 = e0) % 134.53/19.61 | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | REDUCE: (8993), (9133) imply: % 134.53/19.61 | | | | | | | | | | | | (9137) ~ (e1 = e0) % 134.53/19.61 | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | REDUCE: (42), (9133) imply: % 134.53/19.61 | | | | | | | | | | | | (9138) op(e2, e2) = e0 % 134.53/19.61 | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | BETA: splitting (9131) gives: % 134.53/19.61 | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | Case 1: % 134.53/19.61 | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | (9139) ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 & % 134.53/19.61 | | | | | | | | | | | | | $i(all_30_0) % 134.53/19.61 | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | ALPHA: (9139) implies: % 134.53/19.61 | | | | | | | | | | | | | (9140) ~ (all_30_0 = e3) % 134.53/19.61 | | | | | | | | | | | | | (9141) op(e0, e2) = all_30_0 % 134.53/19.61 | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, % 134.53/19.61 | | | | | | | | | | | | | all_30_0, e2, e0, simplifying with (158), (9141) % 134.53/19.61 | | | | | | | | | | | | | gives: % 134.53/19.61 | | | | | | | | | | | | | (9142) all_52_7 = all_30_0 % 134.53/19.61 | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | COMBINE_EQS: (247), (9142) imply: % 134.53/19.61 | | | | | | | | | | | | | (9143) all_54_13 = all_30_0 % 134.53/19.61 | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | REDUCE: (135), (9142) imply: % 134.53/19.61 | | | | | | | | | | | | | (9144) ~ (all_52_4 = all_30_0) % 134.53/19.61 | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | REDUCE: (128), (9142) imply: % 134.53/19.61 | | | | | | | | | | | | | (9145) ~ (all_52_6 = all_30_0) % 134.53/19.61 | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | BETA: splitting (191) gives: % 134.53/19.61 | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | Case 1: % 134.53/19.61 | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | (9146) all_54_13 = e3 % 134.53/19.61 | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | REF_CLOSE: (9140), (9143), (9146) are inconsistent by % 134.53/19.61 | | | | | | | | | | | | | | sub-proof #54. % 134.53/19.61 | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | Case 2: % 134.53/19.61 | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | (9147) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 134.53/19.61 | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | BETA: splitting (9147) gives: % 134.53/19.61 | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | Case 1: % 134.53/19.61 | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | (9148) all_54_13 = e2 % 134.53/19.61 | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | COMBINE_EQS: (9143), (9148) imply: % 134.53/19.61 | | | | | | | | | | | | | | | (9149) all_30_0 = e2 % 134.53/19.61 | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | SIMP: (9149) implies: % 134.53/19.61 | | | | | | | | | | | | | | | (9150) all_30_0 = e2 % 134.53/19.61 | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | REDUCE: (9144), (9150) imply: % 134.53/19.61 | | | | | | | | | | | | | | | (9151) ~ (all_52_4 = e2) % 134.53/19.61 | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | REDUCE: (9145), (9150) imply: % 134.53/19.61 | | | | | | | | | | | | | | | (9152) ~ (all_52_6 = e2) % 134.53/19.61 | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | REDUCE: (9141), (9150) imply: % 134.53/19.61 | | | | | | | | | | | | | | | (9153) op(e0, e2) = e2 % 134.53/19.61 | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 134.53/19.61 | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | Case 1: % 134.53/19.61 | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | (9154) ~ (all_32_2 = e1) % 134.53/19.61 | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | REDUCE: (312), (9154) imply: % 134.53/19.61 | | | | | | | | | | | | | | | | (9155) ~ (all_10_2 = e1) % 134.53/19.61 | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 134.53/19.61 | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | Case 1: % 134.53/19.61 | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | (9156) all_54_0 = e3 % 134.53/19.61 | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (9156) imply: % 134.53/19.61 | | | | | | | | | | | | | | | | | (9157) all_10_2 = e3 % 134.53/19.61 | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | REDUCE: (346), (9157) imply: % 134.53/19.61 | | | | | | | | | | | | | | | | | (9158) ~ (all_52_12 = e3) % 134.53/19.61 | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | REDUCE: (45), (9157) imply: % 134.53/19.61 | | | | | | | | | | | | | | | | | (9159) op(e3, e3) = e3 % 134.53/19.61 | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 134.53/19.61 | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.61 | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | (9160) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.61 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.61 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.61 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.61 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.61 | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | BETA: splitting (9160) gives: % 134.53/19.61 | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.61 | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | (9161) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (9159), (9161), (function-axioms) are % 134.53/19.61 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623. % 134.53/19.61 | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.61 | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | (9162) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (9138), (9158), (9162), % 134.53/19.61 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.61 | | | | | | | | | | | | | | | | | | | #622. % 134.53/19.61 | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.61 | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.61 | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | (9163) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.61 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.61 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.61 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.61 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.53/19.61 | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.53/19.61 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.53/19.61 | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.53/19.61 | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.53/19.61 | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.61 | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.53/19.61 | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.61 | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.53/19.61 | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.61 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.61 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.61 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.61 | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.61 | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | BETA: splitting (9163) gives: % 134.53/19.61 | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.61 | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | (9164) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (9003), (9138), (9164), % 134.53/19.61 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.61 | | | | | | | | | | | | | | | | | | | #621. % 134.53/19.61 | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.61 | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | (9165) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | BETA: splitting (9165) gives: % 134.53/19.61 | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | (9166) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | ALPHA: (9166) implies: % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | (9167) ~ (all_56_15 = e2) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | (9168) op(e0, e2) = all_56_15 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9153), (9167), (9168), (function-axioms) are % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609. % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | (9169) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9169) gives: % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (9170) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9170) implies: % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (9171) op(e1, e1) = e2 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (9171), (function-axioms) are % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (9172) op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.61 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9172) implies: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9173) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (42), (157), (158), (160), (194), (199), % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (267), (334), (354), (364), (8984), (8992), % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (8993), (8999), (9003), (9159), (9173), % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | #58. % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.62 | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.62 | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | End of split % 134.53/19.62 | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | Case 2: % 134.53/19.62 | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | (9174) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 134.53/19.62 | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (8994), (9001), (9155), (9174) are % 134.53/19.62 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #777. % 134.53/19.62 | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | End of split % 134.53/19.62 | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | Case 2: % 134.53/19.62 | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | (9175) all_32_2 = e1 % 134.53/19.62 | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | COMBINE_EQS: (312), (9175) imply: % 134.53/19.62 | | | | | | | | | | | | | | | | (9176) all_10_2 = e1 % 134.53/19.62 | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | SIMP: (9176) implies: % 134.53/19.62 | | | | | | | | | | | | | | | | (9177) all_10_2 = e1 % 134.53/19.62 | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | REDUCE: (336), (9177) imply: % 134.53/19.62 | | | | | | | | | | | | | | | | (9178) ~ (all_52_1 = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | REDUCE: (342), (9177) imply: % 134.53/19.62 | | | | | | | | | | | | | | | | (9179) ~ (all_52_4 = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | REDUCE: (9001), (9177) imply: % 134.53/19.62 | | | | | | | | | | | | | | | | (9180) ~ (e2 = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | REDUCE: (45), (9177) imply: % 134.53/19.62 | | | | | | | | | | | | | | | | (9181) op(e3, e3) = e1 % 134.53/19.62 | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 134.53/19.62 | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | Case 1: % 134.53/19.62 | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | (9182) all_54_1 = e3 % 134.53/19.62 | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (9182) imply: % 134.53/19.62 | | | | | | | | | | | | | | | | | (9183) all_52_4 = e3 % 134.53/19.62 | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | REDUCE: (136), (9183) imply: % 134.53/19.62 | | | | | | | | | | | | | | | | | (9184) ~ (all_52_6 = e3) % 134.53/19.62 | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | SIMP: (9184) implies: % 134.53/19.62 | | | | | | | | | | | | | | | | | (9185) ~ (all_52_6 = e3) % 134.53/19.62 | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 134.53/19.62 | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.62 | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | (9186) all_54_9 = e3 % 134.53/19.62 | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (9185), (9186) are inconsistent by % 134.53/19.62 | | | | | | | | | | | | | | | | | | sub-proof #64. % 134.53/19.62 | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.62 | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | (9187) ~ (all_54_9 = e3) % 134.53/19.62 | | | | | | | | | | | | | | | | | | (9188) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 134.53/19.62 | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 134.53/19.62 | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | (9189) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | BETA: splitting (9189) gives: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (9190) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9190) gives: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9191) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9191) implies: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9192) op(e3, e3) = e2 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9181), (9192), (function-axioms) are % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743. % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9193) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9193) implies: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9194) op(e3, e1) = e3 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (134), (169), (203), (271), (9134), (9151), % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9179), (9194), (function-axioms) are inconsistent % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | by sub-proof #700. % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (9195) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (133), (168), (203), (271), (9134), (9138), % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (9151), (9179), (9195), (function-axioms) are % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #215. % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.62 | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | (9196) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | BETA: splitting (9196) gives: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (9197) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (9003), (9138), (9197), % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | #621. % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (9198) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9198) gives: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9199) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9199) implies: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9200) ~ (all_56_15 = e2) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9201) op(e0, e2) = all_56_15 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9153), (9200), (9201), (function-axioms) are % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609. % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (9202) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9202) gives: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (9203) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9203) implies: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (9204) op(e1, e1) = e2 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (9204), (function-axioms) are % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (9205) op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9205) implies: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (9206) op(e0, e0) = all_56_31 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (9207) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | (9208) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (9138), (9178), (9208), % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | #674. % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | (9209) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9209) gives: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | (9210) all_57_5 = e1 & op(e2, e1) = e1 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9210) implies: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | (9211) op(e2, e1) = e1 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9188) gives: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (9212) all_54_9 = e2 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (9152), (9212) are inconsistent by % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #582. % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (9213) all_54_9 = e1 | all_54_9 = e0 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9213) gives: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (9214) all_54_9 = e1 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (9214) imply: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (9215) all_52_6 = e1 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9215) implies: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (9216) all_52_6 = e1 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (9216) imply: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (9217) ~ (all_52_14 = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (9216) imply: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (9218) ~ (all_6_2 = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9218) implies: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (9219) ~ (all_6_2 = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9185), (9216) imply: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (9220) ~ (e3 = e1) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9221) all_54_10 = e3 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (9003), (9221) are inconsistent by % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #742. % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9222) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9222) gives: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9223) all_54_10 = e2 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (8992), (9223) are inconsistent by % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #741. % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9224) all_54_10 = e1 | all_54_10 = e0 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9224) gives: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9225) all_54_10 = e1 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (9219), (9225) are inconsistent by % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #736. % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9226) all_54_10 = e0 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (9226) imply: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9227) all_6_2 = e0 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9227) implies: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9228) all_6_2 = e0 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (9228) imply: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9229) ~ (all_52_11 = e0) % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (160), (8984), (8991), (9206), (9207), % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9211), (9229), (function-axioms) are inconsistent % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #55. % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (9230) all_54_9 = e0 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (9135), (9230) are inconsistent by % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #568. % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | (9231) all_57_10 = e1 & op(e2, e0) = e1 % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.62 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9231) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | (9232) op(e2, e0) = e1 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8983), (9232), (function-axioms) are % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | (9233) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (9134), (9151), (9179), (9233) are % 134.53/19.63 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #701. % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | (9234) all_54_13 = e1 | all_54_13 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | REF_CLOSE: (247), (8980), (9136), (9234) are inconsistent by % 134.53/19.63 | | | | | | | | | | | | | | | sub-proof #470. % 134.53/19.63 | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | (9235) ~ (all_30_1 = e1) & op(e0, e0) = all_30_1 & % 134.53/19.63 | | | | | | | | | | | | | $i(all_30_1) % 134.53/19.63 | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | REF_CLOSE: (8991), (9235), (function-axioms) are inconsistent % 134.53/19.63 | | | | | | | | | | | | | by sub-proof #53. % 134.53/19.63 | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | (9236) all_28_2 = e3 % 134.53/19.63 | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | COMBINE_EQS: (316), (9236) imply: % 134.53/19.63 | | | | | | | | | | | (9237) all_6_2 = e3 % 134.53/19.63 | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | SIMP: (9237) implies: % 134.53/19.63 | | | | | | | | | | | (9238) all_6_2 = e3 % 134.53/19.63 | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | REDUCE: (348), (9238) imply: % 134.53/19.63 | | | | | | | | | | | (9239) ~ (all_52_2 = e3) % 134.53/19.63 | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | REDUCE: (359), (9238) imply: % 134.53/19.63 | | | | | | | | | | | (9240) ~ (all_52_6 = e3) % 134.53/19.63 | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | REDUCE: (362), (9238) imply: % 134.53/19.63 | | | | | | | | | | | (9241) ~ (all_52_9 = e3) % 134.53/19.63 | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | REDUCE: (364), (9238) imply: % 134.53/19.63 | | | | | | | | | | | (9242) ~ (all_52_11 = e3) % 134.53/19.63 | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | REDUCE: (366), (9238) imply: % 134.53/19.63 | | | | | | | | | | | (9243) ~ (all_52_14 = e3) % 134.53/19.63 | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | BETA: splitting (218) gives: % 134.53/19.63 | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | (9244) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 134.53/19.63 | | | | | | | | | | | | & op(e1, e2) = e3) % 134.53/19.63 | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | REF_CLOSE: (162), (163), (9239), (9240), (9244), % 134.53/19.63 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.63 | | | | | | | | | | | | #323. % 134.53/19.63 | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | (9245) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 134.53/19.63 | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 134.53/19.63 | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | BETA: splitting (9245) gives: % 134.53/19.63 | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | (9246) all_57_8 = e3 & op(e1, e1) = e3 % 134.53/19.63 | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | ALPHA: (9246) implies: % 134.53/19.63 | | | | | | | | | | | | | (9247) all_57_8 = e3 % 134.53/19.63 | | | | | | | | | | | | | (9248) op(e1, e1) = e3 % 134.53/19.63 | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | BETA: splitting (8997) gives: % 134.53/19.63 | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | (9249) ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 & % 134.53/19.63 | | | | | | | | | | | | | | $i(all_12_0) % 134.53/19.63 | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | ALPHA: (9249) implies: % 134.53/19.63 | | | | | | | | | | | | | | (9250) ~ (all_12_0 = e2) % 134.53/19.63 | | | | | | | | | | | | | | (9251) op(e1, e0) = all_12_0 % 134.53/19.63 | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 134.53/19.63 | | | | | | | | | | | | | | all_12_0, e0, e1, simplifying with (160), (9251) % 134.53/19.63 | | | | | | | | | | | | | | gives: % 134.53/19.63 | | | | | | | | | | | | | | (9252) all_52_14 = all_12_0 % 134.53/19.63 | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | COMBINE_EQS: (249), (9252) imply: % 134.53/19.63 | | | | | | | | | | | | | | (9253) all_54_11 = all_12_0 % 134.53/19.63 | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | REDUCE: (141), (9252) imply: % 134.53/19.63 | | | | | | | | | | | | | | (9254) ~ (all_52_2 = all_12_0) % 134.53/19.63 | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | REDUCE: (126), (9252) imply: % 134.53/19.63 | | | | | | | | | | | | | | (9255) ~ (all_52_6 = all_12_0) % 134.53/19.63 | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | REDUCE: (112), (9252) imply: % 134.53/19.63 | | | | | | | | | | | | | | (9256) ~ (all_52_12 = all_12_0) % 134.53/19.63 | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | REDUCE: (9243), (9252) imply: % 134.53/19.63 | | | | | | | | | | | | | | (9257) ~ (all_12_0 = e3) % 134.53/19.63 | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | REDUCE: (8984), (9252) imply: % 134.53/19.63 | | | | | | | | | | | | | | (9258) ~ (all_12_0 = e1) % 134.53/19.63 | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | BETA: splitting (193) gives: % 134.53/19.63 | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | (9259) all_54_11 = e3 % 134.53/19.63 | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | REF_CLOSE: (9253), (9257), (9259) are inconsistent by % 134.53/19.63 | | | | | | | | | | | | | | | sub-proof #52. % 134.53/19.63 | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | (9260) ~ (all_54_11 = e3) % 134.53/19.63 | | | | | | | | | | | | | | | (9261) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | BETA: splitting (9261) gives: % 134.53/19.63 | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | (9262) all_54_11 = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | REF_CLOSE: (9250), (9253), (9262) are inconsistent by % 134.53/19.63 | | | | | | | | | | | | | | | | sub-proof #51. % 134.53/19.63 | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | (9263) ~ (all_54_11 = e2) % 134.53/19.63 | | | | | | | | | | | | | | | | (9264) all_54_11 = e1 | all_54_11 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | BETA: splitting (9264) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | (9265) all_54_11 = e1 % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | REF_CLOSE: (9253), (9258), (9265) are inconsistent by % 134.53/19.63 | | | | | | | | | | | | | | | | | sub-proof #50. % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | (9266) all_54_11 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | COMBINE_EQS: (9253), (9266) imply: % 134.53/19.63 | | | | | | | | | | | | | | | | | (9267) all_12_0 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | SIMP: (9267) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | (9268) all_12_0 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | REDUCE: (9254), (9268) imply: % 134.53/19.63 | | | | | | | | | | | | | | | | | (9269) ~ (all_52_2 = e0) % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | REDUCE: (9255), (9268) imply: % 134.53/19.63 | | | | | | | | | | | | | | | | | (9270) ~ (all_52_6 = e0) % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | REDUCE: (9256), (9268) imply: % 134.53/19.63 | | | | | | | | | | | | | | | | | (9271) ~ (all_52_12 = e0) % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | REDUCE: (9257), (9268) imply: % 134.53/19.63 | | | | | | | | | | | | | | | | | (9272) ~ (e3 = e0) % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | REDUCE: (9250), (9268) imply: % 134.53/19.63 | | | | | | | | | | | | | | | | | (9273) ~ (e2 = e0) % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | REDUCE: (9258), (9268) imply: % 134.53/19.63 | | | | | | | | | | | | | | | | | (9274) ~ (e1 = e0) % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | (9275) all_57_15 = e0 & op(e0, e0) = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | ALPHA: (9275) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | (9276) op(e0, e0) = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8991), (9276), (function-axioms) are % 134.53/19.63 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #220. % 134.53/19.63 | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | (9277) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 134.53/19.63 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 134.53/19.63 | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 134.53/19.63 | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 134.53/19.63 | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 134.53/19.63 | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | ALPHA: (9277) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | (9278) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 134.53/19.63 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, % 134.53/19.63 | | | | | | | | | | | | | | | | | | e0) = e0) % 134.53/19.63 | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | BETA: splitting (9278) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | (9279) all_57_9 = e0 & op(e3, e0) = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (9271), (9279), (function-axioms) are % 134.53/19.63 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #618. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | (9280) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = % 134.53/19.63 | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | BETA: splitting (9280) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | (9281) all_57_10 = e0 & op(e2, e0) = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | ALPHA: (9281) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | (9282) all_57_10 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | (9283) op(e2, e0) = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | (9284) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9284) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9285) all_57_2 = e3 & op(e2, e3) = e3 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9285) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9286) all_57_2 = e3 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | (9287) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9287) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | (9288) all_57_9 = e3 & op(e3, e0) = e3 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9288) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | (9289) op(e3, e0) = e3 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | (9290) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9290) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (9291) all_57_0 = e0 & op(e3, e3) = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9291) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (9292) op(e3, e3) = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (8994), (9292), (function-axioms) are % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #534. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (9293) all_57_2 = e0 & op(e2, e3) = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9286), (9293) are inconsistent by sub-proof % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | #521. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | (9294) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9294) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (9295) all_57_6 = e0 & op(e1, e3) = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9269), (9295), (function-axioms) are % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #73. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (9296) all_57_12 = e0 & op(e0, e3) = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9296) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (9297) all_57_12 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9298) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9298) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9299) all_57_9 = e2 & op(e3, e0) = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9299) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9300) op(e3, e0) = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (9289), (9300), (function-axioms) are % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #111. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9301) all_57_10 = e2 & op(e2, e0) = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9301) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9302) op(e2, e0) = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9283), (9302), (function-axioms) are % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #451. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9303) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9303) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9304) all_57_11 = e2 & op(e1, e0) = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9304) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9305) all_57_11 = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9306) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9306) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9307) all_57_0 = e2 & op(e3, e3) = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9307) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9308) op(e3, e3) = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (9001), (9308), (function-axioms) are % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #536. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9309) all_57_2 = e2 & op(e2, e3) = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9309) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9310) all_57_2 = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9286), (9310) imply: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9311) e3 = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9247), (9311) imply: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9312) all_57_8 = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (215), (216), % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (9240), (9305), (9312), (function-axioms) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #571. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9313) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9313) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9314) all_57_6 = e2 & op(e1, e3) = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9314) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9315) all_57_6 = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9316) op(e1, e3) = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9317) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9317) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9318) all_57_0 = e1 & op(e3, e3) = e1 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9318) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9319) op(e3, e3) = e1 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9320) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9320) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9321) all_57_6 = e0 & op(e1, e3) = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9321) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9322) all_57_6 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (235), (9286), (9297), (9319), % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9322), (function-axioms) are inconsistent by % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #49. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9323) all_57_7 = e0 & op(e1, e2) = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (9270), (9323), (function-axioms) are % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #505. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9324) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9324) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9325) all_57_8 = e0 & op(e1, e1) = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9325) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9326) op(e1, e1) = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9248), (9326), (function-axioms) are % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9327) all_57_11 = e0 & op(e1, e0) = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9327) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9328) all_57_11 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9305), (9328) imply: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9329) e2 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9315), (9329) imply: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9330) all_57_6 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (235), (9286), (9297), (9319), % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9330), (function-axioms) are inconsistent by % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #49. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9331) all_57_2 = e1 & op(e2, e3) = e1 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9286), (9331) are inconsistent by sub-proof % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #453. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9332) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (159), (163), (8979), (9316), (9332), % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #47. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9333) all_57_12 = e2 & op(e0, e3) = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9333) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9334) all_57_12 = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9297), (9334) imply: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9335) e2 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (9335) imply: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9336) $false % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9336) is inconsistent. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9337) all_57_15 = e2 & op(e0, e0) = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9337) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9338) op(e0, e0) = e2 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8991), (9338), (function-axioms) are % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | (9339) all_57_10 = e3 & op(e2, e0) = e3 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9339) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | (9340) all_57_10 = e3 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9282), (9340) are inconsistent by sub-proof % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | #448. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | (9341) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (8991), (9243), (9341), % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | #46. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9342) all_57_3 = e3 & op(e2, e2) = e3 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9342) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9343) op(e2, e2) = e3 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (8999), (9343), (function-axioms) are % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | (9344) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9344) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9345) all_57_5 = e3 & op(e2, e1) = e3 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9241), (9345), (function-axioms) are % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9346) all_57_10 = e3 & op(e2, e0) = e3 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9346) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9347) all_57_10 = e3 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9282), (9347) are inconsistent by sub-proof % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | #448. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | (9348) all_57_11 = e0 & op(e1, e0) = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | ALPHA: (9348) implies: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | (9349) all_57_11 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | (9350) op(e1, e0) = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | (9351) ~ (all_30_2 = e0) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | REDUCE: (309), (9351) imply: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | (9352) ~ (all_8_2 = e0) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9353) all_54_5 = e3 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (9353) imply: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9354) all_8_2 = e3 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8999), (9354) imply: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9355) $false % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9355) is inconsistent. % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9356) ~ (all_54_5 = e3) % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | (9357) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.63 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (9358) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (45), (8994), (8999), (9001), (9350), % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (9358), (function-axioms) are inconsistent by % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #43. % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (9359) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9359) gives: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (9360) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9360) gives: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9361) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9361) implies: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9362) op(e1, e3) = e1 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9357) gives: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9363) all_54_5 = e2 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (9363) imply: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9364) all_8_2 = e2 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (352), (9364) imply: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9365) ~ (all_52_6 = e2) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8999), (9364) imply: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9366) ~ (e3 = e2) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9367) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9367) gives: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9368) all_57_6 = e2 & op(e1, e3) = e2 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9368) implies: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9369) op(e1, e3) = e2 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (9362), (9369), (function-axioms) are % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #517. % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9370) all_57_7 = e2 & op(e1, e2) = e2 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (9365), (9370), (function-axioms) are % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515. % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9371) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9371) gives: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9372) all_57_8 = e2 & op(e1, e1) = e2 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9372) implies: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9373) op(e1, e1) = e2 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (42), (45), (158), (160), (164), (199), % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (267), (354), (358), (8984), (8991), % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8993), (8994), (8999), (9001), (9350), (9352), % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9357), (9373), (function-axioms) are inconsistent % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #38. % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9374) all_57_11 = e2 & op(e1, e0) = e2 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9374) implies: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9375) all_57_11 = e2 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9349), (9375) are inconsistent by sub-proof % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #638. % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9376) all_54_5 = e1 | all_54_5 = e0 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (8993), (9352), (9376) are inconsistent by % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #624. % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9377) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9377) implies: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9378) ~ (all_56_29 = e0) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9379) op(e1, e0) = all_56_29 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9350), (9378), (9379), (function-axioms) are % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #45. % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (9380) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9380) gives: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9381) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9381) implies: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9382) op(e2, e0) = e2 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (267), (358), (8993), (9352), (9357), % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9382), (function-axioms) are inconsistent by % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #60. % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9383) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9383) gives: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9384) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9384) implies: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9385) op(e1, e1) = e2 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (42), (45), (158), (160), (164), (199), % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (267), (354), (358), (8984), (8991), % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (8993), (8994), (8999), (9001), (9350), (9352), % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9357), (9385), (function-axioms) are inconsistent % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #38. % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9386) op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (42), (158), (160), (199), (267), (354), % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (8984), (8991), (8993), (8999), (9350), (9386), % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | #39. % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | (9387) all_30_2 = e0 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | (9388) ( ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | $i(all_30_0)) | ( ~ (all_30_1 = e1) & op(e0, e0) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | = all_30_1 & $i(all_30_1)) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (9387) imply: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | (9389) all_8_2 = e0 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | SIMP: (9389) implies: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | (9390) all_8_2 = e0 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | REDUCE: (347), (9390) imply: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | (9391) ~ (all_52_1 = e0) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | (9392) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (167), (8994), (9391), (9392), % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | #142. % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | (9393) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9393) gives: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (9394) all_57_6 = e0 & op(e1, e3) = e0 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9269), (9394), (function-axioms) are % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #73. % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (9395) all_57_12 = e0 & op(e0, e3) = e0 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9395) implies: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | (9396) all_57_12 = e0 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (9397) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9397) gives: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9398) all_57_12 = e3 & op(e0, e3) = e3 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9398) implies: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9399) all_57_12 = e3 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9396), (9399) are inconsistent by sub-proof % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | #492. % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9400) all_57_13 = e3 & op(e0, e2) = e3 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9400) implies: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (9401) op(e0, e2) = e3 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9388) gives: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9402) ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_30_0) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9402) implies: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9403) ~ (all_30_0 = e3) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9404) op(e0, e2) = all_30_0 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_0, % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (9401), (9404) gives: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9405) all_30_0 = e3 % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9403), (9405) imply: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9406) $false % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9406) is inconsistent. % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (9407) ~ (all_30_1 = e1) & op(e0, e0) = all_30_1 & % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_30_1) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8991), (9407), (function-axioms) are inconsistent % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #53. % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (9408) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (8991), (9242), (9408), % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | #37. % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | (9409) ~ (all_12_1 = e3) & op(e1, e1) = all_12_1 & % 134.53/19.64 | | | | | | | | | | | | | | $i(all_12_1) % 134.53/19.64 | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | ALPHA: (9409) implies: % 134.53/19.64 | | | | | | | | | | | | | | (9410) ~ (all_12_1 = e3) % 134.53/19.64 | | | | | | | | | | | | | | (9411) op(e1, e1) = all_12_1 % 134.53/19.64 | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | | REF_CLOSE: (9248), (9410), (9411), (function-axioms) are % 134.53/19.64 | | | | | | | | | | | | | | inconsistent by sub-proof #36. % 134.53/19.64 | | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | (9412) all_57_11 = e3 & op(e1, e0) = e3 % 134.53/19.64 | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | REF_CLOSE: (160), (9243), (9412), (function-axioms) are % 134.53/19.64 | | | | | | | | | | | | | inconsistent by sub-proof #750. % 134.53/19.64 | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | End of split % 134.53/19.64 | | | | | | | | | | % 134.53/19.64 | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | (9413) all_16_2 = e2 % 134.53/19.64 | | | | | | | | | | (9414) ( ~ (all_16_0 = e1) & op(e2, e3) = all_16_0 & % 134.53/19.64 | | | | | | | | | | $i(all_16_0)) | ( ~ (all_16_1 = e0) & op(e2, e2) % 134.53/19.64 | | | | | | | | | | = all_16_1 & $i(all_16_1)) % 134.53/19.64 | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | COMBINE_EQS: (327), (9413) imply: % 134.53/19.64 | | | | | | | | | | (9415) all_10_2 = e2 % 134.53/19.64 | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | SIMP: (9415) implies: % 134.53/19.64 | | | | | | | | | | (9416) all_10_2 = e2 % 134.53/19.64 | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | REDUCE: (344), (9416) imply: % 134.53/19.64 | | | | | | | | | | (9417) ~ (all_52_8 = e2) % 134.53/19.64 | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | REDUCE: (346), (9416) imply: % 134.53/19.64 | | | | | | | | | | (9418) ~ (all_52_12 = e2) % 134.53/19.64 | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | REDUCE: (45), (9416) imply: % 134.53/19.64 | | | | | | | | | | (9419) op(e3, e3) = e2 % 134.53/19.64 | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | BETA: splitting (76) gives: % 134.53/19.64 | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | Case 1: % 134.53/19.64 | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | (9420) ~ (all_30_2 = e0) % 134.53/19.64 | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | REDUCE: (309), (9420) imply: % 134.53/19.64 | | | | | | | | | | | (9421) ~ (all_8_2 = e0) % 134.53/19.64 | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | BETA: splitting (199) gives: % 134.53/19.64 | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | Case 1: % 134.53/19.64 | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | (9422) all_54_5 = e3 % 134.53/19.64 | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | REF_CLOSE: (267), (8999), (9422) are inconsistent by % 134.53/19.64 | | | | | | | | | | | | sub-proof #554. % 134.53/19.64 | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | Case 2: % 134.53/19.64 | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | (9423) ~ (all_54_5 = e3) % 134.53/19.64 | | | | | | | | | | | | (9424) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 134.53/19.64 | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | BETA: splitting (9424) gives: % 134.53/19.64 | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | Case 1: % 134.53/19.64 | | | | | | | | | | | | | % 134.53/19.64 | | | | | | | | | | | | | (9425) all_54_5 = e2 % 134.53/19.65 | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | COMBINE_EQS: (267), (9425) imply: % 134.53/19.65 | | | | | | | | | | | | | (9426) all_8_2 = e2 % 134.53/19.65 | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | SIMP: (9426) implies: % 134.53/19.65 | | | | | | | | | | | | | (9427) all_8_2 = e2 % 134.53/19.65 | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | REDUCE: (354), (9427) imply: % 134.53/19.65 | | | | | | | | | | | | | (9428) ~ (all_52_7 = e2) % 134.53/19.65 | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | REDUCE: (358), (9427) imply: % 134.53/19.65 | | | | | | | | | | | | | (9429) ~ (all_52_13 = e2) % 134.53/19.65 | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | REDUCE: (8999), (9427) imply: % 134.53/19.65 | | | | | | | | | | | | | (9430) ~ (e3 = e2) % 134.53/19.65 | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | REDUCE: (42), (9427) imply: % 134.53/19.65 | | | | | | | | | | | | | (9431) op(e2, e2) = e2 % 134.53/19.65 | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | BETA: splitting (213) gives: % 134.53/19.65 | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | Case 1: % 134.53/19.65 | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | (9432) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 134.53/19.65 | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 134.53/19.65 | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (9418), (9429), (9432), % 134.53/19.65 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.65 | | | | | | | | | | | | | | #440. % 134.53/19.65 | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | Case 2: % 134.53/19.65 | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | (9433) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 134.53/19.65 | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 134.53/19.65 | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | BETA: splitting (9433) gives: % 134.53/19.65 | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | Case 1: % 134.53/19.65 | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | (9434) all_57_11 = e2 & op(e1, e0) = e2 % 134.53/19.65 | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | ALPHA: (9434) implies: % 134.53/19.65 | | | | | | | | | | | | | | | (9435) op(e1, e0) = e2 % 134.53/19.65 | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 134.53/19.65 | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | Case 1: % 134.53/19.65 | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | (9436) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 134.53/19.65 | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 134.53/19.65 | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | BETA: splitting (9436) gives: % 134.53/19.65 | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | Case 1: % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | (9437) all_57_12 = e2 & op(e0, e3) = e2 % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | ALPHA: (9437) implies: % 134.53/19.65 | | | | | | | | | | | | | | | | | (9438) all_57_12 = e2 % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237), % 134.53/19.65 | | | | | | | | | | | | | | | | | (9419), (9438), (function-axioms) are inconsistent % 134.53/19.65 | | | | | | | | | | | | | | | | | by sub-proof #290. % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | Case 2: % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | (9439) all_57_13 = e2 & op(e0, e2) = e2 % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9428), (9439), (function-axioms) are % 134.53/19.65 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #100. % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | End of split % 134.53/19.65 | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | Case 2: % 134.53/19.65 | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | (9440) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 134.53/19.65 | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 134.53/19.65 | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | BETA: splitting (9440) gives: % 134.53/19.65 | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | Case 1: % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | (9441) all_57_14 = e2 & op(e0, e1) = e2 % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | ALPHA: (9441) implies: % 134.53/19.65 | | | | | | | | | | | | | | | | | (9442) op(e0, e1) = e2 % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11, % 134.53/19.65 | | | | | | | | | | | | | | | | | e2, e1, e0, simplifying with (157), (9442) gives: % 134.53/19.65 | | | | | | | | | | | | | | | | | (9443) all_52_11 = e2 % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 134.53/19.65 | | | | | | | | | | | | | | | | | e2, e0, e1, simplifying with (160), (9435) gives: % 134.53/19.65 | | | | | | | | | | | | | | | | | (9444) all_52_14 = e2 % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | REDUCE: (118), (9443) imply: % 134.53/19.65 | | | | | | | | | | | | | | | | | (9445) ~ (all_52_9 = e2) % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | REDUCE: (366), (9444) imply: % 134.53/19.65 | | | | | | | | | | | | | | | | | (9446) ~ (all_6_2 = e2) % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | BETA: splitting (8997) gives: % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.65 | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | (9447) ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | $i(all_12_0) % 134.53/19.65 | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | ALPHA: (9447) implies: % 134.53/19.65 | | | | | | | | | | | | | | | | | | (9448) ~ (all_12_0 = e2) % 134.53/19.65 | | | | | | | | | | | | | | | | | | (9449) op(e1, e0) = all_12_0 % 134.53/19.65 | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9435), (9448), (9449), (function-axioms) are % 134.53/19.65 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #35. % 134.53/19.65 | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.65 | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | (9450) ~ (all_12_1 = e3) & op(e1, e1) = all_12_1 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | $i(all_12_1) % 134.53/19.65 | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | ALPHA: (9450) implies: % 134.53/19.65 | | | | | | | | | | | | | | | | | | (9451) ~ (all_12_1 = e3) % 134.53/19.65 | | | | | | | | | | | | | | | | | | (9452) op(e1, e1) = all_12_1 % 134.53/19.65 | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 134.53/19.65 | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | (9453) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (42), (8999), (9419), (9431), (9453), % 134.53/19.65 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.65 | | | | | | | | | | | | | | | | | | | #80. % 134.53/19.65 | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | (9454) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | BETA: splitting (9454) gives: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | (9455) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9455) gives: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (9456) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9456) implies: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (9457) op(e1, e1) = e3 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9451), (9452), (9457), (function-axioms) are % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #36. % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (9458) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9458) implies: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (9459) op(e2, e1) = e2 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9445), (9459), (function-axioms) are % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770. % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | (9460) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9460) gives: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (9461) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9461) implies: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (9462) op(e2, e0) = e2 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9429), (9462), (function-axioms) are % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768. % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (9463) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9463) gives: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (9464) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9464) implies: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (9465) op(e1, e1) = e2 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (9465), (function-axioms) are % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (9466) op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9466) implies: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (9467) op(e0, e0) = all_56_31 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (9468) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9468) gives: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | (9469) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (42), (158), (199), (267), (354), (8991), % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | (8993), (8999), (9467), (9469), (function-axioms) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #41. % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | (9470) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9435), (9442), (9470), % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | #428. % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.65 | | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.65 | | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.65 | | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | End of split % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | Case 2: % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | (9471) all_57_15 = e2 & op(e0, e0) = e2 % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | ALPHA: (9471) implies: % 134.53/19.65 | | | | | | | | | | | | | | | | | (9472) op(e0, e0) = e2 % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8991), (9472), (function-axioms) are % 134.53/19.65 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636. % 134.53/19.65 | | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | | End of split % 134.53/19.65 | | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | End of split % 134.53/19.65 | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | Case 2: % 134.53/19.65 | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | (9473) all_57_15 = e2 & op(e0, e0) = e2 % 134.53/19.65 | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | ALPHA: (9473) implies: % 134.53/19.65 | | | | | | | | | | | | | | | (9474) op(e0, e0) = e2 % 134.53/19.65 | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | | REF_CLOSE: (6), (8991), (9474), (function-axioms) are % 134.53/19.65 | | | | | | | | | | | | | | | inconsistent by sub-proof #636. % 134.53/19.65 | | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | | End of split % 134.53/19.65 | | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | End of split % 134.53/19.65 | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | Case 2: % 134.53/19.65 | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | (9475) all_54_5 = e1 | all_54_5 = e0 % 134.53/19.65 | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | | REF_CLOSE: (267), (8993), (9421), (9475) are inconsistent by % 134.53/19.65 | | | | | | | | | | | | | sub-proof #624. % 134.53/19.65 | | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | | End of split % 134.53/19.65 | | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | End of split % 134.53/19.65 | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | Case 2: % 134.53/19.65 | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | (9476) all_30_2 = e0 % 134.53/19.65 | | | | | | | | | | | (9477) ( ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 & % 134.53/19.65 | | | | | | | | | | | $i(all_30_0)) | ( ~ (all_30_1 = e1) & op(e0, e0) % 134.53/19.65 | | | | | | | | | | | = all_30_1 & $i(all_30_1)) % 134.53/19.65 | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | COMBINE_EQS: (309), (9476) imply: % 134.53/19.65 | | | | | | | | | | | (9478) all_8_2 = e0 % 134.53/19.65 | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | SIMP: (9478) implies: % 134.53/19.65 | | | | | | | | | | | (9479) all_8_2 = e0 % 134.53/19.65 | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | REDUCE: (354), (9479) imply: % 134.53/19.65 | | | | | | | | | | | (9480) ~ (all_52_7 = e0) % 134.53/19.65 | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | REDUCE: (8999), (9479) imply: % 134.53/19.65 | | | | | | | | | | | (9481) ~ (e3 = e0) % 134.53/19.65 | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | REDUCE: (8993), (9479) imply: % 134.53/19.65 | | | | | | | | | | | (9482) ~ (e1 = e0) % 134.53/19.65 | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | REDUCE: (42), (9479) imply: % 134.53/19.65 | | | | | | | | | | | (9483) op(e2, e2) = e0 % 134.53/19.65 | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | BETA: splitting (9477) gives: % 134.53/19.65 | | | | | | | | | | | % 134.53/19.65 | | | | | | | | | | | Case 1: % 134.53/19.65 | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | (9484) ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 & % 134.53/19.66 | | | | | | | | | | | | $i(all_30_0) % 134.53/19.66 | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | ALPHA: (9484) implies: % 134.53/19.66 | | | | | | | | | | | | (9485) ~ (all_30_0 = e3) % 134.53/19.66 | | | | | | | | | | | | (9486) op(e0, e2) = all_30_0 % 134.53/19.66 | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | BETA: splitting (9414) gives: % 134.53/19.66 | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | (9487) ~ (all_16_0 = e1) & op(e2, e3) = all_16_0 & % 134.53/19.66 | | | | | | | | | | | | | $i(all_16_0) % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | ALPHA: (9487) implies: % 134.53/19.66 | | | | | | | | | | | | | (9488) ~ (all_16_0 = e1) % 134.53/19.66 | | | | | | | | | | | | | (9489) op(e2, e3) = all_16_0 % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, % 134.53/19.66 | | | | | | | | | | | | | all_30_0, e2, e0, simplifying with (158), (9486) % 134.53/19.66 | | | | | | | | | | | | | gives: % 134.53/19.66 | | | | | | | | | | | | | (9490) all_52_7 = all_30_0 % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, % 134.53/19.66 | | | | | | | | | | | | | all_16_0, e3, e2, simplifying with (167), (9489) % 134.53/19.66 | | | | | | | | | | | | | gives: % 134.53/19.66 | | | | | | | | | | | | | (9491) all_52_1 = all_16_0 % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | COMBINE_EQS: (247), (9490) imply: % 134.53/19.66 | | | | | | | | | | | | | (9492) all_54_13 = all_30_0 % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | REDUCE: (125), (9490) imply: % 134.53/19.66 | | | | | | | | | | | | | (9493) ~ (all_52_11 = all_30_0) % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | SIMP: (9493) implies: % 134.53/19.66 | | | | | | | | | | | | | (9494) ~ (all_52_11 = all_30_0) % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | REDUCE: (8980), (9490) imply: % 134.53/19.66 | | | | | | | | | | | | | (9495) ~ (all_30_0 = e1) % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | REDUCE: (9480), (9490) imply: % 134.53/19.66 | | | | | | | | | | | | | (9496) ~ (all_30_0 = e0) % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | BETA: splitting (191) gives: % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | (9497) all_54_13 = e3 % 134.53/19.66 | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | REF_CLOSE: (9485), (9492), (9497) are inconsistent by % 134.53/19.66 | | | | | | | | | | | | | | sub-proof #54. % 134.53/19.66 | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | (9498) ~ (all_54_13 = e3) % 134.53/19.66 | | | | | | | | | | | | | | (9499) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 134.53/19.66 | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | BETA: splitting (9499) gives: % 134.53/19.66 | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | (9500) all_54_13 = e2 % 134.53/19.66 | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | COMBINE_EQS: (9492), (9500) imply: % 134.53/19.66 | | | | | | | | | | | | | | | (9501) all_30_0 = e2 % 134.53/19.66 | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | SIMP: (9501) implies: % 134.53/19.66 | | | | | | | | | | | | | | | (9502) all_30_0 = e2 % 134.53/19.66 | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | REDUCE: (9494), (9502) imply: % 134.53/19.66 | | | | | | | | | | | | | | | (9503) ~ (all_52_11 = e2) % 134.53/19.66 | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | REDUCE: (9485), (9502) imply: % 134.53/19.66 | | | | | | | | | | | | | | | (9504) ~ (e3 = e2) % 134.53/19.66 | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 134.53/19.66 | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | (9505) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 134.53/19.66 | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 134.53/19.66 | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9483), (9488), (9489), (9505), % 134.53/19.66 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.66 | | | | | | | | | | | | | | | | #415. % 134.53/19.66 | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | (9506) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 134.53/19.66 | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 134.53/19.66 | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | BETA: splitting (9506) gives: % 134.53/19.66 | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | (9507) all_57_5 = e1 & op(e2, e1) = e1 % 134.53/19.66 | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | ALPHA: (9507) implies: % 134.53/19.66 | | | | | | | | | | | | | | | | | (9508) all_57_5 = e1 % 134.53/19.66 | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 134.53/19.66 | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | (9509) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | BETA: splitting (9509) gives: % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | (9510) all_57_12 = e2 & op(e0, e3) = e2 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | ALPHA: (9510) implies: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | (9511) all_57_12 = e2 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237), % 134.53/19.66 | | | | | | | | | | | | | | | | | | | (9419), (9511), (function-axioms) are inconsistent % 134.53/19.66 | | | | | | | | | | | | | | | | | | | by sub-proof #290. % 134.53/19.66 | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | (9512) all_57_13 = e2 & op(e0, e2) = e2 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | ALPHA: (9512) implies: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | (9513) all_57_13 = e2 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | (9514) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9514) gives: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | (9515) all_57_4 = e2 & op(e3, e1) = e2 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (9417), (9515), (function-axioms) are % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442. % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | (9516) all_57_5 = e2 & op(e2, e1) = e2 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9516) implies: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | (9517) all_57_5 = e2 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9508), (9517) are inconsistent by sub-proof % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | #418. % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | (9518) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9518) gives: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | (9519) all_57_8 = e2 & op(e1, e1) = e2 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9519) implies: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | (9520) op(e1, e1) = e2 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (9520), (function-axioms) are % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | (9521) all_57_14 = e2 & op(e0, e1) = e2 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9521) implies: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | (9522) all_57_14 = e2 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209), (211), % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | (9513), (9522) are inconsistent by sub-proof #401. % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.66 | | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | End of split % 134.53/19.66 | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | (9523) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (8991), (9503), (9523), % 134.53/19.66 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.66 | | | | | | | | | | | | | | | | | | #34. % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | End of split % 134.53/19.66 | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | (9524) all_57_10 = e1 & op(e2, e0) = e1 % 134.53/19.66 | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | ALPHA: (9524) implies: % 134.53/19.66 | | | | | | | | | | | | | | | | | (9525) op(e2, e0) = e1 % 134.53/19.66 | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8983), (9525), (function-axioms) are % 134.53/19.66 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180. % 134.53/19.66 | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | End of split % 134.53/19.66 | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | End of split % 134.53/19.66 | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | (9526) all_54_13 = e1 | all_54_13 = e0 % 134.53/19.66 | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | REF_CLOSE: (247), (8980), (9480), (9526) are inconsistent by % 134.53/19.66 | | | | | | | | | | | | | | | sub-proof #470. % 134.53/19.66 | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | End of split % 134.53/19.66 | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | End of split % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | (9527) ~ (all_16_1 = e0) & op(e2, e2) = all_16_1 & % 134.53/19.66 | | | | | | | | | | | | | $i(all_16_1) % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | REF_CLOSE: (9483), (9527), (function-axioms) are inconsistent % 134.53/19.66 | | | | | | | | | | | | | by sub-proof #380. % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | End of split % 134.53/19.66 | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | (9528) ~ (all_30_1 = e1) & op(e0, e0) = all_30_1 & % 134.53/19.66 | | | | | | | | | | | | $i(all_30_1) % 134.53/19.66 | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | REF_CLOSE: (8991), (9528), (function-axioms) are inconsistent % 134.53/19.66 | | | | | | | | | | | | by sub-proof #53. % 134.53/19.66 | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | End of split % 134.53/19.66 | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | End of split % 134.53/19.66 | | | | | | | | | | % 134.53/19.66 | | | | | | | | | End of split % 134.53/19.66 | | | | | | | | | % 134.53/19.66 | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | % 134.53/19.66 | | | | | | | | | (9529) all_14_2 = e3 % 134.53/19.66 | | | | | | | | | % 134.53/19.66 | | | | | | | | | COMBINE_EQS: (329), (9529) imply: % 134.53/19.66 | | | | | | | | | (9530) all_8_2 = e3 % 134.53/19.66 | | | | | | | | | % 134.53/19.66 | | | | | | | | | SIMP: (9530) implies: % 134.53/19.66 | | | | | | | | | (9531) all_8_2 = e3 % 134.53/19.66 | | | | | | | | | % 134.53/19.66 | | | | | | | | | COMBINE_EQS: (322), (9531) imply: % 134.53/19.66 | | | | | | | | | (9532) all_22_2 = e3 % 134.53/19.66 | | | | | | | | | % 134.53/19.66 | | | | | | | | | REDUCE: (347), (9531) imply: % 134.53/19.66 | | | | | | | | | (9533) ~ (all_52_1 = e3) % 134.53/19.66 | | | | | | | | | % 134.53/19.66 | | | | | | | | | REDUCE: (350), (9531) imply: % 134.53/19.66 | | | | | | | | | (9534) ~ (all_52_4 = e3) % 134.53/19.66 | | | | | | | | | % 134.53/19.66 | | | | | | | | | REDUCE: (354), (9531) imply: % 134.53/19.66 | | | | | | | | | (9535) ~ (all_52_7 = e3) % 134.53/19.66 | | | | | | | | | % 134.53/19.66 | | | | | | | | | REDUCE: (356), (9531) imply: % 134.53/19.66 | | | | | | | | | (9536) ~ (all_52_9 = e3) % 134.53/19.66 | | | | | | | | | % 134.53/19.66 | | | | | | | | | REDUCE: (358), (9531) imply: % 134.53/19.66 | | | | | | | | | (9537) ~ (all_52_13 = e3) % 134.53/19.66 | | | | | | | | | % 134.53/19.66 | | | | | | | | | BETA: splitting (226) gives: % 134.53/19.66 | | | | | | | | | % 134.53/19.66 | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | (9538) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 134.53/19.66 | | | | | | | | | | & op(e2, e2) = e3) % 134.53/19.66 | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | BETA: splitting (9538) gives: % 134.53/19.66 | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | (9539) all_57_2 = e3 & op(e2, e3) = e3 % 134.53/19.66 | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | ALPHA: (9539) implies: % 134.53/19.66 | | | | | | | | | | | (9540) op(e2, e3) = e3 % 134.53/19.66 | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | REF_CLOSE: (167), (9533), (9540), (function-axioms) are % 134.53/19.66 | | | | | | | | | | | inconsistent by sub-proof #763. % 134.53/19.66 | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | (9541) all_57_3 = e3 & op(e2, e2) = e3 % 134.53/19.66 | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | ALPHA: (9541) implies: % 134.53/19.66 | | | | | | | | | | | (9542) all_57_3 = e3 % 134.53/19.66 | | | | | | | | | | | (9543) op(e2, e2) = e3 % 134.53/19.66 | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | BETA: splitting (55) gives: % 134.53/19.66 | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | (9544) ~ (all_16_2 = e2) % 134.53/19.66 | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | REDUCE: (327), (9544) imply: % 134.53/19.66 | | | | | | | | | | | | (9545) ~ (all_10_2 = e2) % 134.53/19.66 | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | BETA: splitting (64) gives: % 134.53/19.66 | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | (9546) ~ (all_22_2 = e3) % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | REDUCE: (9532), (9546) imply: % 134.53/19.66 | | | | | | | | | | | | | (9547) $false % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | CLOSE: (9547) is inconsistent. % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | (9548) ( ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 & % 134.53/19.66 | | | | | | | | | | | | | $i(all_22_0)) | ( ~ (all_22_1 = e1) & op(e3, e3) % 134.53/19.66 | | | | | | | | | | | | | = all_22_1 & $i(all_22_1)) % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | BETA: splitting (73) gives: % 134.53/19.66 | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | (9549) ~ (all_28_2 = e3) % 134.53/19.66 | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | REDUCE: (316), (9549) imply: % 134.53/19.66 | | | | | | | | | | | | | | (9550) ~ (all_6_2 = e3) % 134.53/19.66 | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | BETA: splitting (79) gives: % 134.53/19.66 | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | (9551) ~ (all_32_2 = e1) % 134.53/19.66 | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | REDUCE: (312), (9551) imply: % 134.53/19.66 | | | | | | | | | | | | | | | (9552) ~ (all_10_2 = e1) % 134.53/19.66 | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 134.53/19.66 | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | (9553) all_54_0 = e3 % 134.53/19.66 | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (9553) imply: % 134.53/19.66 | | | | | | | | | | | | | | | | (9554) all_10_2 = e3 % 134.53/19.66 | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | SIMP: (9554) implies: % 134.53/19.66 | | | | | | | | | | | | | | | | (9555) all_10_2 = e3 % 134.53/19.66 | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | REDUCE: (346), (9555) imply: % 134.53/19.66 | | | | | | | | | | | | | | | | (9556) ~ (all_52_12 = e3) % 134.53/19.66 | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | REDUCE: (45), (9555) imply: % 134.53/19.66 | | | | | | | | | | | | | | | | (9557) op(e3, e3) = e3 % 134.53/19.66 | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 134.53/19.66 | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | (9558) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.66 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.66 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.66 | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.66 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.66 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.66 | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.66 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.66 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.66 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.66 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.66 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.66 | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | BETA: splitting (9558) gives: % 134.53/19.66 | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | (9559) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 134.53/19.66 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.66 | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 134.53/19.66 | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (9557), (9559), (function-axioms) are % 134.53/19.66 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623. % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | (9560) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.66 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.66 | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.66 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (9556), (9557), (9560), (function-axioms) % 134.53/19.66 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #553. % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | End of split % 134.53/19.66 | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | (9561) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.66 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.66 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.66 | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.66 | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.66 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.66 | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 134.53/19.66 | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 134.53/19.66 | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.66 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 134.53/19.66 | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 134.53/19.66 | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 134.53/19.66 | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 134.53/19.66 | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 134.53/19.66 | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 134.53/19.66 | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 134.53/19.66 | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 134.53/19.66 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 134.53/19.66 | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 134.53/19.66 | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 134.53/19.66 | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.66 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 134.53/19.66 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 134.53/19.66 | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 134.53/19.66 | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 134.53/19.66 | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 134.53/19.66 | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.66 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.66 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.66 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.66 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.66 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.66 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.66 | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.66 | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | BETA: splitting (9561) gives: % 134.53/19.66 | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | (9562) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 134.53/19.66 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 134.53/19.66 | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 134.53/19.66 | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 134.53/19.66 | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 134.53/19.66 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 134.53/19.66 | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 134.53/19.66 | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (9543), (9550), (9562), % 134.53/19.66 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.66 | | | | | | | | | | | | | | | | | | #324. % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | (9563) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.66 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 134.53/19.66 | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.66 | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.66 | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.66 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.66 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.66 | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.66 | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.66 | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.66 | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.66 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.66 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.66 | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.66 | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.66 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.66 | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.66 | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.66 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.66 | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.66 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.66 | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.66 | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | BETA: splitting (9563) gives: % 134.53/19.66 | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | (9564) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 134.53/19.66 | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 134.53/19.66 | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 134.53/19.66 | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 134.53/19.66 | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 134.53/19.66 | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | ALPHA: (9564) implies: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | (9565) op(e2, e2) = e0 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9543), (9565), (function-axioms) are % 134.53/19.66 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 134.53/19.66 | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.66 | | | | | | | | | | | | | | | | | | | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | (9566) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 134.53/19.66 | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 134.53/19.66 | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 134.53/19.66 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 134.53/19.66 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 134.53/19.66 | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 134.53/19.66 | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 134.53/19.66 | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 134.53/19.66 | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 134.53/19.66 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 134.53/19.66 | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 134.53/19.66 | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 134.53/19.66 | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 134.53/19.66 | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 134.53/19.66 | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 134.53/19.66 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 134.53/19.66 | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 134.53/19.66 | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 134.53/19.66 | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 134.53/19.66 | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (39), (157), (160), (194), (334), (364), % 134.53/19.67 | | | | | | | | | | | | | | | | | | | (8984), (8991), (8992), (9550), (9566), % 134.53/19.67 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.67 | | | | | | | | | | | | | | | | | | | #30. % 134.53/19.67 | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | End of split % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | End of split % 134.53/19.67 | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | End of split % 134.53/19.67 | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | Case 2: % 134.53/19.67 | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | (9567) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 134.53/19.67 | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | REF_CLOSE: (278), (8994), (9545), (9552), (9567) are % 134.53/19.67 | | | | | | | | | | | | | | | | inconsistent by sub-proof #777. % 134.53/19.67 | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | End of split % 134.53/19.67 | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | Case 2: % 134.53/19.67 | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | (9568) all_32_2 = e1 % 134.53/19.67 | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | COMBINE_EQS: (312), (9568) imply: % 134.53/19.67 | | | | | | | | | | | | | | | (9569) all_10_2 = e1 % 134.53/19.67 | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | SIMP: (9569) implies: % 134.53/19.67 | | | | | | | | | | | | | | | (9570) all_10_2 = e1 % 134.53/19.67 | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | COMBINE_EQS: (280), (9570) imply: % 134.53/19.67 | | | | | | | | | | | | | | | (9571) all_50_2 = e1 % 134.53/19.67 | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | REDUCE: (336), (9570) imply: % 134.53/19.67 | | | | | | | | | | | | | | | (9572) ~ (all_52_1 = e1) % 134.53/19.67 | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | REDUCE: (342), (9570) imply: % 134.53/19.67 | | | | | | | | | | | | | | | (9573) ~ (all_52_4 = e1) % 134.53/19.67 | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | REDUCE: (45), (9570) imply: % 134.53/19.67 | | | | | | | | | | | | | | | (9574) op(e3, e3) = e1 % 134.53/19.67 | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 134.53/19.67 | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | Case 1: % 134.53/19.67 | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | (9575) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 134.53/19.67 | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 134.53/19.67 | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (9543), (9572), (9575), % 134.53/19.67 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 134.53/19.67 | | | | | | | | | | | | | | | | #77. % 134.53/19.67 | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | Case 2: % 134.53/19.67 | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | (9576) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 134.53/19.67 | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 134.53/19.67 | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | BETA: splitting (9576) gives: % 134.53/19.67 | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | Case 1: % 134.53/19.67 | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | (9577) all_57_5 = e1 & op(e2, e1) = e1 % 134.53/19.67 | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | ALPHA: (9577) implies: % 134.53/19.67 | | | | | | | | | | | | | | | | | (9578) op(e2, e1) = e1 % 134.53/19.67 | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | BETA: splitting (9548) gives: % 134.53/19.67 | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | (9579) ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 & % 134.53/19.67 | | | | | | | | | | | | | | | | | | $i(all_22_0) % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | ALPHA: (9579) implies: % 134.53/19.67 | | | | | | | | | | | | | | | | | | (9580) ~ (all_22_0 = e0) % 134.53/19.67 | | | | | | | | | | | | | | | | | | (9581) op(e3, e2) = all_22_0 % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1, % 134.53/19.67 | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (9578) gives: % 134.53/19.67 | | | | | | | | | | | | | | | | | | (9582) all_52_9 = e1 % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 134.53/19.67 | | | | | | | | | | | | | | | | | | all_22_0, e2, e3, simplifying with (170), (9581) % 134.53/19.67 | | | | | | | | | | | | | | | | | | gives: % 134.53/19.67 | | | | | | | | | | | | | | | | | | (9583) all_52_4 = all_22_0 % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (9583) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | (9584) all_54_1 = all_22_0 % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | REDUCE: (134), (9583) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | (9585) ~ (all_52_8 = all_22_0) % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | SIMP: (9585) implies: % 134.53/19.67 | | | | | | | | | | | | | | | | | | (9586) ~ (all_52_8 = all_22_0) % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | REDUCE: (133), (9583) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | (9587) ~ (all_52_12 = all_22_0) % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | SIMP: (9587) implies: % 134.53/19.67 | | | | | | | | | | | | | | | | | | (9588) ~ (all_52_12 = all_22_0) % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | REDUCE: (9534), (9583) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | (9589) ~ (all_22_0 = e3) % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | REDUCE: (9573), (9583) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | (9590) ~ (all_22_0 = e1) % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | REDUCE: (123), (9582) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | (9591) ~ (all_52_8 = e1) % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | REDUCE: (117), (9582) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | (9592) ~ (all_52_13 = e1) % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | REDUCE: (362), (9582) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | (9593) ~ (all_6_2 = e1) % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | SIMP: (9593) implies: % 134.53/19.67 | | | | | | | | | | | | | | | | | | (9594) ~ (all_6_2 = e1) % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 134.53/19.67 | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | (9595) all_54_10 = e3 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (9550), (9595) are inconsistent by % 134.53/19.67 | | | | | | | | | | | | | | | | | | | sub-proof #742. % 134.53/19.67 | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | (9596) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | (9597) all_54_1 = e3 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9584), (9597) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | (9598) all_22_0 = e3 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | REDUCE: (9589), (9598) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | (9599) $false % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | CLOSE: (9599) is inconsistent. % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | (9600) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9600) gives: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | (9601) all_54_1 = e2 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9584), (9601) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | (9602) all_22_0 = e2 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9586), (9602) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | (9603) ~ (all_52_8 = e2) % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9588), (9602) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | (9604) ~ (all_52_12 = e2) % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9596) gives: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | (9605) all_54_10 = e2 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (8992), (9605) are inconsistent by % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | sub-proof #741. % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | (9606) all_54_10 = e1 | all_54_10 = e0 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9606) gives: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9607) all_54_10 = e1 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (9594), (9607) are inconsistent by % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #736. % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9608) all_54_10 = e0 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (9608) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9609) all_6_2 = e0 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9609) implies: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9610) all_6_2 = e0 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (9610) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9611) ~ (all_52_8 = e0) % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (9610) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9612) op(e1, e1) = e0 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9613) ~ (all_50_2 = e1) % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9571), (9613) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9614) $false % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9614) is inconsistent. % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9615) ( ~ (all_50_0 = e2) & op(e1, e3) = all_50_0 & % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_50_0)) | ( ~ (all_50_1 = e0) & op(e1, e1) % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | = all_50_1 & $i(all_50_1)) % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9616) all_54_2 = e3 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (9616) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9617) all_52_8 = e3 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9617) implies: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9618) all_52_8 = e3 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (9618) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9619) ~ (all_52_11 = e3) % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9619) implies: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9620) ~ (all_52_11 = e3) % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (9618) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9621) ~ (all_52_12 = e3) % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9621) implies: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9622) ~ (all_52_12 = e3) % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (9623) all_54_3 = e3 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (9622), (9623) are inconsistent by % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #216. % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (9624) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9624) gives: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9625) all_54_3 = e2 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (9625) imply: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9626) all_52_12 = e2 % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9626) implies: % 134.53/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9627) all_52_12 = e2 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9604), (9627) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9628) $false % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9628) is inconsistent. % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9629) all_54_3 = e1 | all_54_3 = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9629) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9630) all_54_3 = e1 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (9630) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9631) all_52_12 = e1 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9631) implies: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9632) all_52_12 = e1 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8982), (9632) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9633) $false % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9633) is inconsistent. % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9634) all_54_3 = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (9634) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9635) all_52_12 = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9635) implies: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9636) all_52_12 = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (9636) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9637) ~ (all_52_13 = e0) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9637) implies: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9638) ~ (all_52_13 = e0) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9639) all_54_7 = e3 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (9639) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9640) all_52_13 = e3 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9537), (9640) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9641) $false % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9641) is inconsistent. % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9642) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9643) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9643) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9644) all_57_0 = e2 & op(e3, e3) = e2 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9644) implies: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9645) op(e3, e3) = e2 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9574), (9645), (function-axioms) are % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743. % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9646) all_57_2 = e2 & op(e2, e3) = e2 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9646) implies: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9647) op(e2, e3) = e2 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (167), (259), (8983), (9638), (9642), % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9647), (function-axioms) are inconsistent by % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #312. % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9648) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9648) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9649) all_57_6 = e2 & op(e1, e3) = e2 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9649) implies: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9650) op(e1, e3) = e2 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9615) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9651) ~ (all_50_0 = e2) & op(e1, e3) = all_50_0 & % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_50_0) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9651) implies: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9652) ~ (all_50_0 = e2) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9653) op(e1, e3) = all_50_0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9650), (9652), (9653), (function-axioms) are % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #735. % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9654) ~ (all_50_1 = e0) & op(e1, e1) = all_50_1 & % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_50_1) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9612), (9654), (function-axioms) are inconsistent % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #719. % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9655) all_57_12 = e2 & op(e0, e3) = e2 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9655) implies: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9656) all_57_12 = e2 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (211), (8991), (9535), % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9620), (9656), (function-axioms) are inconsistent % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #29. % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9657) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (9591), (9603), (9611), (9657) are % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #71. % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | (9658) all_54_1 = e1 | all_54_1 = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9580), (9584), (9590), (9658) are inconsistent by % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | sub-proof #306. % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | (9659) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & % 135.13/19.67 | | | | | | | | | | | | | | | | | | $i(all_22_1) % 135.13/19.67 | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9574), (9659), (function-axioms) are inconsistent % 135.13/19.67 | | | | | | | | | | | | | | | | | | by sub-proof #305. % 135.13/19.67 | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | (9660) all_57_10 = e1 & op(e2, e0) = e1 % 135.13/19.67 | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | ALPHA: (9660) implies: % 135.13/19.67 | | | | | | | | | | | | | | | | | (9661) op(e2, e0) = e1 % 135.13/19.67 | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8983), (9661), (function-axioms) are % 135.13/19.67 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180. % 135.13/19.67 | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | End of split % 135.13/19.67 | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | (9662) all_28_2 = e3 % 135.13/19.67 | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | COMBINE_EQS: (316), (9662) imply: % 135.13/19.67 | | | | | | | | | | | | | | (9663) all_6_2 = e3 % 135.13/19.67 | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | SIMP: (9663) implies: % 135.13/19.67 | | | | | | | | | | | | | | (9664) all_6_2 = e3 % 135.13/19.67 | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | REDUCE: (364), (9664) imply: % 135.13/19.67 | | | | | | | | | | | | | | (9665) ~ (all_52_11 = e3) % 135.13/19.67 | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | REDUCE: (366), (9664) imply: % 135.13/19.67 | | | | | | | | | | | | | | (9666) ~ (all_52_14 = e3) % 135.13/19.67 | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | REDUCE: (39), (9664) imply: % 135.13/19.67 | | | | | | | | | | | | | | (9667) op(e1, e1) = e3 % 135.13/19.67 | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | BETA: splitting (211) gives: % 135.13/19.67 | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | (9668) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 135.13/19.67 | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 135.13/19.67 | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | BETA: splitting (9668) gives: % 135.13/19.67 | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | (9669) all_57_12 = e3 & op(e0, e3) = e3 % 135.13/19.67 | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | ALPHA: (9669) implies: % 135.13/19.67 | | | | | | | | | | | | | | | | (9670) all_57_12 = e3 % 135.13/19.67 | | | | | | | | | | | | | | | | (9671) op(e0, e3) = e3 % 135.13/19.67 | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | (9672) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 135.13/19.67 | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 135.13/19.67 | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | BETA: splitting (9672) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | (9673) all_57_9 = e3 & op(e3, e0) = e3 % 135.13/19.67 | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | ALPHA: (9673) implies: % 135.13/19.67 | | | | | | | | | | | | | | | | | | (9674) op(e3, e0) = e3 % 135.13/19.67 | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | BETA: splitting (8997) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9675) ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 & % 135.13/19.67 | | | | | | | | | | | | | | | | | | | $i(all_12_0) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | ALPHA: (9675) implies: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9676) ~ (all_12_0 = e2) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9677) op(e1, e0) = all_12_0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3, % 135.13/19.67 | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (9671) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9678) all_52_3 = e3 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 135.13/19.67 | | | | | | | | | | | | | | | | | | | all_12_0, e0, e1, simplifying with (160), (9677) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9679) all_52_14 = all_12_0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 135.13/19.67 | | | | | | | | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (9674) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9680) all_52_12 = e3 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (9679) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9681) all_54_11 = all_12_0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (141), (9679) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9682) ~ (all_52_2 = all_12_0) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (140), (9678) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9683) ~ (all_52_7 = e3) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (139), (9678) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9684) ~ (all_52_11 = e3) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (113), (9680) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9685) ~ (all_52_13 = e3) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (346), (9680) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9686) ~ (all_10_2 = e3) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | SIMP: (9686) implies: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9687) ~ (all_10_2 = e3) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (110), (9679) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9688) ~ (all_52_13 = all_12_0) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (9666), (9679) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9689) ~ (all_12_0 = e3) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (8984), (9679) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | (9690) ~ (all_12_0 = e1) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | (9691) all_54_0 = e3 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (9691) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | (9692) all_10_2 = e3 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | REDUCE: (9687), (9692) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | (9693) $false % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | CLOSE: (9693) is inconsistent. % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | (9694) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | (9695) all_54_11 = e3 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9681), (9689), (9695) are inconsistent by % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | sub-proof #52. % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | (9696) ~ (all_54_11 = e3) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | (9697) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9697) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | (9698) all_54_11 = e2 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9676), (9681), (9698) are inconsistent by % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | sub-proof #51. % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | (9699) ~ (all_54_11 = e2) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | (9700) all_54_11 = e1 | all_54_11 = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9694) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9701) all_54_0 = e2 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (9701) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9702) all_10_2 = e2 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9545), (9702) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9703) $false % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9703) is inconsistent. % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9704) ~ (all_54_0 = e2) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | (9705) all_54_0 = e1 | all_54_0 = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9700) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9706) all_54_11 = e1 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9681), (9690), (9706) are inconsistent by % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #50. % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9707) all_54_11 = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9681), (9707) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9708) all_12_0 = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9708) implies: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9709) all_12_0 = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9682), (9709) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9710) ~ (all_52_2 = e0) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9688), (9709) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9711) ~ (all_52_13 = e0) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9689), (9709) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9712) ~ (e3 = e0) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9676), (9709) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9713) ~ (e2 = e0) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9690), (9709) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9714) ~ (e1 = e0) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9677), (9709) imply: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (9715) op(e1, e0) = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (9716) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9716) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (9717) all_57_0 = e0 & op(e3, e3) = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9717) implies: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (9718) op(e3, e3) = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (278), (8994), (9705), (9718), % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | #263. % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (9719) all_57_2 = e0 & op(e2, e3) = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9719) implies: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (9720) all_57_2 = e0 % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9721) all_54_7 = e3 % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (9537), (9721) are inconsistent by % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #338. % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9722) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9723) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9723) gives: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9724) all_57_2 = e1 & op(e2, e3) = e1 % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9724) implies: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9725) all_57_2 = e1 % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9720), (9725) are inconsistent by sub-proof % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #646. % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9726) all_57_3 = e1 & op(e2, e2) = e1 % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9726) implies: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9727) op(e2, e2) = e1 % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9543), (9727), (function-axioms) are % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9728) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9728) gives: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9729) all_57_5 = e1 & op(e2, e1) = e1 % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9729) implies: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9730) op(e2, e1) = e1 % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9731) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2) % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9731) gives: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9732) all_57_0 = e2 & op(e3, e3) = e2 % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9732) implies: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9733) op(e3, e3) = e2 % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (9545), (9733), (function-axioms) are % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #536. % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.13/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9734) all_57_2 = e2 & op(e2, e3) = e2 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9734) implies: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9735) op(e2, e3) = e2 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (167), (259), (8983), (9711), (9722), % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9735), (function-axioms) are inconsistent by % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #312. % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9736) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9736) gives: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9737) all_57_6 = e2 & op(e1, e3) = e2 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9737) implies: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9738) all_57_6 = e2 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9739) op(e1, e3) = e2 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9740) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9740) gives: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9741) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9741) gives: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9742) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9742) implies: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9743) op(e3, e3) = e2 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225), % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (233), (237), (9542), (9738), (9743), % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #360. % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9744) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9744) implies: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9745) ~ (all_56_29 = e0) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9746) op(e1, e0) = all_56_29 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9715), (9745), (9746), (function-axioms) are % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #45. % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9747) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9747) gives: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9748) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9748) implies: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9749) op(e3, e3) = e0 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (278), (8994), (9705), (9749), % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #263. % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9750) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9750) implies: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9751) op(e2, e3) = e2 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (167), (259), (8983), (9711), (9722), % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9751), (function-axioms) are inconsistent by % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #312. % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9752) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9752) gives: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9753) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (9715), (9739), (9753), % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #28. % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9754) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9754) gives: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9755) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9755) implies: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9756) op(e2, e2) = e0 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9543), (9756), (function-axioms) are % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9757) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9757) gives: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9758) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9758) implies: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9759) ~ (all_56_19 = e1) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9760) op(e2, e1) = all_56_19 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9730), (9759), (9760), (function-axioms) are % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106. % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9761) op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9761) implies: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9762) op(e0, e0) = all_56_31 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9763) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9763) gives: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9764) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8991), (9730), (9762), (9764), % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #56. % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9765) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (8984), (9715), (9765), (function-axioms) % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #40. % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9766) all_57_12 = e2 & op(e0, e3) = e2 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9766) implies: % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9767) all_57_12 = e2 % 135.15/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (157), (158), (211), (8991), (9535), % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9665), (9767), (function-axioms) are inconsistent % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #29. % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9768) all_57_10 = e1 & op(e2, e0) = e1 % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9768) implies: % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9769) op(e2, e0) = e1 % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8983), (9769), (function-axioms) are % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180. % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | (9770) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (163), (9670), (9710), (9770), % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | #27. % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.69 | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | (9771) ~ (all_12_1 = e3) & op(e1, e1) = all_12_1 & % 135.15/19.69 | | | | | | | | | | | | | | | | | | | $i(all_12_1) % 135.15/19.69 | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | ALPHA: (9771) implies: % 135.15/19.69 | | | | | | | | | | | | | | | | | | | (9772) ~ (all_12_1 = e3) % 135.15/19.69 | | | | | | | | | | | | | | | | | | | (9773) op(e1, e1) = all_12_1 % 135.15/19.69 | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9667), (9772), (9773), (function-axioms) are % 135.15/19.69 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #36. % 135.15/19.69 | | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.69 | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | (9774) all_57_10 = e3 & op(e2, e0) = e3 % 135.15/19.69 | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9537), (9774), (function-axioms) are % 135.15/19.69 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749. % 135.15/19.69 | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | Case 2: % 135.15/19.69 | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | (9775) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 135.15/19.69 | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 135.15/19.69 | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (8991), (9666), (9775), % 135.15/19.69 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.15/19.69 | | | | | | | | | | | | | | | | | #46. % 135.15/19.69 | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | Case 2: % 135.15/19.69 | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | (9776) all_57_13 = e3 & op(e0, e2) = e3 % 135.15/19.69 | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9535), (9776), (function-axioms) are % 135.15/19.69 | | | | | | | | | | | | | | | | inconsistent by sub-proof #556. % 135.15/19.69 | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | Case 2: % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | (9777) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 135.15/19.69 | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (8991), (9665), (9777), % 135.15/19.69 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.15/19.69 | | | | | | | | | | | | | | | #37. % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | Case 2: % 135.15/19.69 | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | (9778) all_16_2 = e2 % 135.15/19.69 | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | COMBINE_EQS: (327), (9778) imply: % 135.15/19.69 | | | | | | | | | | | | (9779) all_10_2 = e2 % 135.15/19.69 | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | REDUCE: (336), (9779) imply: % 135.15/19.69 | | | | | | | | | | | | (9780) ~ (all_52_1 = e2) % 135.15/19.69 | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | REDUCE: (342), (9779) imply: % 135.15/19.69 | | | | | | | | | | | | (9781) ~ (all_52_4 = e2) % 135.15/19.69 | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | REDUCE: (344), (9779) imply: % 135.15/19.69 | | | | | | | | | | | | (9782) ~ (all_52_8 = e2) % 135.15/19.69 | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | REDUCE: (346), (9779) imply: % 135.15/19.69 | | | | | | | | | | | | (9783) ~ (all_52_12 = e2) % 135.15/19.69 | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | REDUCE: (45), (9779) imply: % 135.15/19.69 | | | | | | | | | | | | (9784) op(e3, e3) = e2 % 135.15/19.69 | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | BETA: splitting (73) gives: % 135.15/19.69 | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | Case 1: % 135.15/19.69 | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | (9785) ~ (all_28_2 = e3) % 135.15/19.69 | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | REDUCE: (316), (9785) imply: % 135.15/19.69 | | | | | | | | | | | | | (9786) ~ (all_6_2 = e3) % 135.15/19.69 | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | BETA: splitting (206) gives: % 135.15/19.69 | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | Case 1: % 135.15/19.69 | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | (9787) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.15/19.69 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.15/19.69 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.15/19.69 | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.15/19.69 | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.15/19.69 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.15/19.69 | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.15/19.69 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.15/19.69 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.15/19.69 | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.15/19.69 | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.15/19.69 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.15/19.69 | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.15/19.69 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.15/19.69 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.15/19.69 | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.69 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.69 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.15/19.69 | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.15/19.69 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.15/19.69 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.69 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.15/19.69 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.15/19.69 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.15/19.69 | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | BETA: splitting (9787) gives: % 135.15/19.69 | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | Case 1: % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | (9788) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.15/19.69 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.15/19.69 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.15/19.69 | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.15/19.69 | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.15/19.69 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.15/19.69 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.15/19.69 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.15/19.69 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.15/19.69 | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.15/19.69 | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.15/19.69 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (9534), (9784), (9788), % 135.15/19.69 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.15/19.69 | | | | | | | | | | | | | | | #254. % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | Case 2: % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | (9789) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.15/19.69 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.15/19.69 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.15/19.69 | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.69 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.69 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.15/19.69 | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.15/19.69 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.15/19.69 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.69 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.15/19.69 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.15/19.69 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (9780), (9784), (9789), % 135.15/19.69 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.15/19.69 | | | | | | | | | | | | | | | #443. % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | Case 2: % 135.15/19.69 | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | (9790) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.15/19.69 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.15/19.69 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.69 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.15/19.69 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.15/19.69 | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.15/19.69 | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.15/19.69 | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.15/19.69 | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.15/19.69 | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.15/19.69 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.15/19.69 | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 135.15/19.69 | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.15/19.69 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.15/19.69 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 135.15/19.69 | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.15/19.69 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 135.15/19.69 | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 135.15/19.69 | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.15/19.69 | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.15/19.69 | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.15/19.69 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.15/19.69 | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 135.15/19.69 | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.15/19.69 | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.15/19.69 | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.15/19.69 | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.15/19.69 | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.69 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 135.15/19.69 | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.15/19.69 | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 135.15/19.69 | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 135.15/19.69 | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.15/19.69 | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.15/19.69 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.15/19.69 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.15/19.69 | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 135.15/19.69 | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 135.15/19.69 | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.15/19.69 | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.15/19.69 | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.15/19.69 | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 135.15/19.69 | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.15/19.69 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.15/19.69 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.15/19.69 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.15/19.69 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.15/19.69 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.15/19.69 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.15/19.69 | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.15/19.69 | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | BETA: splitting (9790) gives: % 135.15/19.69 | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | Case 1: % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | (9791) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.15/19.69 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.15/19.69 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.69 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.15/19.69 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.15/19.69 | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.15/19.69 | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.15/19.69 | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.15/19.69 | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.15/19.69 | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.15/19.69 | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.15/19.69 | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (9543), (9786), (9791), % 135.15/19.69 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.15/19.69 | | | | | | | | | | | | | | | #324. % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | Case 2: % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | (9792) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.15/19.69 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.15/19.69 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 135.15/19.69 | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.69 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.69 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.15/19.69 | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.15/19.69 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.15/19.69 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.15/19.69 | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.15/19.69 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.15/19.69 | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.15/19.69 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.15/19.69 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.15/19.69 | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.15/19.69 | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.15/19.69 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.15/19.69 | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.15/19.69 | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.15/19.69 | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.15/19.69 | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.15/19.69 | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.15/19.69 | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.15/19.69 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.15/19.69 | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.15/19.69 | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.15/19.69 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.15/19.69 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.15/19.69 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.69 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.15/19.69 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.15/19.69 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.15/19.69 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.15/19.69 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.15/19.69 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.15/19.69 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.15/19.69 | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | BETA: splitting (9792) gives: % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | Case 1: % 135.15/19.69 | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | (9793) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.15/19.69 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.15/19.69 | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 135.15/19.69 | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.15/19.69 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.15/19.69 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.15/19.69 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.15/19.69 | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | ALPHA: (9793) implies: % 135.15/19.69 | | | | | | | | | | | | | | | | (9794) op(e2, e2) = e0 % 135.15/19.69 | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9543), (9794), (function-axioms) are % 135.15/19.69 | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 135.15/19.69 | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | Case 2: % 135.15/19.69 | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | (9795) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.15/19.69 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.15/19.69 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.15/19.69 | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.15/19.69 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.15/19.69 | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.15/19.69 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.15/19.69 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.15/19.69 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.15/19.69 | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.15/19.69 | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.15/19.69 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.15/19.69 | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.15/19.69 | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.15/19.69 | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.15/19.69 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.15/19.69 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.15/19.69 | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.15/19.69 | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.15/19.69 | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.15/19.69 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.15/19.69 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.15/19.69 | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.15/19.69 | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.15/19.69 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.15/19.69 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.15/19.69 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.69 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.69 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.15/19.69 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.15/19.69 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.15/19.69 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.15/19.69 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.15/19.69 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.15/19.69 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.15/19.69 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.15/19.69 | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.15/19.69 | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | BETA: splitting (9795) gives: % 135.15/19.69 | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | Case 1: % 135.15/19.69 | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | (9796) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.15/19.69 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 135.15/19.69 | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.15/19.69 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.15/19.69 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.15/19.69 | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.15/19.69 | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | ALPHA: (9796) implies: % 135.15/19.69 | | | | | | | | | | | | | | | | | (9797) op(e1, e1) = e2 % 135.15/19.69 | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (9797), (function-axioms) are % 135.15/19.69 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 135.15/19.69 | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | Case 2: % 135.15/19.69 | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | (9798) op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.15/19.69 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.15/19.69 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.15/19.69 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.15/19.69 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 135.15/19.69 | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.15/19.69 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 135.15/19.69 | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.15/19.69 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.15/19.69 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.15/19.69 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.15/19.69 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.15/19.69 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.69 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.15/19.69 | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.15/19.69 | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 135.15/19.69 | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.15/19.69 | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_29))) % 135.15/19.69 | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | ALPHA: (9798) implies: % 135.15/19.69 | | | | | | | | | | | | | | | | | (9799) op(e0, e0) = all_56_31 % 135.15/19.69 | | | | | | | | | | | | | | | | | (9800) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.15/19.69 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.15/19.69 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.69 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.15/19.69 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.15/19.69 | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 135.15/19.69 | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.15/19.69 | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.15/19.69 | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 135.15/19.69 | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 135.15/19.69 | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.15/19.69 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 135.15/19.69 | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.15/19.69 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.15/19.69 | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.15/19.69 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.15/19.69 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.15/19.69 | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.15/19.69 | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 135.15/19.69 | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 135.15/19.69 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.15/19.69 | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (39), (157), (160), (194), (334), (364), % 135.15/19.69 | | | | | | | | | | | | | | | | | (8984), (8991), (8992), (9786), (9799), (9800), % 135.15/19.69 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.15/19.69 | | | | | | | | | | | | | | | | | #31. % 135.15/19.69 | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | End of split % 135.15/19.69 | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | Case 2: % 135.15/19.69 | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | (9801) all_28_2 = e3 % 135.15/19.69 | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | COMBINE_EQS: (316), (9801) imply: % 135.15/19.69 | | | | | | | | | | | | | (9802) all_6_2 = e3 % 135.15/19.69 | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | SIMP: (9802) implies: % 135.15/19.69 | | | | | | | | | | | | | (9803) all_6_2 = e3 % 135.15/19.69 | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | COMBINE_EQS: (302), (9803) imply: % 135.15/19.69 | | | | | | | | | | | | | (9804) all_36_2 = e3 % 135.15/19.69 | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | REDUCE: (361), (9803) imply: % 135.15/19.69 | | | | | | | | | | | | | (9805) ~ (all_52_8 = e3) % 135.15/19.69 | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | REDUCE: (366), (9803) imply: % 135.15/19.69 | | | | | | | | | | | | | (9806) ~ (all_52_14 = e3) % 135.15/19.69 | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | REDUCE: (39), (9803) imply: % 135.15/19.69 | | | | | | | | | | | | | (9807) op(e1, e1) = e3 % 135.15/19.69 | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | BETA: splitting (85) gives: % 135.15/19.69 | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | Case 1: % 135.15/19.69 | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | (9808) ~ (all_36_2 = e3) % 135.15/19.69 | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | REDUCE: (9804), (9808) imply: % 135.15/19.69 | | | | | | | | | | | | | | (9809) $false % 135.15/19.69 | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | CLOSE: (9809) is inconsistent. % 135.15/19.69 | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | Case 2: % 135.15/19.69 | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | (9810) ( ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 & % 135.15/19.69 | | | | | | | | | | | | | | $i(all_36_0)) | ( ~ (all_36_1 = e2) & op(e3, e3) % 135.15/19.69 | | | | | | | | | | | | | | = all_36_1 & $i(all_36_1)) % 135.15/19.69 | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | BETA: splitting (9810) gives: % 135.15/19.69 | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | Case 1: % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | (9811) ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 & % 135.15/19.69 | | | | | | | | | | | | | | | $i(all_36_0) % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | ALPHA: (9811) implies: % 135.15/19.69 | | | | | | | | | | | | | | | (9812) ~ (all_36_0 = e0) % 135.15/19.69 | | | | | | | | | | | | | | | (9813) op(e3, e1) = all_36_0 % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 135.15/19.69 | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | Case 1: % 135.15/19.69 | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | (9814) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 135.15/19.69 | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 135.15/19.69 | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | BETA: splitting (9814) gives: % 135.15/19.69 | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | Case 1: % 135.15/19.69 | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | (9815) all_57_9 = e3 & op(e3, e0) = e3 % 135.15/19.69 | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | ALPHA: (9815) implies: % 135.15/19.69 | | | | | | | | | | | | | | | | | (9816) all_57_9 = e3 % 135.15/19.69 | | | | | | | | | | | | | | | | | (9817) op(e3, e0) = e3 % 135.15/19.69 | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | BETA: splitting (8997) gives: % 135.15/19.69 | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.69 | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | (9818) ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 & % 135.15/19.69 | | | | | | | | | | | | | | | | | | $i(all_12_0) % 135.15/19.69 | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | ALPHA: (9818) implies: % 135.15/19.69 | | | | | | | | | | | | | | | | | | (9819) ~ (all_12_0 = e2) % 135.15/19.69 | | | | | | | | | | | | | | | | | | (9820) op(e1, e0) = all_12_0 % 135.15/19.69 | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 135.15/19.69 | | | | | | | | | | | | | | | | | | all_12_0, e0, e1, simplifying with (160), (9820) % 135.15/19.69 | | | | | | | | | | | | | | | | | | gives: % 135.15/19.69 | | | | | | | | | | | | | | | | | | (9821) all_52_14 = all_12_0 % 135.15/19.69 | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 135.15/19.69 | | | | | | | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (9817) gives: % 135.15/19.69 | | | | | | | | | | | | | | | | | | (9822) all_52_12 = e3 % 135.15/19.69 | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 135.15/19.69 | | | | | | | | | | | | | | | | | | all_36_0, e1, e3, simplifying with (169), (9813) % 135.15/19.69 | | | | | | | | | | | | | | | | | | gives: % 135.15/19.69 | | | | | | | | | | | | | | | | | | (9823) all_52_8 = all_36_0 % 135.15/19.69 | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (9823) imply: % 135.15/19.69 | | | | | | | | | | | | | | | | | | (9824) all_54_2 = all_36_0 % 135.15/19.69 | | | | | | | | | | | | | | | | | | % 135.15/19.69 | | | | | | | | | | | | | | | | | | REDUCE: (134), (9823) imply: % 135.15/19.70 | | | | | | | | | | | | | | | | | | (9825) ~ (all_52_4 = all_36_0) % 135.15/19.70 | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | REDUCE: (9805), (9823) imply: % 135.15/19.70 | | | | | | | | | | | | | | | | | | (9826) ~ (all_36_0 = e3) % 135.15/19.70 | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | REDUCE: (9782), (9823) imply: % 135.15/19.70 | | | | | | | | | | | | | | | | | | (9827) ~ (all_36_0 = e2) % 135.15/19.70 | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 135.15/19.70 | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | (9828) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 135.15/19.70 | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 135.15/19.70 | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | BETA: splitting (9828) gives: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (9829) all_57_9 = e2 & op(e3, e0) = e2 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | ALPHA: (9829) implies: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (9830) all_57_9 = e2 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234), % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (238), (9534), (9784), (9830), (function-axioms) % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #250. % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (9831) all_57_10 = e2 & op(e2, e0) = e2 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | ALPHA: (9831) implies: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (9832) all_57_10 = e2 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | (9833) all_54_2 = e3 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9824), (9833) imply: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | (9834) all_36_0 = e3 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9826), (9834) imply: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | (9835) $false % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | CLOSE: (9835) is inconsistent. % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | (9836) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | (9837) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9837) gives: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | (9838) all_57_6 = e2 & op(e1, e3) = e2 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9838) implies: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | (9839) all_57_6 = e2 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (231), % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | (233), (237), (9542), (9784), (9832), (9839), % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | #361. % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | (9840) all_57_7 = e2 & op(e1, e2) = e2 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9840) implies: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | (9841) all_57_7 = e2 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | (9842) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9842) gives: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (9843) all_57_1 = e1 & op(e3, e2) = e1 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9843) implies: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (9844) op(e3, e2) = e1 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (203), (271), (9534), (9781), (9812), % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (9824), (9825), (9827), (9836), (9844), % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | #235. % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (9845) all_57_3 = e1 & op(e2, e2) = e1 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9845) implies: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (9846) op(e2, e2) = e1 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9543), (9846), (function-axioms) are % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | (9847) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9847) gives: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (9848) all_57_7 = e1 & op(e1, e2) = e1 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9848) implies: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (9849) all_57_7 = e1 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9841), (9849) are inconsistent by sub-proof % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | #288. % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (9850) all_57_13 = e1 & op(e0, e2) = e1 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8980), (9850), (function-axioms) are % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #178. % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | (9851) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (208), (8990), (9807), (9816), % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | (9832), (9851), (function-axioms) are inconsistent % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #26. % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | (9852) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 135.15/19.70 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 135.15/19.70 | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | BETA: splitting (9852) gives: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (9853) all_57_11 = e2 & op(e1, e0) = e2 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | ALPHA: (9853) implies: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (9854) op(e1, e0) = e2 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9819), (9820), (9854), (function-axioms) are % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #35. % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (9855) all_57_15 = e2 & op(e0, e0) = e2 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | ALPHA: (9855) implies: % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | (9856) op(e0, e0) = e2 % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8991), (9856), (function-axioms) are % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636. % 135.15/19.70 | | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | (9857) ~ (all_12_1 = e3) & op(e1, e1) = all_12_1 & % 135.15/19.70 | | | | | | | | | | | | | | | | | | $i(all_12_1) % 135.15/19.70 | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | ALPHA: (9857) implies: % 135.15/19.70 | | | | | | | | | | | | | | | | | | (9858) ~ (all_12_1 = e3) % 135.15/19.70 | | | | | | | | | | | | | | | | | | (9859) op(e1, e1) = all_12_1 % 135.15/19.70 | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9807), (9858), (9859), (function-axioms) are % 135.15/19.70 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #36. % 135.15/19.70 | | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | (9860) all_57_10 = e3 & op(e2, e0) = e3 % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9537), (9860), (function-axioms) are % 135.15/19.70 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749. % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | (9861) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 135.15/19.70 | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 135.15/19.70 | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (8991), (9806), (9861), % 135.15/19.70 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.15/19.70 | | | | | | | | | | | | | | | | #46. % 135.15/19.70 | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | (9862) ~ (all_36_1 = e2) & op(e3, e3) = all_36_1 & % 135.15/19.70 | | | | | | | | | | | | | | | $i(all_36_1) % 135.15/19.70 | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | REF_CLOSE: (9784), (9862), (function-axioms) are inconsistent % 135.15/19.70 | | | | | | | | | | | | | | | by sub-proof #342. % 135.15/19.70 | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | % 135.15/19.70 | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | (9863) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 135.15/19.70 | | | | | | | | | | e3 & op(e2, e0) = e3) % 135.15/19.70 | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | BETA: splitting (9863) gives: % 135.15/19.70 | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | (9864) all_57_5 = e3 & op(e2, e1) = e3 % 135.15/19.70 | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | REF_CLOSE: (165), (9536), (9864), (function-axioms) are % 135.15/19.70 | | | | | | | | | | | inconsistent by sub-proof #547. % 135.15/19.70 | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | (9865) all_57_10 = e3 & op(e2, e0) = e3 % 135.15/19.70 | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | REF_CLOSE: (164), (9537), (9865), (function-axioms) are % 135.15/19.70 | | | | | | | | | | | inconsistent by sub-proof #749. % 135.15/19.70 | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | % 135.15/19.70 | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | % 135.15/19.70 | | | | | | | | End of split % 135.15/19.70 | | | | | | | | % 135.15/19.70 | | | | | | | End of split % 135.15/19.70 | | | | | | | % 135.15/19.70 | | | | | | Case 2: % 135.15/19.70 | | | | | | | % 135.15/19.70 | | | | | | | (9866) all_10_2 = e0 % 135.15/19.70 | | | | | | | (9867) ( ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 & % 135.15/19.70 | | | | | | | $i(all_10_0)) | ( ~ (all_10_1 = e1) & op(e0, e0) = % 135.15/19.70 | | | | | | | all_10_1 & $i(all_10_1)) % 135.15/19.70 | | | | | | | % 135.15/19.70 | | | | | | | REDUCE: (336), (9866) imply: % 135.15/19.70 | | | | | | | (9868) ~ (all_52_1 = e0) % 135.15/19.70 | | | | | | | % 135.15/19.70 | | | | | | | REDUCE: (338), (9866) imply: % 135.15/19.70 | | | | | | | (9869) ~ (all_52_2 = e0) % 135.15/19.70 | | | | | | | % 135.15/19.70 | | | | | | | REDUCE: (340), (9866) imply: % 135.15/19.70 | | | | | | | (9870) ~ (all_52_3 = e0) % 135.15/19.70 | | | | | | | % 135.15/19.70 | | | | | | | REDUCE: (342), (9866) imply: % 135.15/19.70 | | | | | | | (9871) ~ (all_52_4 = e0) % 135.15/19.70 | | | | | | | % 135.15/19.70 | | | | | | | REDUCE: (346), (9866) imply: % 135.15/19.70 | | | | | | | (9872) ~ (all_52_12 = e0) % 135.15/19.70 | | | | | | | % 135.15/19.70 | | | | | | | REDUCE: (45), (9866) imply: % 135.15/19.70 | | | | | | | (9873) op(e3, e3) = e0 % 135.15/19.70 | | | | | | | % 135.15/19.70 | | | | | | | BETA: splitting (9867) gives: % 135.15/19.70 | | | | | | | % 135.15/19.70 | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | % 135.15/19.70 | | | | | | | | (9874) ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 & % 135.15/19.70 | | | | | | | | $i(all_10_0) % 135.15/19.70 | | | | | | | | % 135.15/19.70 | | | | | | | | ALPHA: (9874) implies: % 135.15/19.70 | | | | | | | | (9875) ~ (all_10_0 = e2) % 135.15/19.70 | | | | | | | | (9876) op(e0, e3) = all_10_0 % 135.15/19.70 | | | | | | | | % 135.15/19.70 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, % 135.15/19.70 | | | | | | | | all_10_0, e3, e0, simplifying with (159), (9876) % 135.15/19.70 | | | | | | | | gives: % 135.15/19.70 | | | | | | | | (9877) all_52_3 = all_10_0 % 135.15/19.70 | | | | | | | | % 135.15/19.70 | | | | | | | | COMBINE_EQS: (248), (9877) imply: % 135.15/19.70 | | | | | | | | (9878) all_54_12 = all_10_0 % 135.15/19.70 | | | | | | | | % 135.15/19.70 | | | | | | | | REDUCE: (140), (9877) imply: % 135.15/19.70 | | | | | | | | (9879) ~ (all_52_7 = all_10_0) % 135.15/19.70 | | | | | | | | % 135.15/19.70 | | | | | | | | SIMP: (9879) implies: % 135.15/19.70 | | | | | | | | (9880) ~ (all_52_7 = all_10_0) % 135.15/19.70 | | | | | | | | % 135.15/19.70 | | | | | | | | REDUCE: (139), (9877) imply: % 135.15/19.70 | | | | | | | | (9881) ~ (all_52_11 = all_10_0) % 135.15/19.70 | | | | | | | | % 135.15/19.70 | | | | | | | | SIMP: (9881) implies: % 135.15/19.70 | | | | | | | | (9882) ~ (all_52_11 = all_10_0) % 135.15/19.70 | | | | | | | | % 135.15/19.70 | | | | | | | | REDUCE: (8979), (9877) imply: % 135.15/19.70 | | | | | | | | (9883) ~ (all_10_0 = e1) % 135.15/19.70 | | | | | | | | % 135.15/19.70 | | | | | | | | REDUCE: (9870), (9877) imply: % 135.15/19.70 | | | | | | | | (9884) ~ (all_10_0 = e0) % 135.15/19.70 | | | | | | | | % 135.15/19.70 | | | | | | | | BETA: splitting (192) gives: % 135.15/19.70 | | | | | | | | % 135.15/19.70 | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | % 135.15/19.70 | | | | | | | | | (9885) all_54_12 = e3 % 135.15/19.70 | | | | | | | | | % 135.15/19.70 | | | | | | | | | COMBINE_EQS: (9878), (9885) imply: % 135.15/19.70 | | | | | | | | | (9886) all_10_0 = e3 % 135.15/19.70 | | | | | | | | | % 135.15/19.70 | | | | | | | | | SIMP: (9886) implies: % 135.15/19.70 | | | | | | | | | (9887) all_10_0 = e3 % 135.15/19.70 | | | | | | | | | % 135.15/19.70 | | | | | | | | | REDUCE: (9880), (9887) imply: % 135.15/19.70 | | | | | | | | | (9888) ~ (all_52_7 = e3) % 135.15/19.70 | | | | | | | | | % 135.15/19.70 | | | | | | | | | REDUCE: (9882), (9887) imply: % 135.15/19.70 | | | | | | | | | (9889) ~ (all_52_11 = e3) % 135.15/19.70 | | | | | | | | | % 135.15/19.70 | | | | | | | | | BETA: splitting (211) gives: % 135.15/19.70 | | | | | | | | | % 135.15/19.70 | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | (9890) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 135.15/19.70 | | | | | | | | | | e3 & op(e0, e2) = e3) % 135.15/19.70 | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | BETA: splitting (9890) gives: % 135.15/19.70 | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | (9891) all_57_12 = e3 & op(e0, e3) = e3 % 135.15/19.70 | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | ALPHA: (9891) implies: % 135.15/19.70 | | | | | | | | | | | (9892) all_57_12 = e3 % 135.15/19.70 | | | | | | | | | | | (9893) op(e0, e3) = e3 % 135.15/19.70 | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | BETA: splitting (49) gives: % 135.15/19.70 | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | (9894) ~ (all_12_2 = e1) % 135.15/19.70 | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | REDUCE: (8978), (9894) imply: % 135.15/19.70 | | | | | | | | | | | | (9895) $false % 135.15/19.70 | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | CLOSE: (9895) is inconsistent. % 135.15/19.70 | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | (9896) ( ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 & % 135.15/19.70 | | | | | | | | | | | | $i(all_12_0)) | ( ~ (all_12_1 = e3) & op(e1, e1) % 135.15/19.70 | | | | | | | | | | | | = all_12_1 & $i(all_12_1)) % 135.15/19.70 | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | BETA: splitting (52) gives: % 135.15/19.70 | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | (9897) ~ (all_14_2 = e3) % 135.15/19.70 | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | REDUCE: (329), (9897) imply: % 135.15/19.70 | | | | | | | | | | | | | (9898) ~ (all_8_2 = e3) % 135.15/19.70 | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | BETA: splitting (73) gives: % 135.15/19.70 | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | (9899) ~ (all_28_2 = e3) % 135.15/19.70 | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | REDUCE: (316), (9899) imply: % 135.15/19.70 | | | | | | | | | | | | | | (9900) ~ (all_6_2 = e3) % 135.15/19.70 | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | BETA: splitting (206) gives: % 135.15/19.70 | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | (9901) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.15/19.70 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.15/19.70 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.15/19.70 | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.15/19.70 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.15/19.70 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.15/19.70 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.15/19.70 | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.15/19.70 | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.15/19.70 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.15/19.70 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.70 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.15/19.70 | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.15/19.70 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.15/19.70 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.15/19.70 | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | BETA: splitting (9901) gives: % 135.15/19.70 | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | (9902) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.15/19.70 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.15/19.70 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.15/19.70 | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.15/19.70 | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.15/19.70 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.15/19.70 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.15/19.70 | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.15/19.70 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.15/19.70 | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.15/19.70 | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.15/19.70 | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.15/19.70 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.15/19.70 | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.15/19.70 | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | BETA: splitting (9902) gives: % 135.15/19.70 | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | (9903) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 135.15/19.70 | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.15/19.70 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 135.15/19.70 | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.15/19.70 | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 135.15/19.70 | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 135.15/19.70 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | ALPHA: (9903) implies: % 135.15/19.70 | | | | | | | | | | | | | | | | | (9904) op(e3, e3) = e2 % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (163), (167), (231), (9868), (9869), % 135.15/19.70 | | | | | | | | | | | | | | | | | (9892), (9904), (function-axioms) are inconsistent % 135.15/19.70 | | | | | | | | | | | | | | | | | by sub-proof #25. % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | (9905) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.15/19.70 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 135.15/19.70 | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 135.15/19.70 | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.15/19.70 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.15/19.70 | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.15/19.70 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | ALPHA: (9905) implies: % 135.15/19.70 | | | | | | | | | | | | | | | | | (9906) op(e3, e3) = e1 % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9873), (9906), (function-axioms) are % 135.15/19.70 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | (9907) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.15/19.70 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.15/19.70 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.15/19.70 | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.70 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.70 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.15/19.70 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.15/19.70 | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.15/19.70 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.15/19.70 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.70 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.15/19.70 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.15/19.70 | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.70 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.15/19.70 | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | REF_CLOSE: (42), (9893), (9898), (9907), (function-axioms) % 135.15/19.70 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #68. % 135.15/19.70 | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | (9908) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.15/19.70 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.15/19.70 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.15/19.70 | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.15/19.70 | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.15/19.70 | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.15/19.70 | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.15/19.70 | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.15/19.70 | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 135.15/19.70 | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.15/19.70 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.15/19.70 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 135.15/19.70 | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.15/19.70 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 135.15/19.70 | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 135.15/19.70 | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.15/19.70 | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.15/19.70 | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.15/19.70 | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.15/19.70 | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.15/19.70 | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.15/19.70 | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.15/19.70 | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 135.15/19.70 | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.15/19.70 | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 135.15/19.70 | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 135.15/19.70 | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.15/19.70 | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.15/19.70 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.15/19.70 | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 135.15/19.70 | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 135.15/19.70 | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.15/19.70 | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 135.15/19.70 | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.15/19.70 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.15/19.70 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.15/19.70 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.15/19.70 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.15/19.70 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.15/19.70 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.15/19.70 | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.15/19.70 | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | BETA: splitting (9908) gives: % 135.15/19.70 | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | (9909) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.15/19.70 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.15/19.70 | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.70 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.15/19.70 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.15/19.70 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.70 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.15/19.70 | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.15/19.70 | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.15/19.70 | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.15/19.70 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.15/19.70 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.15/19.70 | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.15/19.70 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.15/19.70 | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | BETA: splitting (9909) gives: % 135.15/19.70 | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | Case 1: % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | (9910) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.15/19.70 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 135.15/19.70 | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.15/19.70 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.15/19.70 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 135.15/19.70 | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.15/19.70 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | ALPHA: (9910) implies: % 135.15/19.70 | | | | | | | | | | | | | | | | | (9911) op(e1, e1) = e3 % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (9900), (9911), (function-axioms) are % 135.15/19.70 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #771. % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | (9912) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 135.15/19.70 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 135.15/19.70 | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 135.15/19.70 | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.15/19.70 | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.15/19.70 | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.15/19.70 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | ALPHA: (9912) implies: % 135.15/19.70 | | | | | | | | | | | | | | | | | (9913) op(e2, e2) = e1 % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (8993), (9913), (function-axioms) are % 135.15/19.70 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #57. % 135.15/19.70 | | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | | End of split % 135.15/19.70 | | | | | | | | | | | | | | | | % 135.15/19.70 | | | | | | | | | | | | | | | Case 2: % 135.15/19.70 | | | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | | | (9914) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.15/19.71 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.15/19.71 | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 135.15/19.71 | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.71 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.71 | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.15/19.71 | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.15/19.71 | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.15/19.71 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.15/19.71 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.15/19.71 | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.15/19.71 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.15/19.71 | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.15/19.71 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.15/19.71 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.15/19.71 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.15/19.71 | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.15/19.71 | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.15/19.71 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.15/19.71 | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.15/19.71 | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.15/19.71 | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.15/19.71 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.15/19.71 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.15/19.71 | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.15/19.71 | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.15/19.71 | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.15/19.71 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.15/19.71 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.15/19.71 | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.15/19.71 | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.15/19.71 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.15/19.71 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.15/19.71 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.71 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.71 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.15/19.71 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.15/19.71 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.15/19.71 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.15/19.71 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.15/19.71 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.15/19.71 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.15/19.71 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.15/19.71 | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.15/19.71 | | | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | | | BETA: splitting (9914) gives: % 135.15/19.71 | | | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | | | Case 1: % 135.15/19.71 | | | | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | | | | (9915) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.15/19.71 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.15/19.71 | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 135.15/19.71 | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.15/19.71 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.15/19.71 | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.15/19.71 | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.15/19.71 | | | | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | | | | ALPHA: (9915) implies: % 135.15/19.71 | | | | | | | | | | | | | | | | | (9916) ~ (all_56_7 = e3) % 135.15/19.71 | | | | | | | | | | | | | | | | | (9917) op(e0, e3) = all_56_7 % 135.15/19.71 | | | | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | | | | REF_CLOSE: (9893), (9916), (9917), (function-axioms) are % 135.15/19.71 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #209. % 135.15/19.71 | | | | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | | | Case 2: % 135.15/19.71 | | | | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | | | | (9918) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.15/19.71 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.15/19.71 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.15/19.71 | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.15/19.71 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.15/19.71 | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.15/19.71 | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.15/19.71 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.15/19.71 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.15/19.71 | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.15/19.71 | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.15/19.71 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.15/19.71 | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.15/19.71 | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.15/19.71 | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.15/19.71 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.15/19.71 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.15/19.71 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.15/19.71 | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.15/19.71 | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.15/19.71 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.15/19.71 | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.15/19.71 | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.15/19.71 | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.15/19.71 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.15/19.71 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.15/19.71 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.15/19.71 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.15/19.71 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.15/19.71 | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.15/19.71 | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.15/19.71 | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.15/19.71 | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.15/19.71 | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.15/19.71 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.15/19.71 | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.15/19.71 | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.15/19.71 | | | | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (39), (157), (160), (194), (334), (364), % 135.15/19.71 | | | | | | | | | | | | | | | | | (8984), (8991), (8992), (9900), (9918), % 135.15/19.71 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.15/19.71 | | | | | | | | | | | | | | | | | #30. % 135.15/19.71 | | | | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | | | End of split % 135.15/19.71 | | | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | | End of split % 135.15/19.71 | | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | End of split % 135.15/19.71 | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | Case 2: % 135.15/19.71 | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | (9919) all_28_2 = e3 % 135.15/19.71 | | | | | | | | | | | | | | (9920) ( ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 & % 135.15/19.71 | | | | | | | | | | | | | | $i(all_28_0)) | ( ~ (all_28_1 = e0) & op(e3, e3) % 135.15/19.71 | | | | | | | | | | | | | | = all_28_1 & $i(all_28_1)) % 135.15/19.71 | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | COMBINE_EQS: (316), (9919) imply: % 135.15/19.71 | | | | | | | | | | | | | | (9921) all_6_2 = e3 % 135.15/19.71 | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | SIMP: (9921) implies: % 135.15/19.71 | | | | | | | | | | | | | | (9922) all_6_2 = e3 % 135.15/19.71 | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | REDUCE: (359), (9922) imply: % 135.15/19.71 | | | | | | | | | | | | | | (9923) ~ (all_52_6 = e3) % 135.15/19.71 | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | REDUCE: (361), (9922) imply: % 135.15/19.71 | | | | | | | | | | | | | | (9924) ~ (all_52_8 = e3) % 135.15/19.71 | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | REDUCE: (366), (9922) imply: % 135.15/19.71 | | | | | | | | | | | | | | (9925) ~ (all_52_14 = e3) % 135.15/19.71 | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | REDUCE: (39), (9922) imply: % 135.15/19.71 | | | | | | | | | | | | | | (9926) op(e1, e1) = e3 % 135.15/19.71 | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | BETA: splitting (230) gives: % 135.15/19.71 | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | Case 1: % 135.15/19.71 | | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | | (9927) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 135.15/19.71 | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 135.15/19.71 | | | | | | | | | | | | | | | % 135.15/19.71 | | | | | | | | | | | | | | | BETA: splitting (9927) gives: % 135.18/19.71 | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | (9928) all_57_1 = e3 & op(e3, e2) = e3 % 135.18/19.71 | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | ALPHA: (9928) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | (9929) all_57_1 = e3 % 135.18/19.71 | | | | | | | | | | | | | | | | (9930) op(e3, e2) = e3 % 135.18/19.71 | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | (9931) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 135.18/19.71 | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | BETA: splitting (9931) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | (9932) all_57_1 = e1 & op(e3, e2) = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | ALPHA: (9932) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | (9933) op(e3, e2) = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9930), (9933), (function-axioms) are % 135.18/19.71 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #413. % 135.18/19.71 | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.71 | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | (9934) all_57_3 = e1 & op(e2, e2) = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | ALPHA: (9934) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | (9935) op(e2, e2) = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (8993), (9935), (function-axioms) are % 135.18/19.71 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #57. % 135.18/19.71 | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | End of split % 135.18/19.71 | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | Case 2: % 135.18/19.71 | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | (9936) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 135.18/19.71 | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 135.18/19.71 | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | BETA: splitting (9936) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | (9937) all_57_7 = e1 & op(e1, e2) = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | ALPHA: (9937) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | (9938) all_57_7 = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | (9939) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | BETA: splitting (9939) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | (9940) all_57_0 = e1 & op(e3, e3) = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | ALPHA: (9940) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | (9941) op(e3, e3) = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9873), (9941), (function-axioms) are % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | (9942) all_57_1 = e1 & op(e3, e2) = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | ALPHA: (9942) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | (9943) op(e3, e2) = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9930), (9943), (function-axioms) are % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #413. % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.71 | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | (9944) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | BETA: splitting (9944) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | (9945) all_57_4 = e1 & op(e3, e1) = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | ALPHA: (9945) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | (9946) all_57_4 = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | (9947) op(e3, e1) = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | (9948) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9948) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9949) all_57_6 = e0 & op(e1, e3) = e0 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9869), (9949), (function-axioms) are % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #73. % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9950) all_57_7 = e0 & op(e1, e2) = e0 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9950) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9951) all_57_7 = e0 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9938), (9951) imply: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9952) e1 = e0 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (9952) imply: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9953) $false % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9953) is inconsistent. % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | (9954) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9954) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9955) all_57_8 = e0 & op(e1, e1) = e0 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9955) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9956) op(e1, e1) = e0 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9926), (9956), (function-axioms) are % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9957) all_57_11 = e0 & op(e1, e0) = e0 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9957) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | (9958) op(e1, e0) = e0 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | (9959) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9959) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9960) all_57_0 = e2 & op(e3, e3) = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9960) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9961) op(e3, e3) = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (163), (167), (231), (9868), (9869), % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9892), (9961), (function-axioms) are inconsistent % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #25. % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9962) all_57_1 = e2 & op(e3, e2) = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9962) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9963) all_57_1 = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9929), (9963) imply: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9964) e3 = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9892), (9964) imply: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9965) all_57_12 = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (192), (211), (8991), (9875), % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9878), (9880), (9882), (9883), (9884), (9965), % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | #23. % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | (9966) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9966) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9967) all_57_4 = e2 & op(e3, e1) = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9967) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9968) all_57_4 = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9946), (9968) are inconsistent by sub-proof % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | #669. % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9969) all_57_9 = e2 & op(e3, e0) = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9969) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9970) all_57_9 = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (9971) op(e3, e0) = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | (9972) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9972) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (9973) all_57_9 = e3 & op(e3, e0) = e3 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9973) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (9974) op(e3, e0) = e3 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (9971), (9974), (function-axioms) are % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #111. % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (9975) all_57_10 = e3 & op(e2, e0) = e3 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9975) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (9976) op(e2, e0) = e3 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9896) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9977) ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_12_0) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9977) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9978) ~ (all_12_0 = e2) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9979) op(e1, e0) = all_12_0 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9920) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9980) ~ (all_28_0 = e2) & op(e3, e1) = all_28_0 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_28_0) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9980) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9981) ~ (all_28_0 = e2) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9982) op(e3, e1) = all_28_0 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9983) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9983) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9984) all_57_6 = e2 & op(e1, e3) = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9984) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9985) op(e1, e3) = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9986) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9986) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9987) all_57_0 = e1 & op(e3, e3) = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9987) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9988) op(e3, e3) = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (232), (236), % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (9924), (9946), (9970), (9988), % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #163. % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9989) all_57_2 = e1 & op(e2, e3) = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9989) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9990) all_57_2 = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9991) op(e2, e3) = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e0, e1, simplifying with (160), (9958) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9992) all_52_14 = e0 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_12_0, e0, e1, simplifying with (160), (9979) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9993) all_52_14 = all_12_0 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2, % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (9985) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9994) all_52_2 = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, e2, simplifying with (164), (9976) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9995) all_52_13 = e3 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e1, % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (167), (9991) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9996) all_52_1 = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e3, simplifying with (168), (9971) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9997) all_52_12 = e2 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1, % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (9947) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9998) all_52_8 = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_28_0, e1, e3, simplifying with (169), (9982) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9999) all_52_8 = all_28_0 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9998), (9999) imply: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10000) all_28_0 = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10000) implies: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10001) all_28_0 = e1 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9992), (9993) imply: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10002) all_12_0 = e0 % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (9995), (9997) imply: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10003) ~ (e3 = e2) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (9995) imply: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10004) ~ (all_8_2 = e3) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9925), (9992) imply: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10005) ~ (e3 = e0) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8984), (9992) imply: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10006) ~ (e1 = e0) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9981), (10001) imply: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10007) ~ (e2 = e1) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9978), (10002) imply: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10008) ~ (e2 = e0) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10009) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10009) gives: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10010) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (163), (167), (231), % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (9868), (9869), (9892), (9990), (9991), % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10010), (function-axioms) are inconsistent by % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #22. % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10011) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (168), (9898), (9971), (10011), % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #110. % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10012) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10012) gives: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10013) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (9958), (9985), (10013), % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #28. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10014) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10014) gives: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10015) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10015) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10016) op(e2, e0) = e2 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (9976), (10016), (function-axioms) are % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #546. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10017) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10017) gives: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10018) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10018) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10019) op(e1, e1) = e2 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9926), (10019), (function-axioms) are % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10020) op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10020) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10021) op(e0, e0) = all_56_31 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10022) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (8984), (8991), (9947), (9958), % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10021), (10022), (function-axioms) are % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #20. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10023) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (159), (163), (8979), (9985), (10023), % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #47. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10024) all_57_7 = e2 & op(e1, e2) = e2 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10024) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10025) all_57_7 = e2 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9938), (10025) are inconsistent by sub-proof % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #288. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10026) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10026) gives: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10027) all_57_8 = e2 & op(e1, e1) = e2 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10027) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10028) op(e1, e1) = e2 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9926), (10028), (function-axioms) are % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10029) all_57_11 = e2 & op(e1, e0) = e2 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10029) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10030) op(e1, e0) = e2 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9978), (9979), (10030), (function-axioms) are % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #35. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10031) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_28_1) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9873), (10031), (function-axioms) are % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #211. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10032) ~ (all_12_1 = e3) & op(e1, e1) = all_12_1 & % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_12_1) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10032) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10033) ~ (all_12_1 = e3) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10034) op(e1, e1) = all_12_1 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9926), (10033), (10034), (function-axioms) are % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #36. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | (10035) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (8991), (9925), (10035), % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | #46. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | (10036) all_57_9 = e1 & op(e3, e0) = e1 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8982), (10036), (function-axioms) are % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #181. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | (10037) all_57_13 = e1 & op(e0, e2) = e1 % 135.18/19.72 | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8980), (10037), (function-axioms) are % 135.18/19.72 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #178. % 135.18/19.72 | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | (10038) all_57_3 = e3 & op(e2, e2) = e3 % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | ALPHA: (10038) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | (10039) op(e2, e2) = e3 % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | REF_CLOSE: (42), (9898), (10039), (function-axioms) are % 135.18/19.72 | | | | | | | | | | | | | | | | inconsistent by sub-proof #228. % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | (10040) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 135.18/19.72 | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 135.18/19.72 | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (9888), (9923), (10040), % 135.18/19.72 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.18/19.72 | | | | | | | | | | | | | | | #555. % 135.18/19.72 | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | (10041) all_14_2 = e3 % 135.18/19.72 | | | | | | | | | | | | | (10042) ( ~ (all_14_0 = e1) & op(e3, e2) = all_14_0 & % 135.18/19.72 | | | | | | | | | | | | | $i(all_14_0)) | ( ~ (all_14_1 = e0) & op(e3, e3) % 135.18/19.72 | | | | | | | | | | | | | = all_14_1 & $i(all_14_1)) % 135.18/19.72 | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | COMBINE_EQS: (329), (10041) imply: % 135.18/19.72 | | | | | | | | | | | | | (10043) all_8_2 = e3 % 135.18/19.72 | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | REDUCE: (350), (10043) imply: % 135.18/19.72 | | | | | | | | | | | | | (10044) ~ (all_52_4 = e3) % 135.18/19.72 | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | REDUCE: (352), (10043) imply: % 135.18/19.72 | | | | | | | | | | | | | (10045) ~ (all_52_6 = e3) % 135.18/19.72 | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | REDUCE: (356), (10043) imply: % 135.18/19.72 | | | | | | | | | | | | | (10046) ~ (all_52_9 = e3) % 135.18/19.72 | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | BETA: splitting (10042) gives: % 135.18/19.72 | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | Case 1: % 135.18/19.72 | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | (10047) ~ (all_14_0 = e1) & op(e3, e2) = all_14_0 & % 135.18/19.72 | | | | | | | | | | | | | | $i(all_14_0) % 135.18/19.72 | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | ALPHA: (10047) implies: % 135.18/19.72 | | | | | | | | | | | | | | (10048) ~ (all_14_0 = e1) % 135.18/19.72 | | | | | | | | | | | | | | (10049) op(e3, e2) = all_14_0 % 135.18/19.72 | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | BETA: splitting (230) gives: % 135.18/19.72 | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | Case 1: % 135.18/19.72 | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | (10050) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 135.18/19.72 | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 135.18/19.72 | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | BETA: splitting (10050) gives: % 135.18/19.72 | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | Case 1: % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | (10051) all_57_1 = e3 & op(e3, e2) = e3 % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | ALPHA: (10051) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | (10052) op(e3, e2) = e3 % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | REF_CLOSE: (170), (10044), (10052), (function-axioms) are % 135.18/19.72 | | | | | | | | | | | | | | | | inconsistent by sub-proof #738. % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | (10053) all_57_3 = e3 & op(e2, e2) = e3 % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | ALPHA: (10053) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | (10054) all_57_3 = e3 % 135.18/19.72 | | | | | | | | | | | | | | | | (10055) op(e2, e2) = e3 % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, % 135.18/19.72 | | | | | | | | | | | | | | | | all_14_0, e2, e3, simplifying with (170), (10049) % 135.18/19.72 | | | | | | | | | | | | | | | | gives: % 135.18/19.72 | | | | | | | | | | | | | | | | (10056) all_52_4 = all_14_0 % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (10056) imply: % 135.18/19.72 | | | | | | | | | | | | | | | | (10057) all_54_1 = all_14_0 % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | REDUCE: (136), (10056) imply: % 135.18/19.72 | | | | | | | | | | | | | | | | (10058) ~ (all_52_6 = all_14_0) % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | SIMP: (10058) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | (10059) ~ (all_52_6 = all_14_0) % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | REDUCE: (134), (10056) imply: % 135.18/19.72 | | | | | | | | | | | | | | | | (10060) ~ (all_52_8 = all_14_0) % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | SIMP: (10060) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | (10061) ~ (all_52_8 = all_14_0) % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | REDUCE: (133), (10056) imply: % 135.18/19.72 | | | | | | | | | | | | | | | | (10062) ~ (all_52_12 = all_14_0) % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | SIMP: (10062) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | (10063) ~ (all_52_12 = all_14_0) % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | REDUCE: (10044), (10056) imply: % 135.18/19.72 | | | | | | | | | | | | | | | | (10064) ~ (all_14_0 = e3) % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | REDUCE: (9871), (10056) imply: % 135.18/19.72 | | | | | | | | | | | | | | | | (10065) ~ (all_14_0 = e0) % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 135.18/19.72 | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | Case 1: % 135.18/19.72 | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | (10066) all_54_1 = e3 % 135.18/19.72 | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | COMBINE_EQS: (10057), (10066) imply: % 135.18/19.72 | | | | | | | | | | | | | | | | | (10067) all_14_0 = e3 % 135.18/19.72 | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | REDUCE: (10064), (10067) imply: % 135.18/19.72 | | | | | | | | | | | | | | | | | (10068) $false % 135.18/19.72 | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | CLOSE: (10068) is inconsistent. % 135.18/19.72 | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | (10069) ~ (all_54_1 = e3) % 135.18/19.72 | | | | | | | | | | | | | | | | | (10070) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 135.18/19.72 | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 135.18/19.72 | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.72 | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | (10071) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 135.18/19.72 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 135.18/19.72 | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | BETA: splitting (10071) gives: % 135.18/19.72 | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | (10072) all_57_1 = e1 & op(e3, e2) = e1 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | ALPHA: (10072) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | (10073) all_57_1 = e1 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (10070) gives: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | (10074) all_54_1 = e2 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10057), (10074) imply: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | (10075) all_14_0 = e2 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | REDUCE: (10061), (10075) imply: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | (10076) ~ (all_52_8 = e2) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | REDUCE: (10063), (10075) imply: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | (10077) ~ (all_52_12 = e2) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | (10078) all_54_3 = e3 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (10078) imply: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | (10079) all_52_12 = e3 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | SIMP: (10079) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | (10080) all_52_12 = e3 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (10080) imply: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | (10081) op(e3, e0) = e3 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | (10082) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10082) gives: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | (10083) all_57_0 = e2 & op(e3, e3) = e2 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10083) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | (10084) op(e3, e3) = e2 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (163), (167), (231), (9868), (9869), % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | (9892), (10084), (function-axioms) are % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #25. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | (10085) all_57_1 = e2 & op(e3, e2) = e2 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10073), (10085) are inconsistent by % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #616. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | (10086) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2) % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (169), (10076), (10081), (10086), % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | #19. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | (10087) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (8982), (9872), (10077), (10087) are % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | (10088) all_54_1 = e1 | all_54_1 = e0 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10048), (10057), (10065), (10088) are % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #192. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | (10089) all_57_3 = e1 & op(e2, e2) = e1 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | ALPHA: (10089) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | (10090) op(e2, e2) = e1 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10055), (10090), (function-axioms) are % 135.18/19.72 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 135.18/19.72 | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | End of split % 135.18/19.72 | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.72 | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | (10091) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 135.18/19.72 | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 135.18/19.72 | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | BETA: splitting (10091) gives: % 135.18/19.72 | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | (10092) all_57_7 = e1 & op(e1, e2) = e1 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | ALPHA: (10092) implies: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | (10093) all_57_7 = e1 % 135.18/19.72 | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | % 135.18/19.72 | | | | | | | | | | | | | | | | | | | | (10094) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1) % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | BETA: splitting (10094) gives: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | (10095) all_57_0 = e1 & op(e3, e3) = e1 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | ALPHA: (10095) implies: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | (10096) op(e3, e3) = e1 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9873), (10096), (function-axioms) are % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #717. % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | (10097) all_57_1 = e1 & op(e3, e2) = e1 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | ALPHA: (10097) implies: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | (10098) all_57_1 = e1 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | (10099) op(e3, e2) = e1 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10070) gives: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10100) all_54_1 = e2 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10057), (10100) imply: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10101) all_14_0 = e2 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10059), (10101) imply: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10102) ~ (all_52_6 = e2) % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | (10103) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2) % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10103) gives: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10104) all_57_1 = e2 & op(e3, e2) = e2 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10098), (10104) are inconsistent by % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #616. % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10105) all_57_3 = e2 & op(e2, e2) = e2 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10105) implies: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10106) all_57_3 = e2 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10054), (10106) imply: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10107) e3 = e2 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10107) implies: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10108) e3 = e2 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9892), (10108) imply: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10109) all_57_12 = e2 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (192), (211), (8991), (9875), % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (9878), (9880), (9882), (9883), (9884), (10109), % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | #23. % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | (10110) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10110) gives: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10111) all_57_7 = e2 & op(e1, e2) = e2 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10102), (10111), (function-axioms) are % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515. % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10112) all_57_13 = e2 & op(e0, e2) = e2 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10112) implies: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10113) all_57_13 = e2 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | (10114) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10114) gives: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10115) all_57_1 = e0 & op(e3, e2) = e0 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10115) implies: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10116) op(e3, e2) = e0 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0, % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (10049), (10099) gives: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10117) all_14_0 = e1 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0, % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (10049), (10116) gives: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10118) all_14_0 = e0 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10117), (10118) imply: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10119) e1 = e0 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10119) implies: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10120) e1 = e0 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (10120) imply: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10121) $false % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10121) is inconsistent. % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10122) all_57_3 = e0 & op(e2, e2) = e0 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10054), (10122) are inconsistent by % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #374. % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | (10123) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10123) gives: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10124) all_57_7 = e0 & op(e1, e2) = e0 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10124) implies: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10125) all_57_7 = e0 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10093), (10125) are inconsistent by % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #464. % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10126) all_57_13 = e0 & op(e0, e2) = e0 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10113), (10126) are inconsistent by % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #411. % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10127) all_54_1 = e1 | all_54_1 = e0 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10048), (10057), (10065), (10127) are % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #192. % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | End of split % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | (10128) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1) % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | BETA: splitting (10128) gives: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | (10129) all_57_4 = e1 & op(e3, e1) = e1 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | ALPHA: (10129) implies: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | (10130) all_57_4 = e1 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | (10131) op(e3, e1) = e1 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10070) gives: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10132) all_54_1 = e2 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10057), (10132) imply: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10133) all_14_0 = e2 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10059), (10133) imply: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10134) ~ (all_52_6 = e2) % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10061), (10133) imply: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10135) ~ (all_52_8 = e2) % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10063), (10133) imply: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10136) ~ (all_52_12 = e2) % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10064), (10133) imply: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10137) ~ (e3 = e2) % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10049), (10133) imply: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | (10138) op(e3, e2) = e2 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | (10139) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10139) gives: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10140) all_57_12 = e2 & op(e0, e3) = e2 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10140) implies: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10141) all_57_12 = e2 % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (192), (211), (8991), (9875), % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (9878), (9880), (9882), (9883), (9884), (10141), % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | #23. % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.18/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10142) all_57_13 = e2 & op(e0, e2) = e2 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (168), (169), (227), % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (228), (236), (9873), (10054), (10135), (10136), % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10142), (function-axioms) are inconsistent by % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #193. % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | (10143) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10143) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10144) all_57_14 = e2 & op(e0, e1) = e2 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10144) implies: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (10145) all_57_14 = e2 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | (10146) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10146) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10147) all_57_4 = e3 & op(e3, e1) = e3 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10147) implies: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10148) op(e3, e1) = e3 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (169), (201), (269), (8982), (9872), % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10136), (10148), (function-axioms) are % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #319. % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10149) all_57_5 = e3 & op(e2, e1) = e3 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10046), (10149), (function-axioms) are % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | (10150) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10150) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10151) all_57_8 = e3 & op(e1, e1) = e3 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10151) implies: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (10152) op(e1, e1) = e3 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10153) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (9873), (10044), (10153), % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | #197. % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10154) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10154) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10155) all_57_4 = e3 & op(e3, e1) = e3 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10155) implies: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10156) op(e3, e1) = e3 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (169), (201), (269), (8982), (9872), % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10136), (10156), (function-axioms) are % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #319. % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10157) all_57_9 = e3 & op(e3, e0) = e3 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10157) implies: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10158) all_57_9 = e3 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10159) op(e3, e0) = e3 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10160) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10160) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10161) all_57_6 = e0 & op(e1, e3) = e0 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9869), (10161), (function-axioms) are % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #73. % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10162) all_57_7 = e0 & op(e1, e2) = e0 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10162) implies: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10163) all_57_7 = e0 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10093), (10163) are inconsistent by % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #464. % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10164) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10164) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10165) all_57_8 = e0 & op(e1, e1) = e0 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10165) implies: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10166) op(e1, e1) = e0 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10152), (10166), (function-axioms) are % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10167) all_57_11 = e0 & op(e1, e0) = e0 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10167) implies: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10168) all_57_11 = e0 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10169) op(e1, e0) = e0 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10170) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10170) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10171) all_57_9 = e2 & op(e3, e0) = e2 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10171) implies: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10172) op(e3, e0) = e2 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (10159), (10172), (function-axioms) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #111. % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10173) all_57_10 = e2 & op(e2, e0) = e2 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10173) implies: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10174) all_57_10 = e2 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10175) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10175) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10176) all_57_6 = e2 & op(e1, e3) = e2 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10176) implies: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10177) op(e1, e3) = e2 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10178) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10178) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10179) all_57_0 = e1 & op(e3, e3) = e1 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10179) implies: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10180) op(e3, e3) = e1 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (169), (232), % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236), (238), (10130), (10131), (10135), (10159), % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10180), (function-axioms) are inconsistent by % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #18. % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10181) all_57_2 = e1 & op(e2, e3) = e1 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10181) implies: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10182) all_57_2 = e1 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10183) op(e2, e3) = e1 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10184) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10184) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10185) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (163), (167), (231), % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (9868), (9869), (9892), (10182), (10183), % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10185), (function-axioms) are inconsistent by % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #22. % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10186) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9893), (10138), (10186), (function-axioms) are % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #194. % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10187) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10187) gives: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10188) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (10169), (10177), (10188), % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #28. % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10189) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10189) gives: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10190) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10190) implies: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10191) op(e2, e2) = e0 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10055), (10191), (function-axioms) are % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #641. % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10192) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10192) gives: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10193) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10193) implies: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10194) op(e1, e1) = e2 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10152), (10194), (function-axioms) are % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109. % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10195) op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (169), (8984), (8991), (10131), (10135), % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10169), (10195), (function-axioms) are % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #17. % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10196) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (159), (163), (8979), (10177), (10196), % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #47. % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10197) all_57_7 = e2 & op(e1, e2) = e2 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10134), (10197), (function-axioms) are % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515. % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10198) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (208), (8990), (10152), % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10158), (10174), (10198), (function-axioms) are % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #26. % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10199) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10199) gives: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10200) all_57_11 = e2 & op(e1, e0) = e2 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10200) implies: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10201) all_57_11 = e2 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10168), (10201) are inconsistent by % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #638. % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10202) all_57_15 = e2 & op(e0, e0) = e2 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10202) implies: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10203) all_57_15 = e2 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (208), (209), (9892), % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10145), (10203) are inconsistent by sub-proof % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #434. % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (10204) all_57_14 = e3 & op(e0, e1) = e3 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (9889), (10204), (function-axioms) are % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #652. % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | (10205) all_57_15 = e2 & op(e0, e0) = e2 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10205) implies: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | (10206) op(e0, e0) = e2 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8991), (10206), (function-axioms) are % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636. % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | (10207) all_54_1 = e1 | all_54_1 = e0 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10048), (10057), (10065), (10207) are % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #192. % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | (10208) all_57_9 = e1 & op(e3, e0) = e1 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8982), (10208), (function-axioms) are % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #181. % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10209) all_57_13 = e1 & op(e0, e2) = e1 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8980), (10209), (function-axioms) are % 135.21/19.74 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #178. % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | (10210) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 135.21/19.74 | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 135.21/19.74 | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (9888), (10045), (10210), % 135.21/19.74 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.74 | | | | | | | | | | | | | | | #555. % 135.21/19.74 | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | (10211) ~ (all_14_1 = e0) & op(e3, e3) = all_14_1 & % 135.21/19.74 | | | | | | | | | | | | | | $i(all_14_1) % 135.21/19.74 | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | REF_CLOSE: (9873), (10211), (function-axioms) are % 135.21/19.74 | | | | | | | | | | | | | | inconsistent by sub-proof #191. % 135.21/19.74 | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | (10212) all_57_13 = e3 & op(e0, e2) = e3 % 135.21/19.74 | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | REF_CLOSE: (158), (9888), (10212), (function-axioms) are % 135.21/19.74 | | | | | | | | | | | inconsistent by sub-proof #556. % 135.21/19.74 | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | % 135.21/19.74 | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | (10213) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 135.21/19.74 | | | | | | | | | | e3 & op(e0, e0) = e3) % 135.21/19.74 | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | REF_CLOSE: (8), (157), (8991), (9889), (10213), % 135.21/19.74 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.74 | | | | | | | | | | #37. % 135.21/19.74 | | | | | | | | | | % 135.21/19.74 | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | % 135.21/19.74 | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | % 135.21/19.74 | | | | | | | | | (10214) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 135.21/19.74 | | | | | | | | | % 135.21/19.74 | | | | | | | | | REF_CLOSE: (9875), (9878), (9883), (9884), (10214) are % 135.21/19.74 | | | | | | | | | inconsistent by sub-proof #24. % 135.21/19.74 | | | | | | | | | % 135.21/19.74 | | | | | | | | End of split % 135.21/19.74 | | | | | | | | % 135.21/19.74 | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | % 135.21/19.74 | | | | | | | | (10215) ~ (all_10_1 = e1) & op(e0, e0) = all_10_1 & % 135.21/19.74 | | | | | | | | $i(all_10_1) % 135.21/19.74 | | | | | | | | % 135.21/19.74 | | | | | | | | REF_CLOSE: (8991), (10215), (function-axioms) are inconsistent % 135.21/19.74 | | | | | | | | by sub-proof #16. % 135.21/19.74 | | | | | | | | % 135.21/19.74 | | | | | | | End of split % 135.21/19.74 | | | | | | | % 135.21/19.74 | | | | | | End of split % 135.21/19.74 | | | | | | % 135.21/19.74 | | | | | Case 2: % 135.21/19.74 | | | | | | % 135.21/19.74 | | | | | | (10216) all_8_2 = e1 % 135.21/19.74 | | | | | | (10217) ( ~ (all_8_0 = e0) & op(e1, e2) = all_8_0 & $i(all_8_0)) % 135.21/19.74 | | | | | | | ( ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 & % 135.21/19.74 | | | | | | $i(all_8_1)) % 135.21/19.74 | | | | | | % 135.21/19.74 | | | | | | COMBINE_EQS: (291), (10216) imply: % 135.21/19.74 | | | | | | (10218) all_48_2 = e1 % 135.21/19.74 | | | | | | % 135.21/19.74 | | | | | | REDUCE: (347), (10216) imply: % 135.21/19.74 | | | | | | (10219) ~ (all_52_1 = e1) % 135.21/19.74 | | | | | | % 135.21/19.74 | | | | | | REDUCE: (350), (10216) imply: % 135.21/19.74 | | | | | | (10220) ~ (all_52_4 = e1) % 135.21/19.74 | | | | | | % 135.21/19.74 | | | | | | REDUCE: (352), (10216) imply: % 135.21/19.74 | | | | | | (10221) ~ (all_52_6 = e1) % 135.21/19.74 | | | | | | % 135.21/19.74 | | | | | | REDUCE: (356), (10216) imply: % 135.21/19.74 | | | | | | (10222) ~ (all_52_9 = e1) % 135.21/19.74 | | | | | | % 135.21/19.74 | | | | | | REDUCE: (42), (10216) imply: % 135.21/19.74 | | | | | | (10223) op(e2, e2) = e1 % 135.21/19.74 | | | | | | % 135.21/19.74 | | | | | | BETA: splitting (46) gives: % 135.21/19.74 | | | | | | % 135.21/19.74 | | | | | | Case 1: % 135.21/19.74 | | | | | | | % 135.21/19.74 | | | | | | | (10224) ~ (all_10_2 = e0) % 135.21/19.74 | | | | | | | % 135.21/19.74 | | | | | | | BETA: splitting (49) gives: % 135.21/19.74 | | | | | | | % 135.21/19.74 | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | % 135.21/19.74 | | | | | | | | (10225) ~ (all_12_2 = e1) % 135.21/19.74 | | | | | | | | % 135.21/19.74 | | | | | | | | REDUCE: (8978), (10225) imply: % 135.21/19.74 | | | | | | | | (10226) $false % 135.21/19.74 | | | | | | | | % 135.21/19.74 | | | | | | | | CLOSE: (10226) is inconsistent. % 135.21/19.74 | | | | | | | | % 135.21/19.74 | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | % 135.21/19.74 | | | | | | | | (10227) ( ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 & % 135.21/19.74 | | | | | | | | $i(all_12_0)) | ( ~ (all_12_1 = e3) & op(e1, e1) = % 135.21/19.74 | | | | | | | | all_12_1 & $i(all_12_1)) % 135.21/19.74 | | | | | | | | % 135.21/19.74 | | | | | | | | BETA: splitting (55) gives: % 135.21/19.74 | | | | | | | | % 135.21/19.74 | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | % 135.21/19.74 | | | | | | | | | (10228) ~ (all_16_2 = e2) % 135.21/19.74 | | | | | | | | | % 135.21/19.74 | | | | | | | | | REDUCE: (327), (10228) imply: % 135.21/19.74 | | | | | | | | | (10229) ~ (all_10_2 = e2) % 135.21/19.74 | | | | | | | | | % 135.21/19.74 | | | | | | | | | BETA: splitting (73) gives: % 135.21/19.74 | | | | | | | | | % 135.21/19.74 | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | (10230) ~ (all_28_2 = e3) % 135.21/19.74 | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | REDUCE: (316), (10230) imply: % 135.21/19.74 | | | | | | | | | | (10231) ~ (all_6_2 = e3) % 135.21/19.74 | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | BETA: splitting (79) gives: % 135.21/19.74 | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | (10232) ~ (all_32_2 = e1) % 135.21/19.74 | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | REDUCE: (312), (10232) imply: % 135.21/19.74 | | | | | | | | | | | (10233) ~ (all_10_2 = e1) % 135.21/19.74 | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | BETA: splitting (204) gives: % 135.21/19.74 | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | (10234) all_54_0 = e3 % 135.21/19.74 | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | COMBINE_EQS: (278), (10234) imply: % 135.21/19.74 | | | | | | | | | | | | (10235) all_10_2 = e3 % 135.21/19.74 | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | SIMP: (10235) implies: % 135.21/19.74 | | | | | | | | | | | | (10236) all_10_2 = e3 % 135.21/19.74 | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | REDUCE: (344), (10236) imply: % 135.21/19.74 | | | | | | | | | | | | (10237) ~ (all_52_8 = e3) % 135.21/19.74 | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | REDUCE: (346), (10236) imply: % 135.21/19.74 | | | | | | | | | | | | (10238) ~ (all_52_12 = e3) % 135.21/19.74 | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | REDUCE: (45), (10236) imply: % 135.21/19.74 | | | | | | | | | | | | (10239) op(e3, e3) = e3 % 135.21/19.74 | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | BETA: splitting (234) gives: % 135.21/19.74 | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | (10240) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 135.21/19.74 | | | | | | | | | | | | | & op(e3, e2) = e1) % 135.21/19.74 | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | BETA: splitting (10240) gives: % 135.21/19.74 | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | (10241) all_57_0 = e1 & op(e3, e3) = e1 % 135.21/19.74 | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | ALPHA: (10241) implies: % 135.21/19.74 | | | | | | | | | | | | | | (10242) op(e3, e3) = e1 % 135.21/19.74 | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | REF_CLOSE: (8), (10239), (10242), (function-axioms) are % 135.21/19.74 | | | | | | | | | | | | | | inconsistent by sub-proof #775. % 135.21/19.74 | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | (10243) all_57_1 = e1 & op(e3, e2) = e1 % 135.21/19.74 | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | REF_CLOSE: (170), (10220), (10243), (function-axioms) are % 135.21/19.74 | | | | | | | | | | | | | | inconsistent by sub-proof #684. % 135.21/19.74 | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | (10244) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 135.21/19.74 | | | | | | | | | | | | | & op(e3, e0) = e1) % 135.21/19.74 | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | BETA: splitting (10244) gives: % 135.21/19.74 | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | (10245) all_57_4 = e1 & op(e3, e1) = e1 % 135.21/19.74 | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | ALPHA: (10245) implies: % 135.21/19.74 | | | | | | | | | | | | | | (10246) op(e3, e1) = e1 % 135.21/19.74 | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | BETA: splitting (233) gives: % 135.21/19.74 | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | (10247) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 135.21/19.74 | | | | | | | | | | | | | | | & op(e2, e3) = e1) % 135.21/19.74 | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | BETA: splitting (10247) gives: % 135.21/19.74 | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | (10248) all_57_0 = e1 & op(e3, e3) = e1 % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | ALPHA: (10248) implies: % 135.21/19.74 | | | | | | | | | | | | | | | | (10249) op(e3, e3) = e1 % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10239), (10249), (function-axioms) are % 135.21/19.74 | | | | | | | | | | | | | | | | inconsistent by sub-proof #775. % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | (10250) all_57_2 = e1 & op(e2, e3) = e1 % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10219), (10250), (function-axioms) are % 135.21/19.74 | | | | | | | | | | | | | | | | inconsistent by sub-proof #676. % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | End of split % 135.21/19.74 | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | (10251) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 135.21/19.74 | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 135.21/19.74 | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | BETA: splitting (10251) gives: % 135.21/19.74 | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | (10252) all_57_6 = e1 & op(e1, e3) = e1 % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | ALPHA: (10252) implies: % 135.21/19.74 | | | | | | | | | | | | | | | | (10253) all_57_6 = e1 % 135.21/19.74 | | | | | | | | | | | | | | | | (10254) op(e1, e3) = e1 % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1, % 135.21/19.74 | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (10254) gives: % 135.21/19.74 | | | | | | | | | | | | | | | | (10255) all_52_2 = e1 % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1, % 135.21/19.74 | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (10246) gives: % 135.21/19.74 | | | | | | | | | | | | | | | | (10256) all_52_8 = e1 % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | REDUCE: (143), (10255) imply: % 135.21/19.74 | | | | | | | | | | | | | | | | (10257) ~ (all_52_6 = e1) % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | REDUCE: (141), (10255) imply: % 135.21/19.74 | | | | | | | | | | | | | | | | (10258) ~ (all_52_14 = e1) % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | REDUCE: (361), (10256) imply: % 135.21/19.74 | | | | | | | | | | | | | | | | (10259) ~ (all_6_2 = e1) % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | SIMP: (10259) implies: % 135.21/19.74 | | | | | | | | | | | | | | | | (10260) ~ (all_6_2 = e1) % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | REDUCE: (10237), (10256) imply: % 135.21/19.74 | | | | | | | | | | | | | | | | (10261) ~ (e3 = e1) % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 135.21/19.74 | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | (10262) all_54_10 = e3 % 135.21/19.74 | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (10231), (10262) are inconsistent by % 135.21/19.74 | | | | | | | | | | | | | | | | | sub-proof #742. % 135.21/19.74 | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | (10263) ~ (all_54_10 = e3) % 135.21/19.74 | | | | | | | | | | | | | | | | | (10264) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 135.21/19.74 | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | BETA: splitting (10264) gives: % 135.21/19.74 | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | (10265) all_54_10 = e2 % 135.21/19.74 | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (8992), (10265) are inconsistent by % 135.21/19.74 | | | | | | | | | | | | | | | | | | sub-proof #741. % 135.21/19.74 | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | (10266) ~ (all_54_10 = e2) % 135.21/19.74 | | | | | | | | | | | | | | | | | | (10267) all_54_10 = e1 | all_54_10 = e0 % 135.21/19.74 | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | BETA: splitting (10267) gives: % 135.21/19.74 | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10268) all_54_10 = e1 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (10260), (10268) are inconsistent by % 135.21/19.74 | | | | | | | | | | | | | | | | | | | sub-proof #736. % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10269) all_54_10 = e0 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (10269) imply: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10270) all_6_2 = e0 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | SIMP: (10270) implies: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10271) all_6_2 = e0 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | REDUCE: (359), (10271) imply: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10272) ~ (all_52_6 = e0) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | REDUCE: (364), (10271) imply: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10273) ~ (all_52_11 = e0) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | REDUCE: (10231), (10271) imply: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10274) ~ (e3 = e0) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | REDUCE: (8992), (10271) imply: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10275) ~ (e2 = e0) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | REDUCE: (10260), (10271) imply: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10276) ~ (e1 = e0) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | REDUCE: (39), (10271) imply: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | (10277) op(e1, e1) = e0 % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | (10278) ~ (all_48_2 = e1) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | REDUCE: (10218), (10278) imply: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | (10279) $false % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | CLOSE: (10279) is inconsistent. % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | (10280) ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | = all_48_1 & $i(all_48_1)) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | (10281) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10281) gives: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | (10282) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (10239), (10282), (function-axioms) are % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623. % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.74 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (10283) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (10223), (10238), (10283), % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | #190. % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (10284) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10284) gives: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (10285) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10285) gives: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10286) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10286) implies: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10287) op(e1, e1) = e3 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10277), (10287), (function-axioms) are % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753. % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10288) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10288) implies: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10289) ~ (all_56_29 = e0) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10290) ~ (all_56_13 = e2) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10291) op(e1, e0) = all_56_29 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10292) op(e1, e1) = all_56_21 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10293) op(e1, e2) = all_56_13 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (10294) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10294) gives: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10295) all_57_6 = e0 & op(e1, e3) = e0 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10295) implies: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10296) all_57_6 = e0 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10253), (10296) imply: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10297) e1 = e0 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (10297) imply: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10298) $false % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10298) is inconsistent. % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10299) all_57_7 = e0 & op(e1, e2) = e0 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10272), (10299), (function-axioms) are % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #505. % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (10300) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10300) gives: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10301) all_57_8 = e0 & op(e1, e1) = e0 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21, e1, e1, simplifying with (10277), % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10292) gives: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10302) all_56_21 = e0 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e2, e1, simplifying with (162), (10293) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10303) all_56_13 = all_52_6 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10290), (10303) imply: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10304) ~ (all_52_6 = e2) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10280) gives: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (10305) ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_0) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10305) implies: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (10306) ~ (all_48_0 = e3) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (10307) op(e1, e2) = all_48_0 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10308) all_54_9 = e3 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (10308) imply: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10309) all_52_6 = e3 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10309) implies: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10310) all_52_6 = e3 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (10310) imply: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10311) op(e1, e2) = e3 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10306), (10307), (10311), (function-axioms) are % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #188. % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10312) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10312) gives: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10313) all_54_9 = e2 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (10304), (10313) are inconsistent by % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #582. % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10314) all_54_9 = e1 | all_54_9 = e0 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (10221), (10272), (10314) are inconsistent % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #168. % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (10315) ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_1) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10277), (10315), (function-axioms) are % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #187. % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10316) all_57_11 = e0 & op(e1, e0) = e0 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10316) implies: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (10317) op(e1, e0) = e0 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10289), (10291), (10317), (function-axioms) are % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #45. % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (10318) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10318) gives: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10319) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10319) implies: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10320) op(e2, e2) = e0 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10223), (10320), (function-axioms) are % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (10321) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10321) gives: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (10322) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10322) implies: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (10323) op(e1, e1) = e2 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10277), (10323), (function-axioms) are % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #98. % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (10324) op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (160), (8984), (8991), (10246), % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | (10273), (10324), (function-axioms) are % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #15. % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | (10325) all_57_12 = e1 & op(e0, e3) = e1 % 135.21/19.75 | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8979), (10325), (function-axioms) are % 135.21/19.75 | | | | | | | | | | | | | | | | inconsistent by sub-proof #48. % 135.21/19.75 | | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | (10326) all_57_9 = e1 & op(e3, e0) = e1 % 135.21/19.75 | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | REF_CLOSE: (168), (8982), (10326), (function-axioms) are % 135.21/19.75 | | | | | | | | | | | | | | inconsistent by sub-proof #181. % 135.21/19.75 | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | (10327) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 135.21/19.75 | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | REF_CLOSE: (278), (10224), (10229), (10233), (10327) are % 135.21/19.75 | | | | | | | | | | | | inconsistent by sub-proof #777. % 135.21/19.75 | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | (10328) all_32_2 = e1 % 135.21/19.75 | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | COMBINE_EQS: (312), (10328) imply: % 135.21/19.75 | | | | | | | | | | | (10329) all_10_2 = e1 % 135.21/19.75 | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | SIMP: (10329) implies: % 135.21/19.75 | | | | | | | | | | | (10330) all_10_2 = e1 % 135.21/19.75 | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | REDUCE: (338), (10330) imply: % 135.21/19.75 | | | | | | | | | | | (10331) ~ (all_52_2 = e1) % 135.21/19.75 | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | REDUCE: (45), (10330) imply: % 135.21/19.75 | | | | | | | | | | | (10332) op(e3, e3) = e1 % 135.21/19.75 | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | BETA: splitting (216) gives: % 135.21/19.75 | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | Case 1: % 135.21/19.75 | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | (10333) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 135.21/19.75 | | | | | | | | | | | | & op(e1, e2) = e1) % 135.21/19.75 | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | BETA: splitting (10333) gives: % 135.21/19.75 | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | Case 1: % 135.21/19.75 | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | (10334) all_57_6 = e1 & op(e1, e3) = e1 % 135.21/19.75 | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | ALPHA: (10334) implies: % 135.21/19.75 | | | | | | | | | | | | | (10335) op(e1, e3) = e1 % 135.21/19.75 | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | REF_CLOSE: (163), (10331), (10335), (function-axioms) are % 135.21/19.75 | | | | | | | | | | | | | inconsistent by sub-proof #725. % 135.21/19.75 | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | (10336) all_57_7 = e1 & op(e1, e2) = e1 % 135.21/19.75 | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | ALPHA: (10336) implies: % 135.21/19.75 | | | | | | | | | | | | | (10337) op(e1, e2) = e1 % 135.21/19.75 | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | REF_CLOSE: (162), (10221), (10337), (function-axioms) are % 135.21/19.75 | | | | | | | | | | | | | inconsistent by sub-proof #65. % 135.21/19.75 | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | (10338) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 135.21/19.75 | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 135.21/19.75 | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | BETA: splitting (10338) gives: % 135.21/19.75 | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | Case 1: % 135.21/19.75 | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | (10339) all_57_8 = e1 & op(e1, e1) = e1 % 135.21/19.75 | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | ALPHA: (10339) implies: % 135.21/19.75 | | | | | | | | | | | | | (10340) op(e1, e1) = e1 % 135.21/19.75 | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e1, % 135.21/19.75 | | | | | | | | | | | | | e1, e1, simplifying with (39), (10340) gives: % 135.21/19.75 | | | | | | | | | | | | | (10341) all_6_2 = e1 % 135.21/19.75 | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | REDUCE: (10231), (10341) imply: % 135.21/19.75 | | | | | | | | | | | | | (10342) ~ (e3 = e1) % 135.21/19.75 | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | REDUCE: (8992), (10341) imply: % 135.21/19.75 | | | | | | | | | | | | | (10343) ~ (e2 = e1) % 135.21/19.75 | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | BETA: splitting (206) gives: % 135.21/19.75 | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | Case 1: % 135.21/19.75 | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | (10344) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.21/19.75 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.75 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.21/19.75 | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.21/19.75 | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.75 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.21/19.75 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.75 | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.75 | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.75 | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.21/19.75 | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.21/19.75 | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.75 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.21/19.75 | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.21/19.75 | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.21/19.75 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.75 | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.21/19.75 | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.75 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.75 | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.75 | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.75 | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.21/19.75 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.75 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.75 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.75 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.21/19.75 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.75 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.21/19.75 | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | BETA: splitting (10344) gives: % 135.21/19.75 | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | Case 1: % 135.21/19.75 | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | (10345) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.21/19.75 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.75 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.21/19.75 | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.21/19.75 | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.75 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.21/19.75 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.75 | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.75 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.75 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.21/19.75 | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.21/19.75 | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.75 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.21/19.75 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.21/19.75 | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | REF_CLOSE: (6), (10332), (10340), (10345), (function-axioms) % 135.21/19.75 | | | | | | | | | | | | | | | are inconsistent by sub-proof #509. % 135.21/19.75 | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | (10346) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.21/19.75 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.75 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.21/19.75 | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.75 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.75 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.75 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.75 | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.21/19.75 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.75 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.75 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.75 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.21/19.75 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.75 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.21/19.75 | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (10223), (10332), (10346), % 135.21/19.75 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.75 | | | | | | | | | | | | | | | #175. % 135.21/19.75 | | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | | End of split % 135.21/19.75 | | | | | | | | | | | | | | % 135.21/19.75 | | | | | | | | | | | | | Case 2: % 135.21/19.75 | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | (10347) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.76 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.76 | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.76 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.76 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.21/19.76 | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.76 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.21/19.76 | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.21/19.76 | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.21/19.76 | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.21/19.76 | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.76 | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.21/19.76 | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.76 | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 135.21/19.76 | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.21/19.76 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.76 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 135.21/19.76 | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.76 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 135.21/19.76 | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.76 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 135.21/19.76 | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.21/19.76 | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.76 | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.76 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.21/19.76 | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 135.21/19.76 | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.76 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.21/19.76 | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.21/19.76 | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.21/19.76 | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.21/19.76 | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.76 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 135.21/19.76 | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.21/19.76 | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.76 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 135.21/19.76 | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 135.21/19.76 | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.21/19.76 | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.76 | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.76 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.21/19.76 | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.76 | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 135.21/19.76 | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 135.21/19.76 | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.21/19.76 | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.21/19.76 | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.21/19.76 | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 135.21/19.76 | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.76 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.76 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.76 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.76 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.76 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.76 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.76 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.76 | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.76 | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | BETA: splitting (10347) gives: % 135.21/19.76 | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | (10348) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.76 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.76 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.76 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.76 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.21/19.76 | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.21/19.76 | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.21/19.76 | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.76 | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.21/19.76 | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.21/19.76 | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | BETA: splitting (10348) gives: % 135.21/19.76 | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | (10349) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.76 | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 135.21/19.76 | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.76 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.76 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 135.21/19.76 | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | ALPHA: (10349) implies: % 135.21/19.76 | | | | | | | | | | | | | | | | (10350) op(e1, e1) = e3 % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (10340), (10350), (function-axioms) are % 135.21/19.76 | | | | | | | | | | | | | | | | inconsistent by sub-proof #662. % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | Case 2: % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | (10351) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 135.21/19.76 | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 135.21/19.76 | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 135.21/19.76 | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.76 | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.21/19.76 | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | ALPHA: (10351) implies: % 135.21/19.76 | | | | | | | | | | | | | | | | (10352) ~ (all_56_21 = e1) % 135.21/19.76 | | | | | | | | | | | | | | | | (10353) op(e1, e1) = all_56_21 % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | REF_CLOSE: (10340), (10352), (10353), (function-axioms) are % 135.21/19.76 | | | | | | | | | | | | | | | | inconsistent by sub-proof #510. % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | End of split % 135.21/19.76 | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | Case 2: % 135.21/19.76 | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | (10354) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.21/19.76 | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.76 | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 135.21/19.76 | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.76 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.76 | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.76 | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.76 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.76 | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.21/19.76 | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.76 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.21/19.76 | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.76 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.76 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.21/19.76 | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.21/19.76 | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.76 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.21/19.76 | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.21/19.76 | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.21/19.76 | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.21/19.76 | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.21/19.76 | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.21/19.76 | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.76 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.21/19.76 | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.21/19.76 | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.76 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.76 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.76 | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.76 | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.76 | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.76 | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.76 | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.76 | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.76 | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.76 | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | BETA: splitting (10354) gives: % 135.21/19.76 | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | (10355) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.21/19.76 | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.21/19.76 | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 135.21/19.76 | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.76 | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.21/19.76 | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | ALPHA: (10355) implies: % 135.21/19.76 | | | | | | | | | | | | | | | | (10356) op(e2, e2) = e0 % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10223), (10356), (function-axioms) are % 135.21/19.76 | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | Case 2: % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | (10357) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.76 | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.76 | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.21/19.76 | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.76 | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.21/19.76 | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.76 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.76 | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.21/19.76 | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.21/19.76 | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.76 | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.21/19.76 | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.21/19.76 | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.21/19.76 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.21/19.76 | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.21/19.76 | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.21/19.76 | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.76 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.21/19.76 | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.21/19.76 | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.76 | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.76 | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.76 | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.76 | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.76 | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.76 | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.76 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.76 | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.76 | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | BETA: splitting (10357) gives: % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | (10358) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.76 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 135.21/19.76 | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.76 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.76 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.21/19.76 | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.21/19.76 | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | ALPHA: (10358) implies: % 135.21/19.76 | | | | | | | | | | | | | | | | | (10359) op(e1, e1) = e2 % 135.21/19.76 | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (10359), (function-axioms) are % 135.21/19.76 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 135.21/19.76 | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | Case 2: % 135.21/19.76 | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | (10360) op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.76 | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.21/19.76 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.21/19.76 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.76 | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 135.21/19.76 | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.21/19.76 | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 135.21/19.76 | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.76 | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.76 | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.21/19.76 | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.21/19.76 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.76 | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.76 | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.21/19.76 | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.21/19.76 | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 135.21/19.76 | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.21/19.76 | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_29))) % 135.21/19.76 | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | ALPHA: (10360) implies: % 135.21/19.76 | | | | | | | | | | | | | | | | | (10361) op(e0, e0) = all_56_31 % 135.21/19.76 | | | | | | | | | | | | | | | | | (10362) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.21/19.76 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.76 | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.76 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.76 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.21/19.76 | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 135.21/19.76 | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.21/19.76 | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.21/19.76 | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 135.21/19.76 | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 135.21/19.76 | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.21/19.76 | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 135.21/19.76 | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.76 | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.21/19.76 | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.21/19.76 | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.76 | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.21/19.76 | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.21/19.76 | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 135.21/19.76 | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.76 | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.21/19.76 | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 135.21/19.76 | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (8991), % 135.21/19.76 | | | | | | | | | | | | | | | | | (10361) gives: % 135.21/19.76 | | | | | | | | | | | | | | | | | (10363) all_56_31 = e1 % 135.21/19.76 | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | BETA: splitting (10362) gives: % 135.21/19.76 | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | (10364) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.76 | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 135.21/19.76 | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 135.21/19.76 | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 135.21/19.76 | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (10363), (10364) are inconsistent by % 135.21/19.76 | | | | | | | | | | | | | | | | | | sub-proof #32. % 135.21/19.76 | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.76 | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | (10365) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.76 | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.21/19.76 | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.21/19.76 | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.21/19.76 | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 135.21/19.76 | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.21/19.76 | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (8984), (10340), (10365), (function-axioms) % 135.21/19.76 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #182. % 135.21/19.76 | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | End of split % 135.21/19.76 | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | End of split % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | End of split % 135.21/19.76 | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | End of split % 135.21/19.76 | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | End of split % 135.21/19.76 | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | Case 2: % 135.21/19.76 | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | (10366) all_57_11 = e1 & op(e1, e0) = e1 % 135.21/19.76 | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | ALPHA: (10366) implies: % 135.21/19.76 | | | | | | | | | | | | | (10367) op(e1, e0) = e1 % 135.21/19.76 | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | REF_CLOSE: (160), (8984), (10367), (function-axioms) are % 135.21/19.76 | | | | | | | | | | | | | inconsistent by sub-proof #327. % 135.21/19.76 | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | End of split % 135.21/19.76 | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | End of split % 135.21/19.76 | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | End of split % 135.21/19.76 | | | | | | | | | | % 135.21/19.76 | | | | | | | | | Case 2: % 135.21/19.76 | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | (10368) all_28_2 = e3 % 135.21/19.76 | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | COMBINE_EQS: (316), (10368) imply: % 135.21/19.76 | | | | | | | | | | (10369) all_6_2 = e3 % 135.21/19.76 | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | REDUCE: (348), (10369) imply: % 135.21/19.76 | | | | | | | | | | (10370) ~ (all_52_2 = e3) % 135.21/19.76 | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | REDUCE: (359), (10369) imply: % 135.21/19.76 | | | | | | | | | | (10371) ~ (all_52_6 = e3) % 135.21/19.76 | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | REDUCE: (361), (10369) imply: % 135.21/19.76 | | | | | | | | | | (10372) ~ (all_52_8 = e3) % 135.21/19.76 | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | REDUCE: (366), (10369) imply: % 135.21/19.76 | | | | | | | | | | (10373) ~ (all_52_14 = e3) % 135.21/19.76 | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | REDUCE: (39), (10369) imply: % 135.21/19.76 | | | | | | | | | | (10374) op(e1, e1) = e3 % 135.21/19.76 | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | BETA: splitting (10227) gives: % 135.21/19.76 | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | (10375) ~ (all_12_0 = e2) & op(e1, e0) = all_12_0 & % 135.21/19.76 | | | | | | | | | | | $i(all_12_0) % 135.21/19.76 | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | ALPHA: (10375) implies: % 135.21/19.76 | | | | | | | | | | | (10376) op(e1, e0) = all_12_0 % 135.21/19.76 | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | BETA: splitting (10217) gives: % 135.21/19.76 | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | (10377) ~ (all_8_0 = e0) & op(e1, e2) = all_8_0 & % 135.21/19.76 | | | | | | | | | | | | $i(all_8_0) % 135.21/19.76 | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | ALPHA: (10377) implies: % 135.21/19.76 | | | | | | | | | | | | (10378) ~ (all_8_0 = e0) % 135.21/19.76 | | | | | | | | | | | | (10379) op(e1, e2) = all_8_0 % 135.21/19.76 | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | BETA: splitting (220) gives: % 135.21/19.76 | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | (10380) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 135.21/19.76 | | | | | | | | | | | | | & op(e2, e1) = e1) % 135.21/19.76 | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | BETA: splitting (10380) gives: % 135.21/19.76 | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | (10381) all_57_4 = e1 & op(e3, e1) = e1 % 135.21/19.76 | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | ALPHA: (10381) implies: % 135.21/19.76 | | | | | | | | | | | | | | (10382) all_57_4 = e1 % 135.21/19.76 | | | | | | | | | | | | | | (10383) op(e3, e1) = e1 % 135.21/19.76 | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | BETA: splitting (218) gives: % 135.21/19.76 | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | (10384) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 135.21/19.76 | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 135.21/19.76 | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | REF_CLOSE: (162), (163), (10370), (10371), (10384), % 135.21/19.76 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.76 | | | | | | | | | | | | | | | #323. % 135.21/19.76 | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | Case 2: % 135.21/19.76 | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | (10385) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 135.21/19.76 | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 135.21/19.76 | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | BETA: splitting (10385) gives: % 135.21/19.76 | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | (10386) all_57_8 = e3 & op(e1, e1) = e3 % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 135.21/19.76 | | | | | | | | | | | | | | | | all_12_0, e0, e1, simplifying with (160), (10376) % 135.21/19.76 | | | | | | | | | | | | | | | | gives: % 135.21/19.76 | | | | | | | | | | | | | | | | (10387) all_52_14 = all_12_0 % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, % 135.21/19.76 | | | | | | | | | | | | | | | | all_8_0, e2, e1, simplifying with (162), (10379) % 135.21/19.76 | | | | | | | | | | | | | | | | gives: % 135.21/19.76 | | | | | | | | | | | | | | | | (10388) all_52_6 = all_8_0 % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1, % 135.21/19.76 | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (10383) gives: % 135.21/19.76 | | | | | | | | | | | | | | | | (10389) all_52_8 = e1 % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (10387) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | (10390) all_54_11 = all_12_0 % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (10388) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | (10391) all_54_9 = all_8_0 % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | REDUCE: (136), (10388) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | (10392) ~ (all_52_4 = all_8_0) % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | REDUCE: (126), (10387), (10388) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | (10393) ~ (all_12_0 = all_8_0) % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | SIMP: (10393) implies: % 135.21/19.76 | | | | | | | | | | | | | | | | (10394) ~ (all_12_0 = all_8_0) % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | REDUCE: (10371), (10388) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | (10395) ~ (all_8_0 = e3) % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | REDUCE: (10221), (10388) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | (10396) ~ (all_8_0 = e1) % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | REDUCE: (344), (10389) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | (10397) ~ (all_10_2 = e1) % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | SIMP: (10397) implies: % 135.21/19.76 | | | | | | | | | | | | | | | | (10398) ~ (all_10_2 = e1) % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | REDUCE: (10373), (10387) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | (10399) ~ (all_12_0 = e3) % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | REDUCE: (8984), (10387) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | (10400) ~ (all_12_0 = e1) % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 135.21/19.76 | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | (10401) all_54_11 = e3 % 135.21/19.76 | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | REF_CLOSE: (10390), (10399), (10401) are inconsistent by % 135.21/19.76 | | | | | | | | | | | | | | | | | sub-proof #52. % 135.21/19.76 | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | Case 2: % 135.21/19.76 | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | (10402) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 135.21/19.76 | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 135.21/19.76 | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | (10403) all_54_0 = e3 % 135.21/19.76 | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (10403) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | | | (10404) all_10_2 = e3 % 135.21/19.76 | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | SIMP: (10404) implies: % 135.21/19.76 | | | | | | | | | | | | | | | | | | (10405) all_10_2 = e3 % 135.21/19.76 | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | REDUCE: (346), (10405) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | | | (10406) ~ (all_52_12 = e3) % 135.21/19.76 | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | REDUCE: (45), (10405) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | | | (10407) op(e3, e3) = e3 % 135.21/19.76 | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 135.21/19.76 | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | (10408) all_54_9 = e3 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10391), (10408) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | (10409) all_8_0 = e3 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | SIMP: (10409) implies: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | (10410) all_8_0 = e3 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | REDUCE: (10395), (10410) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | (10411) $false % 135.21/19.76 | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | CLOSE: (10411) is inconsistent. % 135.21/19.76 | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | (10412) ~ (all_54_9 = e3) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | (10413) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | BETA: splitting (10413) gives: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | (10414) all_54_9 = e2 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10391), (10414) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | (10415) all_8_0 = e2 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | REDUCE: (10392), (10415) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | (10416) ~ (all_52_4 = e2) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | REDUCE: (10394), (10415) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | (10417) ~ (all_12_0 = e2) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | REDUCE: (10395), (10415) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | (10418) ~ (e3 = e2) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | REDUCE: (10379), (10415) imply: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | (10419) op(e1, e2) = e2 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (10420) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10420) gives: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | (10421) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10421) gives: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | (10422) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10422) implies: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | (10423) op(e3, e3) = e2 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10407), (10423), (function-axioms) are % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #778. % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | (10424) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10424) implies: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | (10425) op(e3, e3) = e1 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (170), (232), % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | (236), (238), (10372), (10382), (10416), (10425), % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | #162. % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | (10426) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (10223), (10406), (10426), % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | #190. % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (10427) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10427) gives: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | (10428) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10383), (10419), (10428), (function-axioms) are % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #132. % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.76 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (10429) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10429) gives: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | (10430) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10430) implies: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | (10431) op(e2, e2) = e0 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10223), (10431), (function-axioms) are % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | (10432) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10432) gives: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (10433) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10433) implies: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (10434) op(e1, e1) = e2 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10374), (10434), (function-axioms) are % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109. % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (10435) op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10435) implies: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (10436) op(e0, e0) = all_56_31 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (10437) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10402) gives: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | (10438) all_54_11 = e2 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10390), (10417), (10438) are inconsistent by % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #51. % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | (10439) all_54_11 = e1 | all_54_11 = e0 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10439) gives: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (10440) all_54_11 = e1 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10390), (10400), (10440) are inconsistent by % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #50. % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (10441) all_54_11 = e0 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10390), (10441) imply: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (10442) all_12_0 = e0 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10442) implies: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (10443) all_12_0 = e0 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10376), (10443) imply: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (10444) op(e1, e0) = e0 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (8984), (8991), (10383), (10436), % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (10437), (10444), (function-axioms) are % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #20. % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (10445) all_54_9 = e1 | all_54_9 = e0 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10378), (10391), (10396), (10445) are % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #155. % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | (10446) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 135.21/19.77 | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (10224), (10229), (10398), (10446) are % 135.21/19.77 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #777. % 135.21/19.77 | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | (10447) all_57_11 = e3 & op(e1, e0) = e3 % 135.21/19.77 | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10373), (10447), (function-axioms) are % 135.21/19.77 | | | | | | | | | | | | | | | | inconsistent by sub-proof #750. % 135.21/19.77 | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | (10448) all_57_5 = e1 & op(e2, e1) = e1 % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | REF_CLOSE: (165), (10222), (10448), (function-axioms) are % 135.21/19.77 | | | | | | | | | | | | | | inconsistent by sub-proof #161. % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | (10449) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 135.21/19.77 | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 135.21/19.77 | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | BETA: splitting (10449) gives: % 135.21/19.77 | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | (10450) all_57_8 = e1 & op(e1, e1) = e1 % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | ALPHA: (10450) implies: % 135.21/19.77 | | | | | | | | | | | | | | (10451) op(e1, e1) = e1 % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (10374), (10451), (function-axioms) are % 135.21/19.77 | | | | | | | | | | | | | | inconsistent by sub-proof #662. % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | (10452) all_57_14 = e1 & op(e0, e1) = e1 % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | ALPHA: (10452) implies: % 135.21/19.77 | | | | | | | | | | | | | | (10453) op(e0, e1) = e1 % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11, % 135.21/19.77 | | | | | | | | | | | | | | e1, e1, e0, simplifying with (157), (10453) gives: % 135.21/19.77 | | | | | | | | | | | | | | (10454) all_52_11 = e1 % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | REDUCE: (8981), (10454) imply: % 135.21/19.77 | | | | | | | | | | | | | | (10455) $false % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | CLOSE: (10455) is inconsistent. % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | (10456) ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 & % 135.21/19.77 | | | | | | | | | | | | $i(all_8_1) % 135.21/19.77 | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | REF_CLOSE: (10374), (10456), (function-axioms) are % 135.21/19.77 | | | | | | | | | | | | inconsistent by sub-proof #128. % 135.21/19.77 | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | (10457) ~ (all_12_1 = e3) & op(e1, e1) = all_12_1 & % 135.21/19.77 | | | | | | | | | | | $i(all_12_1) % 135.21/19.77 | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | ALPHA: (10457) implies: % 135.21/19.77 | | | | | | | | | | | (10458) ~ (all_12_1 = e3) % 135.21/19.77 | | | | | | | | | | | (10459) op(e1, e1) = all_12_1 % 135.21/19.77 | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | REF_CLOSE: (10374), (10458), (10459), (function-axioms) are % 135.21/19.77 | | | | | | | | | | | inconsistent by sub-proof #36. % 135.21/19.77 | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | % 135.21/19.77 | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | % 135.21/19.77 | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | % 135.21/19.77 | | | | | | | | | (10460) all_16_2 = e2 % 135.21/19.77 | | | | | | | | | % 135.21/19.77 | | | | | | | | | COMBINE_EQS: (327), (10460) imply: % 135.21/19.77 | | | | | | | | | (10461) all_10_2 = e2 % 135.21/19.77 | | | | | | | | | % 135.21/19.77 | | | | | | | | | COMBINE_EQS: (299), (10461) imply: % 135.21/19.77 | | | | | | | | | (10462) all_38_2 = e2 % 135.21/19.77 | | | | | | | | | % 135.21/19.77 | | | | | | | | | REDUCE: (336), (10461) imply: % 135.21/19.77 | | | | | | | | | (10463) ~ (all_52_1 = e2) % 135.21/19.77 | | | | | | | | | % 135.21/19.77 | | | | | | | | | REDUCE: (340), (10461) imply: % 135.21/19.77 | | | | | | | | | (10464) ~ (all_52_3 = e2) % 135.21/19.77 | | | | | | | | | % 135.21/19.77 | | | | | | | | | REDUCE: (344), (10461) imply: % 135.21/19.77 | | | | | | | | | (10465) ~ (all_52_8 = e2) % 135.21/19.77 | | | | | | | | | % 135.21/19.77 | | | | | | | | | REDUCE: (346), (10461) imply: % 135.21/19.77 | | | | | | | | | (10466) ~ (all_52_12 = e2) % 135.21/19.77 | | | | | | | | | % 135.21/19.77 | | | | | | | | | REDUCE: (45), (10461) imply: % 135.21/19.77 | | | | | | | | | (10467) op(e3, e3) = e2 % 135.21/19.77 | | | | | | | | | % 135.21/19.77 | | | | | | | | | BETA: splitting (234) gives: % 135.21/19.77 | | | | | | | | | % 135.21/19.77 | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | (10468) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 % 135.21/19.77 | | | | | | | | | | & op(e3, e2) = e1) % 135.21/19.77 | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | REF_CLOSE: (6), (170), (10220), (10467), (10468), % 135.21/19.77 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.77 | | | | | | | | | | #378. % 135.21/19.77 | | | | | | | | | | % 135.21/19.77 | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | (10469) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 % 135.21/19.77 | | | | | | | | | | & op(e3, e0) = e1) % 135.21/19.77 | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | BETA: splitting (10469) gives: % 135.21/19.77 | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | (10470) all_57_4 = e1 & op(e3, e1) = e1 % 135.21/19.77 | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | ALPHA: (10470) implies: % 135.21/19.77 | | | | | | | | | | | (10471) all_57_4 = e1 % 135.21/19.77 | | | | | | | | | | | (10472) op(e3, e1) = e1 % 135.21/19.77 | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | BETA: splitting (88) gives: % 135.21/19.77 | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | (10473) ~ (all_38_2 = e2) % 135.21/19.77 | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | REDUCE: (10462), (10473) imply: % 135.21/19.77 | | | | | | | | | | | | (10474) $false % 135.21/19.77 | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | CLOSE: (10474) is inconsistent. % 135.21/19.77 | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | (10475) ( ~ (all_38_0 = e0) & op(e2, e3) = all_38_0 & % 135.21/19.77 | | | | | | | | | | | | $i(all_38_0)) | ( ~ (all_38_1 = e1) & op(e2, e2) % 135.21/19.77 | | | | | | | | | | | | = all_38_1 & $i(all_38_1)) % 135.21/19.77 | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | BETA: splitting (233) gives: % 135.21/19.77 | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | (10476) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 135.21/19.77 | | | | | | | | | | | | | & op(e2, e3) = e1) % 135.21/19.77 | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | BETA: splitting (10476) gives: % 135.21/19.77 | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | (10477) all_57_0 = e1 & op(e3, e3) = e1 % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | ALPHA: (10477) implies: % 135.21/19.77 | | | | | | | | | | | | | | (10478) op(e3, e3) = e1 % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (169), (232), % 135.21/19.77 | | | | | | | | | | | | | | (236), (238), (10465), (10471), (10472), (10478), % 135.21/19.77 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.77 | | | | | | | | | | | | | | #14. % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | (10479) all_57_2 = e1 & op(e2, e3) = e1 % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | REF_CLOSE: (167), (10219), (10479), (function-axioms) are % 135.21/19.77 | | | | | | | | | | | | | | inconsistent by sub-proof #676. % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | (10480) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 135.21/19.77 | | | | | | | | | | | | | e1 & op(e0, e3) = e1) % 135.21/19.77 | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | BETA: splitting (10480) gives: % 135.21/19.77 | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | (10481) all_57_6 = e1 & op(e1, e3) = e1 % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | ALPHA: (10481) implies: % 135.21/19.77 | | | | | | | | | | | | | | (10482) op(e1, e3) = e1 % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | BETA: splitting (10475) gives: % 135.21/19.77 | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | (10483) ~ (all_38_0 = e0) & op(e2, e3) = all_38_0 & % 135.21/19.77 | | | | | | | | | | | | | | | $i(all_38_0) % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | ALPHA: (10483) implies: % 135.21/19.77 | | | | | | | | | | | | | | | (10484) ~ (all_38_0 = e0) % 135.21/19.77 | | | | | | | | | | | | | | | (10485) op(e2, e3) = all_38_0 % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1, % 135.21/19.77 | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (10482) gives: % 135.21/19.77 | | | | | | | | | | | | | | | (10486) all_52_2 = e1 % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, % 135.21/19.77 | | | | | | | | | | | | | | | all_38_0, e3, e2, simplifying with (167), (10485) % 135.21/19.77 | | | | | | | | | | | | | | | gives: % 135.21/19.77 | | | | | | | | | | | | | | | (10487) all_52_1 = all_38_0 % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1, % 135.21/19.77 | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (10472) gives: % 135.21/19.77 | | | | | | | | | | | | | | | (10488) all_52_8 = e1 % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | COMBINE_EQS: (268), (10487) imply: % 135.21/19.77 | | | | | | | | | | | | | | | (10489) all_54_4 = all_38_0 % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (148), (10487) imply: % 135.21/19.77 | | | | | | | | | | | | | | | (10490) ~ (all_52_3 = all_38_0) % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | SIMP: (10490) implies: % 135.21/19.77 | | | | | | | | | | | | | | | (10491) ~ (all_52_3 = all_38_0) % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (145), (10487) imply: % 135.21/19.77 | | | | | | | | | | | | | | | (10492) ~ (all_52_13 = all_38_0) % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | SIMP: (10492) implies: % 135.21/19.77 | | | | | | | | | | | | | | | (10493) ~ (all_52_13 = all_38_0) % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (10463), (10487) imply: % 135.21/19.77 | | | | | | | | | | | | | | | (10494) ~ (all_38_0 = e2) % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (10219), (10487) imply: % 135.21/19.77 | | | | | | | | | | | | | | | (10495) ~ (all_38_0 = e1) % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (144), (10486) imply: % 135.21/19.77 | | | | | | | | | | | | | | | (10496) ~ (all_52_3 = e1) % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (141), (10486) imply: % 135.21/19.77 | | | | | | | | | | | | | | | (10497) ~ (all_52_14 = e1) % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (121), (10488) imply: % 135.21/19.77 | | | | | | | | | | | | | | | (10498) ~ (all_52_11 = e1) % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (120), (10488) imply: % 135.21/19.77 | | | | | | | | | | | | | | | (10499) ~ (all_52_12 = e1) % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | REDUCE: (10465), (10488) imply: % 135.21/19.77 | | | | | | | | | | | | | | | (10500) ~ (e2 = e1) % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 135.21/19.77 | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | (10501) all_54_4 = e3 % 135.21/19.77 | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | COMBINE_EQS: (10489), (10501) imply: % 135.21/19.77 | | | | | | | | | | | | | | | | (10502) all_38_0 = e3 % 135.21/19.77 | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | SIMP: (10502) implies: % 135.21/19.77 | | | | | | | | | | | | | | | | (10503) all_38_0 = e3 % 135.21/19.77 | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | REDUCE: (10491), (10503) imply: % 135.21/19.77 | | | | | | | | | | | | | | | | (10504) ~ (all_52_3 = e3) % 135.21/19.77 | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | REDUCE: (10493), (10503) imply: % 135.21/19.77 | | | | | | | | | | | | | | | | (10505) ~ (all_52_13 = e3) % 135.21/19.77 | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | REDUCE: (10485), (10503) imply: % 135.21/19.77 | | | | | | | | | | | | | | | | (10506) op(e2, e3) = e3 % 135.21/19.77 | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | BETA: splitting (192) gives: % 135.21/19.77 | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | (10507) all_54_12 = e3 % 135.21/19.77 | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (10504), (10507) are inconsistent by % 135.21/19.77 | | | | | | | | | | | | | | | | | sub-proof #424. % 135.21/19.77 | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | (10508) ~ (all_54_12 = e3) % 135.21/19.77 | | | | | | | | | | | | | | | | | (10509) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 135.21/19.77 | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | BETA: splitting (10509) gives: % 135.21/19.77 | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | (10510) all_54_12 = e2 % 135.21/19.77 | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (10464), (10510) are inconsistent by % 135.21/19.77 | | | | | | | | | | | | | | | | | | sub-proof #423. % 135.21/19.77 | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | (10511) ~ (all_54_12 = e2) % 135.21/19.77 | | | | | | | | | | | | | | | | | | (10512) all_54_12 = e1 | all_54_12 = e0 % 135.21/19.77 | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | BETA: splitting (10512) gives: % 135.21/19.77 | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10513) all_54_12 = e1 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (8979), (10513) are inconsistent by % 135.21/19.77 | | | | | | | | | | | | | | | | | | | sub-proof #99. % 135.21/19.77 | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10514) all_54_12 = e0 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (10514) imply: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10515) all_52_3 = e0 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | SIMP: (10515) implies: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10516) all_52_3 = e0 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | REDUCE: (139), (10516) imply: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10517) ~ (all_52_11 = e0) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | SIMP: (10517) implies: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10518) ~ (all_52_11 = e0) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | REDUCE: (10504), (10516) imply: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10519) ~ (e3 = e0) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | REDUCE: (10464), (10516) imply: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10520) ~ (e2 = e0) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | REDUCE: (8979), (10516) imply: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | (10521) ~ (e1 = e0) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (10522) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | BETA: splitting (10522) gives: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | (10523) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10523) gives: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (10524) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10524) implies: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (10525) ~ (all_56_3 = e3) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (10526) op(e2, e3) = all_56_3 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10506), (10525), (10526), (function-axioms) are % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #347. % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (10527) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10527) implies: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (10528) op(e3, e3) = e1 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (169), (232), % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (236), (238), (10465), (10471), (10472), (10528), % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | #14. % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | (10529) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (10223), (10467), (10529), % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | #136. % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (10530) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | BETA: splitting (10530) gives: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.77 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (10531) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10531) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10532) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10532) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10533) ~ (all_56_17 = e1) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10534) op(e3, e1) = all_56_17 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10472), (10533), (10534), (function-axioms) are % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349. % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10535) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10535) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10536) ~ (all_56_21 = e1) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10537) ~ (all_56_5 = e3) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10538) op(e1, e0) = all_56_29 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10539) op(e1, e1) = all_56_21 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10540) op(e1, e3) = all_56_5 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10541) op(e2, e1) = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_29, e0, e1, simplifying with (160), (10538) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10542) all_56_29 = all_52_14 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_21, e1, e1, simplifying with (39), (10539) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10543) all_56_21 = all_6_2 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (10541) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10544) all_52_9 = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10536), (10543) imply: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10545) ~ (all_6_2 = e1) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (10544) imply: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10546) ~ (all_52_11 = e2) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | SIMP: (10546) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10547) ~ (all_52_11 = e2) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (10544) imply: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10548) ~ (all_52_13 = e2) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | SIMP: (10548) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10549) ~ (all_52_13 = e2) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (10544) imply: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10550) ~ (all_6_2 = e2) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10551) all_54_7 = e3 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (10551) imply: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10552) all_52_13 = e3 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10505), (10552) imply: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10553) $false % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10553) is inconsistent. % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10554) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | (10555) all_54_14 = e3 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (10555) imply: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | (10556) all_52_11 = e3 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10556) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | (10557) all_52_11 = e3 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (10557) imply: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | (10558) ~ (all_6_2 = e3) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10558) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | (10559) ~ (all_6_2 = e3) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | (10560) all_54_10 = e3 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (10559), (10560) are inconsistent by % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #742. % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | (10561) ~ (all_54_10 = e3) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | (10562) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10562) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | (10563) all_54_10 = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (8992), (10563) are inconsistent by % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #741. % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | (10564) all_54_10 = e1 | all_54_10 = e0 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10554) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10565) all_54_7 = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (10549), (10565) are inconsistent by % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #337. % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10566) all_54_7 = e1 | all_54_7 = e0 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10566) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10567) all_54_7 = e1 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8983), (10567) are inconsistent by % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #314. % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10568) all_54_7 = e0 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (10568) imply: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10569) all_52_13 = e0 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10569) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10570) all_52_13 = e0 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (10570) imply: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10571) ~ (all_52_12 = e0) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10572) all_54_3 = e3 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (10572) imply: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10573) all_52_12 = e3 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (10573) imply: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10574) ~ (all_52_14 = e3) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10574) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10575) ~ (all_52_14 = e3) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (103), (160), (218), (334), (10218), % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10537), (10540), (10545), (10559), (10564), % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10575), (function-axioms) are inconsistent by % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #186. % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10576) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (8982), (10466), (10571), (10576) are % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320. % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | (10577) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (8981), (10518), (10547), (10577) are % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #526. % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (10578) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10578) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10579) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10579) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10580) op(e2, e2) = e0 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10223), (10580), (function-axioms) are % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10581) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10581) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10582) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10582) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10583) op(e1, e1) = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (10583), (function-axioms) are % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10584) op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (160), (8984), (8991), (10472), % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10518), (10584), (function-axioms) are % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #15. % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | (10585) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 135.21/19.78 | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | REF_CLOSE: (10484), (10489), (10494), (10495), (10585) are % 135.21/19.78 | | | | | | | | | | | | | | | | inconsistent by sub-proof #126. % 135.21/19.78 | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | (10586) ~ (all_38_1 = e1) & op(e2, e2) = all_38_1 & % 135.21/19.78 | | | | | | | | | | | | | | | $i(all_38_1) % 135.21/19.78 | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | REF_CLOSE: (10223), (10586), (function-axioms) are % 135.21/19.78 | | | | | | | | | | | | | | | inconsistent by sub-proof #125. % 135.21/19.78 | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | (10587) all_57_12 = e1 & op(e0, e3) = e1 % 135.21/19.78 | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | REF_CLOSE: (159), (8979), (10587), (function-axioms) are % 135.21/19.78 | | | | | | | | | | | | | | inconsistent by sub-proof #48. % 135.21/19.78 | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | (10588) all_57_9 = e1 & op(e3, e0) = e1 % 135.21/19.78 | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | REF_CLOSE: (168), (8982), (10588), (function-axioms) are % 135.21/19.78 | | | | | | | | | | | inconsistent by sub-proof #181. % 135.21/19.78 | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | % 135.21/19.78 | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | % 135.21/19.78 | | | | | | | | End of split % 135.21/19.78 | | | | | | | | % 135.21/19.78 | | | | | | | End of split % 135.21/19.78 | | | | | | | % 135.21/19.78 | | | | | | Case 2: % 135.21/19.78 | | | | | | | % 135.21/19.78 | | | | | | | (10589) all_10_2 = e0 % 135.21/19.78 | | | | | | | (10590) ( ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 & % 135.21/19.78 | | | | | | | $i(all_10_0)) | ( ~ (all_10_1 = e1) & op(e0, e0) = % 135.21/19.78 | | | | | | | all_10_1 & $i(all_10_1)) % 135.21/19.78 | | | | | | | % 135.21/19.78 | | | | | | | REDUCE: (336), (10589) imply: % 135.21/19.78 | | | | | | | (10591) ~ (all_52_1 = e0) % 135.21/19.78 | | | | | | | % 135.21/19.78 | | | | | | | REDUCE: (338), (10589) imply: % 135.21/19.78 | | | | | | | (10592) ~ (all_52_2 = e0) % 135.21/19.78 | | | | | | | % 135.21/19.78 | | | | | | | REDUCE: (340), (10589) imply: % 135.21/19.78 | | | | | | | (10593) ~ (all_52_3 = e0) % 135.21/19.78 | | | | | | | % 135.21/19.78 | | | | | | | REDUCE: (342), (10589) imply: % 135.21/19.78 | | | | | | | (10594) ~ (all_52_4 = e0) % 135.21/19.78 | | | | | | | % 135.21/19.78 | | | | | | | REDUCE: (344), (10589) imply: % 135.21/19.78 | | | | | | | (10595) ~ (all_52_8 = e0) % 135.21/19.78 | | | | | | | % 135.21/19.78 | | | | | | | REDUCE: (45), (10589) imply: % 135.21/19.78 | | | | | | | (10596) op(e3, e3) = e0 % 135.21/19.78 | | | | | | | % 135.21/19.78 | | | | | | | BETA: splitting (234) gives: % 135.21/19.78 | | | | | | | % 135.21/19.78 | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | % 135.21/19.78 | | | | | | | | (10597) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & % 135.21/19.78 | | | | | | | | op(e3, e2) = e1) % 135.21/19.78 | | | | | | | | % 135.21/19.78 | | | | | | | | REF_CLOSE: (4), (170), (10220), (10596), (10597), % 135.21/19.78 | | | | | | | | (function-axioms) are inconsistent by sub-proof #117. % 135.21/19.78 | | | | | | | | % 135.21/19.78 | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | % 135.21/19.78 | | | | | | | | (10598) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & % 135.21/19.78 | | | | | | | | op(e3, e0) = e1) % 135.21/19.78 | | | | | | | | % 135.21/19.78 | | | | | | | | BETA: splitting (10598) gives: % 135.21/19.78 | | | | | | | | % 135.21/19.78 | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | % 135.21/19.78 | | | | | | | | | (10599) all_57_4 = e1 & op(e3, e1) = e1 % 135.21/19.78 | | | | | | | | | % 135.21/19.78 | | | | | | | | | ALPHA: (10599) implies: % 135.21/19.78 | | | | | | | | | (10600) all_57_4 = e1 % 135.21/19.78 | | | | | | | | | (10601) op(e3, e1) = e1 % 135.21/19.78 | | | | | | | | | % 135.21/19.78 | | | | | | | | | BETA: splitting (233) gives: % 135.21/19.78 | | | | | | | | | % 135.21/19.78 | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | (10602) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 % 135.21/19.78 | | | | | | | | | | & op(e2, e3) = e1) % 135.21/19.78 | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | BETA: splitting (10602) gives: % 135.21/19.78 | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | (10603) all_57_0 = e1 & op(e3, e3) = e1 % 135.21/19.78 | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | ALPHA: (10603) implies: % 135.21/19.78 | | | | | | | | | | | (10604) op(e3, e3) = e1 % 135.21/19.78 | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236), % 135.21/19.78 | | | | | | | | | | | (238), (10594), (10600), (10604), % 135.21/19.78 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.78 | | | | | | | | | | | #667. % 135.21/19.78 | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | (10605) all_57_2 = e1 & op(e2, e3) = e1 % 135.21/19.78 | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | REF_CLOSE: (167), (10219), (10605), (function-axioms) are % 135.21/19.78 | | | | | | | | | | | inconsistent by sub-proof #676. % 135.21/19.78 | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | % 135.21/19.78 | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | (10606) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = % 135.21/19.78 | | | | | | | | | | e1 & op(e0, e3) = e1) % 135.21/19.78 | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | BETA: splitting (10606) gives: % 135.21/19.78 | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | (10607) all_57_6 = e1 & op(e1, e3) = e1 % 135.21/19.78 | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | ALPHA: (10607) implies: % 135.21/19.78 | | | | | | | | | | | (10608) op(e1, e3) = e1 % 135.21/19.78 | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | BETA: splitting (10590) gives: % 135.21/19.78 | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | (10609) ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 & % 135.21/19.78 | | | | | | | | | | | | $i(all_10_0) % 135.21/19.78 | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | ALPHA: (10609) implies: % 135.21/19.78 | | | | | | | | | | | | (10610) ~ (all_10_0 = e2) % 135.21/19.78 | | | | | | | | | | | | (10611) op(e0, e3) = all_10_0 % 135.21/19.78 | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, % 135.21/19.78 | | | | | | | | | | | | all_10_0, e3, e0, simplifying with (159), (10611) % 135.21/19.78 | | | | | | | | | | | | gives: % 135.21/19.78 | | | | | | | | | | | | (10612) all_52_3 = all_10_0 % 135.21/19.78 | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1, % 135.21/19.78 | | | | | | | | | | | | e3, e1, simplifying with (163), (10608) gives: % 135.21/19.78 | | | | | | | | | | | | (10613) all_52_2 = e1 % 135.21/19.78 | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1, % 135.21/19.78 | | | | | | | | | | | | e1, e3, simplifying with (169), (10601) gives: % 135.21/19.78 | | | | | | | | | | | | (10614) all_52_8 = e1 % 135.21/19.78 | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | COMBINE_EQS: (248), (10612) imply: % 135.21/19.78 | | | | | | | | | | | | (10615) all_54_12 = all_10_0 % 135.21/19.78 | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | REDUCE: (148), (10612) imply: % 135.21/19.78 | | | | | | | | | | | | (10616) ~ (all_52_1 = all_10_0) % 135.21/19.78 | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | REDUCE: (141), (10613) imply: % 135.21/19.78 | | | | | | | | | | | | (10617) ~ (all_52_14 = e1) % 135.21/19.78 | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | REDUCE: (140), (10612) imply: % 135.21/19.78 | | | | | | | | | | | | (10618) ~ (all_52_7 = all_10_0) % 135.21/19.78 | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | SIMP: (10618) implies: % 135.21/19.78 | | | | | | | | | | | | (10619) ~ (all_52_7 = all_10_0) % 135.21/19.78 | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | REDUCE: (139), (10612) imply: % 135.21/19.78 | | | | | | | | | | | | (10620) ~ (all_52_11 = all_10_0) % 135.21/19.78 | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | SIMP: (10620) implies: % 135.21/19.78 | | | | | | | | | | | | (10621) ~ (all_52_11 = all_10_0) % 135.21/19.78 | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | REDUCE: (8979), (10612) imply: % 135.21/19.78 | | | | | | | | | | | | (10622) ~ (all_10_0 = e1) % 135.21/19.78 | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | REDUCE: (10593), (10612) imply: % 135.21/19.78 | | | | | | | | | | | | (10623) ~ (all_10_0 = e0) % 135.21/19.78 | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | BETA: splitting (192) gives: % 135.21/19.78 | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | (10624) all_54_12 = e3 % 135.21/19.78 | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | COMBINE_EQS: (10615), (10624) imply: % 135.21/19.78 | | | | | | | | | | | | | (10625) all_10_0 = e3 % 135.21/19.78 | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | SIMP: (10625) implies: % 135.21/19.78 | | | | | | | | | | | | | (10626) all_10_0 = e3 % 135.21/19.78 | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | REDUCE: (10616), (10626) imply: % 135.21/19.78 | | | | | | | | | | | | | (10627) ~ (all_52_1 = e3) % 135.21/19.78 | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | REDUCE: (10619), (10626) imply: % 135.21/19.78 | | | | | | | | | | | | | (10628) ~ (all_52_7 = e3) % 135.21/19.78 | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | REDUCE: (10621), (10626) imply: % 135.21/19.78 | | | | | | | | | | | | | (10629) ~ (all_52_11 = e3) % 135.21/19.78 | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | BETA: splitting (211) gives: % 135.21/19.78 | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | (10630) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 135.21/19.78 | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 135.21/19.78 | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | BETA: splitting (10630) gives: % 135.21/19.78 | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | (10631) all_57_12 = e3 & op(e0, e3) = e3 % 135.21/19.78 | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | ALPHA: (10631) implies: % 135.21/19.78 | | | | | | | | | | | | | | | (10632) all_57_12 = e3 % 135.21/19.78 | | | | | | | | | | | | | | | (10633) op(e0, e3) = e3 % 135.21/19.78 | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | BETA: splitting (200) gives: % 135.21/19.78 | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | (10634) all_54_4 = e3 % 135.21/19.78 | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | REF_CLOSE: (268), (10627), (10634) are inconsistent by % 135.21/19.78 | | | | | | | | | | | | | | | | sub-proof #481. % 135.21/19.78 | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | (10635) ~ (all_54_4 = e3) % 135.21/19.78 | | | | | | | | | | | | | | | | (10636) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 135.21/19.78 | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | BETA: splitting (10636) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | (10637) all_54_4 = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (10637) imply: % 135.21/19.78 | | | | | | | | | | | | | | | | | (10638) all_52_1 = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | SIMP: (10638) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | (10639) all_52_1 = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | REDUCE: (146), (10639) imply: % 135.21/19.78 | | | | | | | | | | | | | | | | | (10640) ~ (all_52_9 = e2) % 135.21/19.78 | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | SIMP: (10640) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | (10641) ~ (all_52_9 = e2) % 135.21/19.78 | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | REDUCE: (10627), (10639) imply: % 135.21/19.78 | | | | | | | | | | | | | | | | | (10642) ~ (e3 = e2) % 135.21/19.78 | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | (10643) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2) % 135.21/19.78 | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | BETA: splitting (10643) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10644) all_57_4 = e2 & op(e3, e1) = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | ALPHA: (10644) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10645) all_57_4 = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10600), (10645) are inconsistent by % 135.21/19.78 | | | | | | | | | | | | | | | | | | | sub-proof #669. % 135.21/19.78 | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10646) all_57_5 = e2 & op(e2, e1) = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | ALPHA: (10646) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10647) op(e2, e1) = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10641), (10647), (function-axioms) are % 135.21/19.78 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #770. % 135.21/19.78 | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | End of split % 135.21/19.78 | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | (10648) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 135.21/19.78 | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | BETA: splitting (10648) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10649) all_57_8 = e2 & op(e1, e1) = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | ALPHA: (10649) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10650) op(e1, e1) = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (10650), (function-axioms) are % 135.21/19.78 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 135.21/19.78 | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10651) all_57_14 = e2 & op(e0, e1) = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | ALPHA: (10651) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10652) all_57_14 = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | (10653) op(e0, e1) = e2 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | (10654) all_57_15 = e0 & op(e0, e0) = e0 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | ALPHA: (10654) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | (10655) op(e0, e0) = e0 % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8991), (10655), (function-axioms) are % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #220. % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | (10656) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | ALPHA: (10656) implies: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | (10657) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | e1) = e0) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (10658) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10658) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (10659) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10659) gives: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (10660) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.21/19.78 | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10660) implies: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (10661) op(e3, e3) = e2 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (163), (167), (231), (10591), (10592), % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (10632), (10661), (function-axioms) are % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #25. % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (10662) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10662) implies: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (10663) op(e3, e3) = e1 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236), % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (238), (10594), (10600), (10663), % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | #667. % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (10664) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10223), (10633), (10664), (function-axioms) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #115. % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (10665) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10665) gives: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (10666) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10601), (10641), (10666), % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | #348. % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (10667) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10667) gives: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (10668) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10668) implies: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (10669) op(e2, e2) = e0 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10223), (10669), (function-axioms) are % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (10670) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10670) gives: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (10671) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10671) implies: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (10672) op(e1, e1) = e2 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8992), (10672), (function-axioms) are % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #767. % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (10673) op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10673) implies: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (10674) op(e0, e0) = all_56_31 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (10675) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10675) gives: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | (10676) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10676) gives: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10677) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10677) implies: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10678) op(e0, e3) = e0 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (10593), (10678), (function-axioms) are % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #219. % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10679) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10679) implies: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10680) all_56_31 = e2 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10674), (10680) imply: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10681) op(e0, e0) = e2 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (209), (10632), (10652), % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10657), (10681), (function-axioms) are % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #284. % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | (10682) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10682) gives: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10683) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10683) implies: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10684) op(e1, e0) = e1 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (8984), (10684), (function-axioms) are % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #327. % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10685) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29) % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10685) implies: % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (10686) op(e0, e1) = e0 % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10653), (10686), (function-axioms) are % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660. % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | (10687) all_54_4 = e1 | all_54_4 = e0 % 135.21/19.79 | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (163), (268), (10591), (10608), (10687), % 135.21/19.79 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.79 | | | | | | | | | | | | | | | | | #243. % 135.21/19.79 | | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | (10688) all_57_13 = e3 & op(e0, e2) = e3 % 135.21/19.79 | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | REF_CLOSE: (158), (10628), (10688), (function-axioms) are % 135.21/19.79 | | | | | | | | | | | | | | | inconsistent by sub-proof #556. % 135.21/19.79 | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | (10689) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 135.21/19.79 | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 135.21/19.79 | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (8991), (10629), (10689), % 135.21/19.79 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.79 | | | | | | | | | | | | | | #37. % 135.21/19.79 | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | (10690) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | REF_CLOSE: (10610), (10615), (10622), (10623), (10690) are % 135.21/19.79 | | | | | | | | | | | | | inconsistent by sub-proof #24. % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | (10691) ~ (all_10_1 = e1) & op(e0, e0) = all_10_1 & % 135.21/19.79 | | | | | | | | | | | | $i(all_10_1) % 135.21/19.79 | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | REF_CLOSE: (8991), (10691), (function-axioms) are % 135.21/19.79 | | | | | | | | | | | | inconsistent by sub-proof #16. % 135.21/19.79 | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | (10692) all_57_12 = e1 & op(e0, e3) = e1 % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | REF_CLOSE: (159), (8979), (10692), (function-axioms) are % 135.21/19.79 | | | | | | | | | | | inconsistent by sub-proof #48. % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | % 135.21/19.79 | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | % 135.21/19.79 | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | % 135.21/19.79 | | | | | | | | | (10693) all_57_9 = e1 & op(e3, e0) = e1 % 135.21/19.79 | | | | | | | | | % 135.21/19.79 | | | | | | | | | REF_CLOSE: (168), (8982), (10693), (function-axioms) are % 135.21/19.79 | | | | | | | | | inconsistent by sub-proof #181. % 135.21/19.79 | | | | | | | | | % 135.21/19.79 | | | | | | | | End of split % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | End of split % 135.21/19.79 | | | | | | | % 135.21/19.79 | | | | | | End of split % 135.21/19.79 | | | | | | % 135.21/19.79 | | | | | End of split % 135.21/19.79 | | | | | % 135.21/19.79 | | | | Case 2: % 135.21/19.79 | | | | | % 135.21/19.79 | | | | | (10694) all_6_2 = e2 % 135.21/19.79 | | | | | (10695) ( ~ (all_6_0 = e0) & op(e2, e1) = all_6_0 & $i(all_6_0)) | % 135.21/19.79 | | | | | ( ~ (all_6_1 = e3) & op(e2, e2) = all_6_1 & $i(all_6_1)) % 135.21/19.79 | | | | | % 135.21/19.79 | | | | | COMBINE_EQS: (324), (10694) imply: % 135.21/19.79 | | | | | (10696) all_18_2 = e2 % 135.21/19.79 | | | | | % 135.21/19.79 | | | | | REDUCE: (348), (10694) imply: % 135.21/19.79 | | | | | (10697) ~ (all_52_2 = e2) % 135.21/19.79 | | | | | % 135.21/19.79 | | | | | REDUCE: (359), (10694) imply: % 135.21/19.79 | | | | | (10698) ~ (all_52_6 = e2) % 135.21/19.79 | | | | | % 135.21/19.79 | | | | | REDUCE: (361), (10694) imply: % 135.21/19.79 | | | | | (10699) ~ (all_52_8 = e2) % 135.21/19.79 | | | | | % 135.21/19.79 | | | | | REDUCE: (364), (10694) imply: % 135.21/19.79 | | | | | (10700) ~ (all_52_11 = e2) % 135.21/19.79 | | | | | % 135.21/19.79 | | | | | REDUCE: (366), (10694) imply: % 135.21/19.79 | | | | | (10701) ~ (all_52_14 = e2) % 135.21/19.79 | | | | | % 135.21/19.79 | | | | | REDUCE: (39), (10694) imply: % 135.21/19.79 | | | | | (10702) op(e1, e1) = e2 % 135.21/19.79 | | | | | % 135.21/19.79 | | | | | BETA: splitting (8977) gives: % 135.21/19.79 | | | | | % 135.21/19.79 | | | | | Case 1: % 135.21/19.79 | | | | | | % 135.21/19.79 | | | | | | (10703) ~ (all_4_0 = e3) & op(e1, e0) = all_4_0 & $i(all_4_0) % 135.21/19.79 | | | | | | % 135.21/19.79 | | | | | | ALPHA: (10703) implies: % 135.21/19.79 | | | | | | (10704) ~ (all_4_0 = e3) % 135.21/19.79 | | | | | | (10705) op(e1, e0) = all_4_0 % 135.21/19.79 | | | | | | % 135.21/19.79 | | | | | | BETA: splitting (217) gives: % 135.21/19.79 | | | | | | % 135.21/19.79 | | | | | | Case 1: % 135.21/19.79 | | | | | | | % 135.21/19.79 | | | | | | | (10706) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & % 135.21/19.79 | | | | | | | op(e1, e2) = e2) % 135.21/19.79 | | | | | | | % 135.21/19.79 | | | | | | | BETA: splitting (10706) gives: % 135.21/19.79 | | | | | | | % 135.21/19.79 | | | | | | | Case 1: % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | | (10707) all_57_6 = e2 & op(e1, e3) = e2 % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | | REF_CLOSE: (163), (10697), (10707), (function-axioms) are % 135.21/19.79 | | | | | | | | inconsistent by sub-proof #341. % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | | (10708) all_57_7 = e2 & op(e1, e2) = e2 % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | | REF_CLOSE: (162), (10698), (10708), (function-axioms) are % 135.21/19.79 | | | | | | | | inconsistent by sub-proof #515. % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | End of split % 135.21/19.79 | | | | | | | % 135.21/19.79 | | | | | | Case 2: % 135.21/19.79 | | | | | | | % 135.21/19.79 | | | | | | | (10709) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & % 135.21/19.79 | | | | | | | op(e1, e0) = e2) % 135.21/19.79 | | | | | | | % 135.21/19.79 | | | | | | | BETA: splitting (10709) gives: % 135.21/19.79 | | | | | | | % 135.21/19.79 | | | | | | | Case 1: % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | | (10710) all_57_8 = e2 & op(e1, e1) = e2 % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | | ALPHA: (10710) implies: % 135.21/19.79 | | | | | | | | (10711) all_57_8 = e2 % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, % 135.21/19.79 | | | | | | | | all_4_0, e0, e1, simplifying with (160), (10705) % 135.21/19.79 | | | | | | | | gives: % 135.21/19.79 | | | | | | | | (10712) all_52_14 = all_4_0 % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | | COMBINE_EQS: (249), (10712) imply: % 135.21/19.79 | | | | | | | | (10713) all_54_11 = all_4_0 % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | | REDUCE: (141), (10712) imply: % 135.21/19.79 | | | | | | | | (10714) ~ (all_52_2 = all_4_0) % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | | REDUCE: (126), (10712) imply: % 135.21/19.79 | | | | | | | | (10715) ~ (all_52_6 = all_4_0) % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | | REDUCE: (112), (10712) imply: % 135.21/19.79 | | | | | | | | (10716) ~ (all_52_12 = all_4_0) % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | | REDUCE: (110), (10712) imply: % 135.21/19.79 | | | | | | | | (10717) ~ (all_52_13 = all_4_0) % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | | REDUCE: (10701), (10712) imply: % 135.21/19.79 | | | | | | | | (10718) ~ (all_4_0 = e2) % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | | REDUCE: (8984), (10712) imply: % 135.21/19.79 | | | | | | | | (10719) ~ (all_4_0 = e1) % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | | BETA: splitting (193) gives: % 135.21/19.79 | | | | | | | | % 135.21/19.79 | | | | | | | | Case 1: % 135.21/19.79 | | | | | | | | | % 135.21/19.79 | | | | | | | | | (10720) all_54_11 = e3 % 135.21/19.79 | | | | | | | | | % 135.21/19.79 | | | | | | | | | COMBINE_EQS: (10713), (10720) imply: % 135.21/19.79 | | | | | | | | | (10721) all_4_0 = e3 % 135.21/19.79 | | | | | | | | | % 135.21/19.79 | | | | | | | | | SIMP: (10721) implies: % 135.21/19.79 | | | | | | | | | (10722) all_4_0 = e3 % 135.21/19.79 | | | | | | | | | % 135.21/19.79 | | | | | | | | | REDUCE: (10704), (10722) imply: % 135.21/19.79 | | | | | | | | | (10723) $false % 135.21/19.79 | | | | | | | | | % 135.21/19.79 | | | | | | | | | CLOSE: (10723) is inconsistent. % 135.21/19.79 | | | | | | | | | % 135.21/19.79 | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | % 135.21/19.79 | | | | | | | | | (10724) ~ (all_54_11 = e3) % 135.21/19.79 | | | | | | | | | (10725) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0 % 135.21/19.79 | | | | | | | | | % 135.21/19.79 | | | | | | | | | BETA: splitting (10725) gives: % 135.21/19.79 | | | | | | | | | % 135.21/19.79 | | | | | | | | | Case 1: % 135.21/19.79 | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | (10726) all_54_11 = e2 % 135.21/19.79 | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | COMBINE_EQS: (10713), (10726) imply: % 135.21/19.79 | | | | | | | | | | (10727) all_4_0 = e2 % 135.21/19.79 | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | SIMP: (10727) implies: % 135.21/19.79 | | | | | | | | | | (10728) all_4_0 = e2 % 135.21/19.79 | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | REDUCE: (10718), (10728) imply: % 135.21/19.79 | | | | | | | | | | (10729) $false % 135.21/19.79 | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | CLOSE: (10729) is inconsistent. % 135.21/19.79 | | | | | | | | | | % 135.21/19.79 | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | (10730) ~ (all_54_11 = e2) % 135.21/19.79 | | | | | | | | | | (10731) all_54_11 = e1 | all_54_11 = e0 % 135.21/19.79 | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | BETA: splitting (10731) gives: % 135.21/19.79 | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | Case 1: % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | (10732) all_54_11 = e1 % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | COMBINE_EQS: (10713), (10732) imply: % 135.21/19.79 | | | | | | | | | | | (10733) all_4_0 = e1 % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | SIMP: (10733) implies: % 135.21/19.79 | | | | | | | | | | | (10734) all_4_0 = e1 % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | REDUCE: (10719), (10734) imply: % 135.21/19.79 | | | | | | | | | | | (10735) $false % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | CLOSE: (10735) is inconsistent. % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | (10736) all_54_11 = e0 % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | COMBINE_EQS: (10713), (10736) imply: % 135.21/19.79 | | | | | | | | | | | (10737) all_4_0 = e0 % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | SIMP: (10737) implies: % 135.21/19.79 | | | | | | | | | | | (10738) all_4_0 = e0 % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | REDUCE: (10714), (10738) imply: % 135.21/19.79 | | | | | | | | | | | (10739) ~ (all_52_2 = e0) % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | REDUCE: (10715), (10738) imply: % 135.21/19.79 | | | | | | | | | | | (10740) ~ (all_52_6 = e0) % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | REDUCE: (10716), (10738) imply: % 135.21/19.79 | | | | | | | | | | | (10741) ~ (all_52_12 = e0) % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | REDUCE: (10717), (10738) imply: % 135.21/19.79 | | | | | | | | | | | (10742) ~ (all_52_13 = e0) % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | REDUCE: (10704), (10738) imply: % 135.21/19.79 | | | | | | | | | | | (10743) ~ (e3 = e0) % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | REDUCE: (10718), (10738) imply: % 135.21/19.79 | | | | | | | | | | | (10744) ~ (e2 = e0) % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | REDUCE: (10719), (10738) imply: % 135.21/19.79 | | | | | | | | | | | (10745) ~ (e1 = e0) % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | BETA: splitting (215) gives: % 135.21/19.79 | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | Case 1: % 135.21/19.79 | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | (10746) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 % 135.21/19.79 | | | | | | | | | | | | & op(e1, e2) = e0) % 135.21/19.79 | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | BETA: splitting (10746) gives: % 135.21/19.79 | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | Case 1: % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | (10747) all_57_6 = e0 & op(e1, e3) = e0 % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | REF_CLOSE: (163), (10739), (10747), (function-axioms) are % 135.21/19.79 | | | | | | | | | | | | | inconsistent by sub-proof #73. % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | (10748) all_57_7 = e0 & op(e1, e2) = e0 % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | REF_CLOSE: (162), (10740), (10748), (function-axioms) are % 135.21/19.79 | | | | | | | | | | | | | inconsistent by sub-proof #505. % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | End of split % 135.21/19.79 | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | (10749) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = % 135.21/19.79 | | | | | | | | | | | | e0 & op(e1, e0) = e0) % 135.21/19.79 | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | BETA: splitting (10749) gives: % 135.21/19.79 | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | Case 1: % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | (10750) all_57_8 = e0 & op(e1, e1) = e0 % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | ALPHA: (10750) implies: % 135.21/19.79 | | | | | | | | | | | | | (10751) op(e1, e1) = e0 % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | REF_CLOSE: (5), (10702), (10751), (function-axioms) are % 135.21/19.79 | | | | | | | | | | | | | inconsistent by sub-proof #98. % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | Case 2: % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | (10752) all_57_11 = e0 & op(e1, e0) = e0 % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | ALPHA: (10752) implies: % 135.21/19.79 | | | | | | | | | | | | | (10753) all_57_11 = e0 % 135.21/19.79 | | | | | | | | | | | | | (10754) op(e1, e0) = e0 % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | BETA: splitting (43) gives: % 135.21/19.79 | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | Case 1: % 135.21/19.79 | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | (10755) ~ (all_8_2 = e1) % 135.21/19.79 | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | BETA: splitting (46) gives: % 135.21/19.79 | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | Case 1: % 135.21/19.79 | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | (10756) ~ (all_10_2 = e0) % 135.21/19.79 | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | BETA: splitting (52) gives: % 135.21/19.79 | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | Case 1: % 135.21/19.79 | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | (10757) ~ (all_14_2 = e3) % 135.21/19.79 | | | | | | | | | | | | | | | | % 135.21/19.79 | | | | | | | | | | | | | | | | REDUCE: (329), (10757) imply: % 135.21/19.80 | | | | | | | | | | | | | | | | (10758) ~ (all_8_2 = e3) % 135.21/19.80 | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | BETA: splitting (55) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | (10759) ~ (all_16_2 = e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | REDUCE: (327), (10759) imply: % 135.21/19.80 | | | | | | | | | | | | | | | | | (10760) ~ (all_10_2 = e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | BETA: splitting (58) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | (10761) ~ (all_18_2 = e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | REDUCE: (10696), (10761) imply: % 135.21/19.80 | | | | | | | | | | | | | | | | | | (10762) $false % 135.21/19.80 | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | CLOSE: (10762) is inconsistent. % 135.21/19.80 | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | (10763) ( ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | $i(all_18_0)) | ( ~ (all_18_1 = e0) & op(e2, e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | | = all_18_1 & $i(all_18_1)) % 135.21/19.80 | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | (10764) ~ (all_30_2 = e0) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | REDUCE: (309), (10764) imply: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | (10765) ~ (all_8_2 = e0) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10766) all_54_5 = e3 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (10766) imply: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10767) all_8_2 = e3 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | REDUCE: (10758), (10767) imply: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10768) $false % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | CLOSE: (10768) is inconsistent. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10769) ~ (all_54_5 = e3) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10770) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (42), (45), (158), (160), (164), (199), % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (206), (267), (354), (358), (8984), (8991), % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10702), (10754), (10755), (10756), (10758), % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10760), (10765), (10770), (function-axioms) are % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #38. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | (10771) all_30_2 = e0 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | (10772) ( ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | $i(all_30_0)) | ( ~ (all_30_1 = e1) & op(e0, e0) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | = all_30_1 & $i(all_30_1)) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (10771) imply: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | (10773) all_8_2 = e0 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | SIMP: (10773) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | (10774) all_8_2 = e0 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | REDUCE: (347), (10774) imply: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | (10775) ~ (all_52_1 = e0) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | REDUCE: (42), (10774) imply: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | (10776) op(e2, e2) = e0 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | BETA: splitting (10763) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10777) ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | $i(all_18_0) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | ALPHA: (10777) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10778) ~ (all_18_0 = e3) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10779) op(e2, e1) = all_18_0 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | (10780) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (167), (10756), (10775), (10780), % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | #142. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | (10781) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10781) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | (10782) all_57_6 = e0 & op(e1, e3) = e0 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (10739), (10782), (function-axioms) are % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #73. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | (10783) all_57_12 = e0 & op(e0, e3) = e0 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10783) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | (10784) all_57_12 = e0 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | (10785) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10785) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | (10786) all_57_0 = e2 & op(e3, e3) = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10786) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | (10787) op(e3, e3) = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (10760), (10787), (function-axioms) are % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #536. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | (10788) all_57_2 = e2 & op(e2, e3) = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10788) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | (10789) all_57_2 = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | (10790) op(e2, e3) = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | (10791) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10791) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (10792) all_57_12 = e2 & op(e0, e3) = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10792) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (10793) all_57_12 = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10784), (10793) are inconsistent by % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #682. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (10794) all_57_13 = e2 & op(e0, e2) = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10794) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (10795) all_57_13 = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | (10796) op(e0, e2) = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10797) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (10776), (10790), (10797), % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | #93. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10798) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10798) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10799) all_57_5 = e1 & op(e2, e1) = e1 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10799) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10800) all_57_5 = e1 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10801) op(e2, e1) = e1 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10802) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (10776), (10789), (10802), % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #94. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10803) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10803) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10804) all_57_5 = e3 & op(e2, e1) = e3 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10804) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10805) all_57_5 = e3 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10800), (10805) are inconsistent by % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #88. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10806) all_57_10 = e3 & op(e2, e0) = e3 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10806) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10807) op(e2, e0) = e3 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10772) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10808) ~ (all_30_0 = e3) & op(e0, e2) = all_30_0 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_30_0) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10808) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10809) ~ (all_30_0 = e3) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10810) op(e0, e2) = all_30_0 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10811) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10811) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10812) all_57_9 = e2 & op(e3, e0) = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10812) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10813) op(e3, e0) = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (158), (10796) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10814) all_52_7 = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_30_0, e2, e0, simplifying with (158), (10810) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10815) all_52_7 = all_30_0 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, e2, simplifying with (164), (10807) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10816) all_52_13 = e3 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (10801) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10817) all_52_9 = e1 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_18_0, e1, e2, simplifying with (165), (10779) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10818) all_52_9 = all_18_0 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e3, simplifying with (168), (10813) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10819) all_52_12 = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10814), (10815) imply: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10820) all_30_0 = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10817), (10818) imply: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10821) all_18_0 = e1 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (10819) imply: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10822) ~ (all_10_2 = e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10809), (10820) imply: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10823) ~ (e3 = e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10778), (10821) imply: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10824) ~ (e3 = e1) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10825) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10825) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10826) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (10754), (10760), (10826), (function-axioms) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #44. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10827) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (168), (10776), (10813), (10827), % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #13. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10828) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10828) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10829) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10702), (10754), (10829), (function-axioms) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #42. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10830) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10830) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10831) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10831) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10832) op(e2, e0) = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (10807), (10832), (function-axioms) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #546. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10833) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (42), (158), (160), (199), (267), (354), % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8984), (8991), (10754), (10755), (10758), % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10801), (10833), (function-axioms) are % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #12. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10834) all_57_10 = e2 & op(e2, e0) = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10834) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10835) op(e2, e0) = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (10807), (10835), (function-axioms) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #546. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10836) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10836) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10837) all_57_11 = e2 & op(e1, e0) = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10701), (10837), (function-axioms) are % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #514. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10838) all_57_15 = e2 & op(e0, e0) = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10838) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10839) all_57_15 = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10840) op(e0, e0) = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10841) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10841) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10842) all_57_12 = e3 & op(e0, e3) = e3 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10842) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10843) all_57_12 = e3 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (208), (209), (10795), % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10839), (10843) are inconsistent by sub-proof % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #11. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10844) all_57_13 = e3 & op(e0, e2) = e3 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10844) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10845) all_57_13 = e3 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10795), (10845) are inconsistent by % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #408. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10846) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10846) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10847) all_57_14 = e3 & op(e0, e1) = e3 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10847) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10848) all_57_14 = e3 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10849) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10849) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10850) all_57_12 = e1 & op(e0, e3) = e1 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10850) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10851) all_57_12 = e1 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (208), (10795), (10839), (10848), % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10851) are inconsistent by sub-proof #398. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10852) all_57_13 = e1 & op(e0, e2) = e1 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8980), (10852), (function-axioms) are % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #178. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10853) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10853) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10854) all_57_14 = e1 & op(e0, e1) = e1 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10848), (10854) are inconsistent by % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #247. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8991), (10840), (function-axioms) are % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10855) all_57_15 = e3 & op(e0, e0) = e3 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10855) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10856) op(e0, e0) = e3 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10840), (10856), (function-axioms) are % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #634. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10857) ~ (all_30_1 = e1) & op(e0, e0) = all_30_1 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_30_1) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8991), (10857), (function-axioms) are % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #53. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10858) all_57_10 = e1 & op(e2, e0) = e1 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10858) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10859) op(e2, e0) = e1 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8983), (10859), (function-axioms) are % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | (10860) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (8991), (10700), (10860), % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | #34. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | (10861) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10861) gives: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | (10862) all_57_6 = e2 & op(e1, e3) = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (10697), (10862), (function-axioms) are % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #341. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | (10863) all_57_12 = e2 & op(e0, e3) = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10863) implies: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | (10864) all_57_12 = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10784), (10864) are inconsistent by % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #682. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | (10865) ~ (all_18_1 = e0) & op(e2, e2) = all_18_1 & % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | $i(all_18_1) % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10776), (10865), (function-axioms) are % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #103. % 135.21/19.80 | | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | End of split % 135.21/19.80 | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | Case 2: % 135.21/19.80 | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | (10866) all_16_2 = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | COMBINE_EQS: (327), (10866) imply: % 135.21/19.80 | | | | | | | | | | | | | | | | | (10867) all_10_2 = e2 % 135.21/19.80 | | | | | | | | | | | | | | | | | % 135.21/19.80 | | | | | | | | | | | | | | | | | REDUCE: (342), (10867) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | (10868) ~ (all_52_4 = e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | REDUCE: (346), (10867) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | (10869) ~ (all_52_12 = e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | REDUCE: (45), (10867) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | (10870) op(e3, e3) = e2 % 135.21/19.81 | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | (10871) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | BETA: splitting (10871) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | (10872) all_57_9 = e2 & op(e3, e0) = e2 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (10869), (10872), (function-axioms) are % 135.21/19.81 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | (10873) all_57_10 = e2 & op(e2, e0) = e2 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | ALPHA: (10873) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | (10874) op(e2, e0) = e2 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | (10875) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | BETA: splitting (10875) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | (10876) all_57_9 = e3 & op(e3, e0) = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | ALPHA: (10876) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | (10877) all_57_9 = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | (10878) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10878) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | (10879) all_57_12 = e2 & op(e0, e3) = e2 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10879) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | (10880) all_57_12 = e2 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237), % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | (10870), (10880), (function-axioms) are % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #290. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | (10881) all_57_13 = e2 & op(e0, e2) = e2 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10881) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | (10882) all_57_13 = e2 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | (10883) op(e0, e2) = e2 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | (10884) all_54_3 = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (10884) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | (10885) all_52_12 = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (10885) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | (10886) ~ (all_52_4 = e3) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (10885) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | (10887) ~ (all_52_8 = e3) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (10885) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | (10888) ~ (all_52_13 = e3) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10888) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | (10889) ~ (all_52_13 = e3) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | (10890) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10890) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (10891) all_57_1 = e3 & op(e3, e2) = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10891) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (10892) op(e3, e2) = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (10886), (10892), (function-axioms) are % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #738. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (10893) all_57_3 = e3 & op(e2, e2) = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10893) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (10894) op(e2, e2) = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (10758), (10894), (function-axioms) are % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | (10895) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10895) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (10896) all_57_7 = e3 & op(e1, e2) = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10896) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (10897) all_57_7 = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (10898) op(e1, e2) = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | (10899) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10899) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10900) all_57_1 = e1 & op(e3, e2) = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10900) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10901) all_57_1 = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10902) op(e3, e2) = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10903) all_54_7 = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (10889), (10903) are inconsistent by % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #338. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10904) ~ (all_54_7 = e3) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10905) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10905) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10906) all_54_7 = e2 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (10906) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10907) all_52_13 = e2 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10907) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10908) all_52_13 = e2 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (10908) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10909) ~ (all_8_2 = e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10909) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10910) ~ (all_8_2 = e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10889), (10908) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10911) ~ (e3 = e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10912) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (10870), (10902), (10912), % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #333. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10913) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10913) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10914) all_57_4 = e0 & op(e3, e1) = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10914) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10915) op(e3, e1) = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10916) all_54_5 = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (10758), (10916) are inconsistent by % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #554. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10917) ~ (all_54_5 = e3) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10918) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10919) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10919) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10920) all_57_1 = e0 & op(e3, e2) = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10920) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10921) op(e3, e2) = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10902), (10921), (function-axioms) are % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #730. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10922) all_57_3 = e0 & op(e2, e2) = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10922) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10923) all_57_3 = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10918) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10924) all_54_5 = e2 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (10910), (10924) are inconsistent by % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #340. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10925) ~ (all_54_5 = e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10926) all_54_5 = e1 | all_54_5 = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10927) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10927) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10928) all_57_4 = e1 & op(e3, e1) = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10928) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10929) op(e3, e1) = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10915), (10929), (function-axioms) are % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #343. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10930) all_57_5 = e1 & op(e2, e1) = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10930) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10931) op(e2, e1) = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10926) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10932) all_54_5 = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (10755), (10932) are inconsistent by % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #339. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10933) all_54_5 = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (10933) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10934) all_8_2 = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10934) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10935) all_8_2 = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (10935) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10936) ~ (all_52_4 = e0) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10937) all_54_1 = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (10937) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10938) all_52_4 = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10886), (10938) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10939) $false % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10939) is inconsistent. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10940) ~ (all_54_1 = e3) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10941) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10941) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10942) all_54_1 = e2 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (10942) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10943) all_52_4 = e2 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10868), (10943) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10944) $false % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10944) is inconsistent. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10945) ~ (all_54_1 = e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10946) all_54_1 = e1 | all_54_1 = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10946) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10947) all_54_1 = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (10947) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10948) all_52_4 = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (10948) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10949) ~ (all_52_8 = e1) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10949) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10950) ~ (all_52_8 = e1) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10868), (10948) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10951) ~ (e2 = e1) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10952) all_54_2 = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (10952) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10953) all_52_8 = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10887), (10953) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10954) $false % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10954) is inconsistent. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10955) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10955) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10956) all_54_2 = e2 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (10956) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10957) all_52_8 = e2 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10699), (10957) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10958) $false % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10958) is inconsistent. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10959) ~ (all_54_2 = e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10960) all_54_2 = e1 | all_54_2 = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10961) all_54_9 = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (10961) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10962) all_52_6 = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (10962) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10963) ~ (all_52_7 = e3) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10963) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10964) ~ (all_52_7 = e3) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10960) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10965) all_54_2 = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (10965) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10966) all_52_8 = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10950), (10966) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10967) $false % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10967) is inconsistent. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10968) all_54_2 = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (10968) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10969) all_52_8 = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (10969) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10970) ~ (all_52_11 = e0) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10970) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10971) ~ (all_52_11 = e0) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10972) all_54_14 = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (10972) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10973) all_52_11 = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10973) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10974) all_52_11 = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (10974) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10975) ~ (all_52_3 = e3) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (10974) imply: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10976) ~ (all_52_9 = e3) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10977) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10977) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10978) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10978) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10979) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10979) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10980) ~ (all_56_19 = e1) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10981) op(e2, e1) = all_56_19 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10931), (10980), (10981), (function-axioms) are % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #106. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10982) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10982) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10983) op(e3, e3) = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (236), % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (10886), (10901), (10902), (10983), % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #610. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10984) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10984) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10985) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10985) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10986) ~ (all_56_15 = e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10987) op(e0, e2) = all_56_15 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10883), (10986), (10987), (function-axioms) are % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10988) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10988) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10989) op(e2, e2) = e3 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (45), (117), (145), (146), (157), % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (159), (160), (164), (165), (167), (169), % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (198), (206), (211), (219), (220), (222), % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (224), (259), (260), (8983), (8984), % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8991), (10695), (10700), (10702), (10711), % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10742), (10754), (10756), (10889), (10964), % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10975), (10976), (10989), (function-axioms) are % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #7. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10990) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10990) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10991) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10702), (10754), (10991), (function-axioms) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #42. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10992) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10992) gives: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10993) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10993) implies: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10994) ~ (all_56_15 = e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10995) op(e0, e2) = all_56_15 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10883), (10994), (10995), (function-axioms) are % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #609. % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10996) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.21/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (42), (158), (160), (199), (267), (354), % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8984), (8991), (10754), (10755), (10758), % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10931), (10996), (function-axioms) are % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #12. % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10997) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (8981), (10700), (10971), (10997) are % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #526. % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10998) ~ (all_54_9 = e3) % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (257), (10998) imply: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10999) ~ (all_52_6 = e3) % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10898), (10999), (function-axioms) are % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654. % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11000) all_54_1 = e0 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (11000) imply: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11001) all_52_4 = e0 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10936), (11001) imply: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11002) $false % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11002) is inconsistent. % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11003) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11003) gives: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11004) all_57_8 = e1 & op(e1, e1) = e1 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10711), (11004) are inconsistent by % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #85. % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11005) all_57_14 = e1 & op(e0, e1) = e1 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11005) implies: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11006) all_57_14 = e1 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11007) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11007) gives: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11008) all_57_12 = e3 & op(e0, e3) = e3 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11008) implies: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11009) all_57_12 = e3 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10926) gives: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11010) all_54_5 = e1 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (10755), (11010) are inconsistent by % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #339. % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11011) all_54_5 = e0 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (11011) imply: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11012) all_8_2 = e0 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11012) implies: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11013) all_8_2 = e0 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (347), (11013) imply: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11014) ~ (all_52_1 = e0) % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (163), (167), (231), (10739), (10870), % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11009), (11014), (function-axioms) are % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #25. % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11015) all_57_13 = e3 & op(e0, e2) = e3 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (228), (229), (10897), % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10923), (11015) are inconsistent by sub-proof % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #388. % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11016) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8991), (11006), (11016), (function-axioms) % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #6. % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11017) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (162), (10740), (10882), (11017), % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #170. % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11018) all_57_9 = e0 & op(e3, e0) = e0 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (10741), (11018), (function-axioms) are % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #618. % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11019) all_54_7 = e1 | all_54_7 = e0 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8983), (10742), (11019) are inconsistent % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #313. % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11020) all_57_3 = e1 & op(e2, e2) = e1 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11020) implies: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11021) op(e2, e2) = e1 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (10755), (11021), (function-axioms) are % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #57. % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (11022) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11022) gives: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11023) all_57_7 = e1 & op(e1, e2) = e1 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10897), (11023) are inconsistent by % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #603. % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11024) all_57_13 = e1 & op(e0, e2) = e1 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8980), (11024), (function-axioms) are % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #178. % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11025) all_57_13 = e3 & op(e0, e2) = e3 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11025) implies: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11026) all_57_13 = e3 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10882), (11026) imply: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11027) e3 = e2 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11027) implies: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11028) e3 = e2 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10877), (11028) imply: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11029) all_57_9 = e2 % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (232), (234), % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (10870), (10886), (11029), % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | #250. % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.21/19.82 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11030) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (8982), (10741), (10869), (11030) are % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320. % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | (11031) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (8991), (10700), (11031), % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | #34. % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11032) all_57_10 = e3 & op(e2, e0) = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | ALPHA: (11032) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11033) op(e2, e0) = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (10874), (11033), (function-axioms) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #546. % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11034) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | BETA: splitting (11034) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11035) all_57_11 = e3 & op(e1, e0) = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10753), (11035) are inconsistent by % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | sub-proof #5. % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11036) all_57_15 = e3 & op(e0, e0) = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | ALPHA: (11036) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11037) op(e0, e0) = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8991), (11037), (function-axioms) are % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606. % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | End of split % 135.30/19.82 | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | (11038) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 135.30/19.82 | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | BETA: splitting (11038) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11039) all_57_11 = e2 & op(e1, e0) = e2 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10701), (11039), (function-axioms) are % 135.30/19.82 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #514. % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11040) all_57_15 = e2 & op(e0, e0) = e2 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | ALPHA: (11040) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11041) op(e0, e0) = e2 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8991), (11041), (function-axioms) are % 135.30/19.82 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #636. % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | End of split % 135.30/19.82 | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | End of split % 135.30/19.82 | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | End of split % 135.30/19.82 | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | (11042) all_14_2 = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | COMBINE_EQS: (329), (11042) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | (11043) all_8_2 = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | REDUCE: (352), (11043) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | (11044) ~ (all_52_6 = e3) % 135.30/19.82 | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | REDUCE: (354), (11043) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | (11045) ~ (all_52_7 = e3) % 135.30/19.82 | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | REDUCE: (356), (11043) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | (11046) ~ (all_52_9 = e3) % 135.30/19.82 | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | REDUCE: (358), (11043) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | (11047) ~ (all_52_13 = e3) % 135.30/19.82 | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | REDUCE: (42), (11043) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | (11048) op(e2, e2) = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | (11049) all_54_9 = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (11044), (11049) are inconsistent by % 135.30/19.82 | | | | | | | | | | | | | | | | | sub-proof #64. % 135.30/19.82 | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | (11050) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 135.30/19.82 | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | BETA: splitting (11050) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | (11051) all_54_9 = e2 % 135.30/19.82 | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (10698), (11051) are inconsistent by % 135.30/19.82 | | | | | | | | | | | | | | | | | | sub-proof #582. % 135.30/19.82 | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | (11052) all_54_9 = e1 | all_54_9 = e0 % 135.30/19.82 | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | BETA: splitting (11052) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11053) all_54_9 = e1 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (11053) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11054) all_52_6 = e1 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | SIMP: (11054) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11055) all_52_6 = e1 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | REDUCE: (143), (11055) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11056) ~ (all_52_2 = e1) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11057) all_54_8 = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11057) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11058) all_52_2 = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | SIMP: (11058) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11059) all_52_2 = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (11059) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11060) ~ (all_52_3 = e3) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | SIMP: (11060) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11061) ~ (all_52_3 = e3) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (45), (117), (145), (146), (157), % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (158), (159), (160), (164), (165), (167), (169), % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (197), (198), (206), (211), (219), (220), (222), % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (223), (224), (259), (260), (8983), (8984), % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (8991), (10695), (10700), (10702), (10711), % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (10742), (10754), (10756), (11045), (11046), % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11047), (11048), (11061), (function-axioms) are % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #7. % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11062) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (10697), (10739), (11056), (11062) are % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #429. % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11063) all_54_9 = e0 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (10740), (11063) are inconsistent by % 135.30/19.82 | | | | | | | | | | | | | | | | | | | sub-proof #568. % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | End of split % 135.30/19.82 | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | End of split % 135.30/19.82 | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | End of split % 135.30/19.82 | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | End of split % 135.30/19.82 | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | (11064) all_10_2 = e0 % 135.30/19.82 | | | | | | | | | | | | | | | (11065) ( ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 & % 135.30/19.82 | | | | | | | | | | | | | | | $i(all_10_0)) | ( ~ (all_10_1 = e1) & op(e0, e0) % 135.30/19.82 | | | | | | | | | | | | | | | = all_10_1 & $i(all_10_1)) % 135.30/19.82 | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | REDUCE: (340), (11064) imply: % 135.30/19.82 | | | | | | | | | | | | | | | (11066) ~ (all_52_3 = e0) % 135.30/19.82 | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | REDUCE: (342), (11064) imply: % 135.30/19.82 | | | | | | | | | | | | | | | (11067) ~ (all_52_4 = e0) % 135.30/19.82 | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | REDUCE: (45), (11064) imply: % 135.30/19.82 | | | | | | | | | | | | | | | (11068) op(e3, e3) = e0 % 135.30/19.82 | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (136), (139), (140), % 135.30/19.82 | | | | | | | | | | | | | | | (143), (144), (157), (158), (159), (160), (162), % 135.30/19.82 | | | | | | | | | | | | | | | (163), (164), (168), (170), (192), (195), (196), % 135.30/19.82 | | | | | | | | | | | | | | | (206), (208), (209), (210), (211), (213), (218), % 135.30/19.82 | | | | | | | | | | | | | | | (224), (226), (227), (228), (231), (232), (233), % 135.30/19.82 | | | | | | | | | | | | | | | (235), (237), (238), (248), (257), (258), (8979), % 135.30/19.82 | | | | | | | | | | | | | | | (8980), (8983), (8984), (8991), (10697), (10698), % 135.30/19.82 | | | | | | | | | | | | | | | (10700), (10701), (10702), (10739), (10740), % 135.30/19.82 | | | | | | | | | | | | | | | (10753), (10754), (11065), (11066), (11067), % 135.30/19.82 | | | | | | | | | | | | | | | (11068), (function-axioms) are inconsistent by % 135.30/19.82 | | | | | | | | | | | | | | | sub-proof #2. % 135.30/19.82 | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | End of split % 135.30/19.82 | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | (11069) all_8_2 = e1 % 135.30/19.82 | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | COMBINE_EQS: (291), (11069) imply: % 135.30/19.82 | | | | | | | | | | | | | | (11070) all_48_2 = e1 % 135.30/19.82 | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | REDUCE: (352), (11069) imply: % 135.30/19.82 | | | | | | | | | | | | | | (11071) ~ (all_52_6 = e1) % 135.30/19.82 | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | REDUCE: (356), (11069) imply: % 135.30/19.82 | | | | | | | | | | | | | | (11072) ~ (all_52_9 = e1) % 135.30/19.82 | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | REDUCE: (42), (11069) imply: % 135.30/19.82 | | | | | | | | | | | | | | (11073) op(e2, e2) = e1 % 135.30/19.82 | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | BETA: splitting (220) gives: % 135.30/19.82 | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | (11074) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 % 135.30/19.82 | | | | | | | | | | | | | | | & op(e2, e1) = e1) % 135.30/19.82 | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | BETA: splitting (11074) gives: % 135.30/19.82 | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | (11075) all_57_4 = e1 & op(e3, e1) = e1 % 135.30/19.82 | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | ALPHA: (11075) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | (11076) op(e3, e1) = e1 % 135.30/19.82 | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | (11077) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 135.30/19.82 | | | | | | | | | | | | | | | | | & op(e1, e2) = e1) % 135.30/19.82 | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | BETA: splitting (11077) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | (11078) all_57_6 = e1 & op(e1, e3) = e1 % 135.30/19.82 | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | ALPHA: (11078) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | | | (11079) all_57_6 = e1 % 135.30/19.82 | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | (11080) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | BETA: splitting (11080) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11081) all_57_6 = e3 & op(e1, e3) = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | ALPHA: (11081) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11082) all_57_6 = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11079), (11082) are inconsistent by % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | sub-proof #575. % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11083) all_57_7 = e3 & op(e1, e2) = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | ALPHA: (11083) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | (11084) op(e1, e2) = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11085) all_54_9 = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (11085) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11086) all_52_6 = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | SIMP: (11086) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11087) all_52_6 = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (11087) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11088) ~ (all_52_2 = e3) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (11087) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | (11089) ~ (all_52_4 = e3) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | (11090) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11090) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | (11091) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11091) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11092) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11092) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11093) op(e3, e2) = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (11089), (11093), (function-axioms) are % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #738. % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11094) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11094) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11095) ~ (all_56_29 = e0) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11096) op(e1, e0) = all_56_29 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10754), (11095), (11096), (function-axioms) are % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #45. % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | (11097) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11097) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11098) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11098) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11099) op(e0, e0) = all_56_31 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11100) op(e0, e1) = all_56_23 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11101) op(e0, e2) = all_56_15 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11102) op(e0, e3) = all_56_7 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11103) op(e3, e0) = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (11104) op(e3, e3) = e0 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | (11105) all_54_8 = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11105) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | (11106) all_52_2 = e3 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11088), (11106) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | (11107) $false % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11107) is inconsistent. % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | (11108) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11108) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11109) all_54_8 = e2 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11109) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11110) all_52_2 = e2 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10697), (11110) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11111) $false % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11111) is inconsistent. % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11112) ~ (all_54_8 = e2) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (11113) all_54_8 = e1 | all_54_8 = e0 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (11114) ~ (all_48_2 = e1) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11070), (11114) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (11115) $false % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11115) is inconsistent. % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (11116) ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_48_1 & $i(all_48_1)) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11116) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11117) ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_0) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11117) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11118) ~ (all_48_0 = e3) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11119) op(e1, e2) = all_48_0 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11084), (11118), (11119), (function-axioms) are % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #188. % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11120) ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 & % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_1) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11120) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11121) ~ (all_48_1 = e0) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11122) op(e1, e1) = all_48_1 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11113) gives: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11123) all_54_8 = e1 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11123) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11124) all_52_2 = e1 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11124) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11125) all_52_2 = e1 % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (11125) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11126) ~ (all_52_3 = e1) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (338), (11125) imply: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11127) ~ (all_10_2 = e1) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11127) implies: % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11128) ~ (all_10_2 = e1) % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31, e0, e0, simplifying with (8991), % 135.30/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11099) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11129) all_56_31 = e1 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23, e1, e0, simplifying with (157), (11100) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11130) all_56_23 = all_52_11 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e2, e0, simplifying with (158), (11101) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11131) all_56_15 = all_52_7 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_7, e3, e0, simplifying with (159), (11102) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11132) all_56_7 = all_52_3 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_48_1, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (10702), (11122) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11133) all_48_1 = e2 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (11103) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11134) all_52_12 = e3 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (11076) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11135) all_52_8 = e1 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (45), (11104) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11136) all_10_2 = e0 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (340), (11136) imply: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11137) ~ (all_52_3 = e0) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (342), (11136) imply: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11138) ~ (all_52_4 = e0) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10699), (11135) imply: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11139) ~ (e2 = e1) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11140) ~ (all_10_2 = e0) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11136), (11140) imply: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11141) $false % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11141) is inconsistent. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11142) ( ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_10_0)) | ( ~ (all_10_1 = e1) & op(e0, e0) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_10_1 & $i(all_10_1)) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (136), (139), (140), % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (143), (144), (157), (158), (159), (160), (162), % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163), (164), (168), (170), (192), (195), (196), % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (208), (209), (210), (211), (213), (218), % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (226), (227), (228), (231), (232), (233), % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (237), (238), (248), (257), (258), (8979), % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8980), (8983), (8984), (8991), (10697), (10698), % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10700), (10701), (10702), (10739), (10740), % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (10753), (10754), (11104), (11137), (11138), % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11142), (function-axioms) are inconsistent by % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #2. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11143) all_54_8 = e0 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (10739), (11143) are inconsistent by % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #475. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11144) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11144) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11145) op(e2, e2) = e3 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11073), (11145), (function-axioms) are % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (11146) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11146) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (11147) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10702), (10754), (11147), (function-axioms) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #42. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (11148) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11148) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11149) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11149) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11150) op(e2, e2) = e0 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11073), (11150), (function-axioms) are % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11151) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11151) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (11152) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11152) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (11153) op(e1, e2) = e1 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (11071), (11153), (function-axioms) are % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #65. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (11154) op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (169), (8984), (8991), (10699), (10754), % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (11076), (11154), (function-axioms) are % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #17. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11155) ~ (all_54_9 = e3) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | REDUCE: (257), (11155) imply: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11156) ~ (all_52_6 = e3) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (11084), (11156), (function-axioms) are % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | (11157) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | BETA: splitting (11157) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | (11158) all_57_8 = e3 & op(e1, e1) = e3 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | ALPHA: (11158) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | (11159) op(e1, e1) = e3 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10702), (11159), (function-axioms) are % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | (11160) all_57_11 = e3 & op(e1, e0) = e3 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10753), (11160) are inconsistent by % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | sub-proof #5. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | (11161) all_57_7 = e1 & op(e1, e2) = e1 % 135.30/19.83 | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | ALPHA: (11161) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | | | (11162) op(e1, e2) = e1 % 135.30/19.83 | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (11071), (11162), (function-axioms) are % 135.30/19.83 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #65. % 135.30/19.83 | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | (11163) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 135.30/19.83 | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 135.30/19.83 | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (8984), (10711), (11163), % 135.30/19.83 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.30/19.83 | | | | | | | | | | | | | | | | | #1. % 135.30/19.83 | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | (11164) all_57_5 = e1 & op(e2, e1) = e1 % 135.30/19.83 | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | REF_CLOSE: (165), (11072), (11164), (function-axioms) are % 135.30/19.83 | | | | | | | | | | | | | | | | inconsistent by sub-proof #161. % 135.30/19.83 | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | (11165) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = % 135.30/19.83 | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1) % 135.30/19.83 | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | BETA: splitting (11165) gives: % 135.30/19.83 | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | (11166) all_57_8 = e1 & op(e1, e1) = e1 % 135.30/19.83 | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10711), (11166) are inconsistent by % 135.30/19.83 | | | | | | | | | | | | | | | | sub-proof #574. % 135.30/19.83 | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | (11167) all_57_14 = e1 & op(e0, e1) = e1 % 135.30/19.83 | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | ALPHA: (11167) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | (11168) all_57_14 = e1 % 135.30/19.83 | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | (11169) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 % 135.30/19.83 | | | | | | | | | | | | | | | | | & op(e1, e2) = e1) % 135.30/19.83 | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | BETA: splitting (11169) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | (11170) all_57_6 = e1 & op(e1, e3) = e1 % 135.30/19.83 | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | ALPHA: (11170) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | | | (11171) all_57_6 = e1 % 135.30/19.83 | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | (11172) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | BETA: splitting (11172) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | (11173) all_57_6 = e3 & op(e1, e3) = e3 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | ALPHA: (11173) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | (11174) all_57_6 = e3 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11171), (11174) are inconsistent by % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | sub-proof #575. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | (11175) all_57_7 = e3 & op(e1, e2) = e3 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | ALPHA: (11175) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | (11176) op(e1, e2) = e3 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11177) all_54_9 = e3 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (11177) imply: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11178) all_52_6 = e3 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | SIMP: (11178) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11179) all_52_6 = e3 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (11179) imply: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11180) ~ (all_52_7 = e3) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | SIMP: (11180) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11181) ~ (all_52_7 = e3) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (11182) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11182) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (11183) all_57_12 = e3 & op(e0, e3) = e3 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11183) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (11184) all_57_12 = e3 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11185) all_57_15 = e0 & op(e0, e0) = e0 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11185) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11186) op(e0, e0) = e0 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8991), (11186), (function-axioms) are % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #220. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11187) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11187) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (11188) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11188) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (11189) all_57_12 = e0 & op(e0, e3) = e0 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11189) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (11190) all_57_12 = e0 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11184), (11190) are inconsistent by % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #492. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | (11191) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11191) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | (11192) all_57_13 = e0 & op(e0, e2) = e0 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11192) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | (11193) all_57_13 = e0 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (11194) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11194) gives: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11195) all_57_12 = e2 & op(e0, e3) = e2 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11184), (11195) are inconsistent by % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #196. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11196) all_57_13 = e2 & op(e0, e2) = e2 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11196) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11197) all_57_13 = e2 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11193), (11197) are inconsistent by % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #404. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (11198) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (8991), (10700), (11198), % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | #34. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | (11199) all_57_14 = e0 & op(e0, e1) = e0 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11168), (11199) are inconsistent by % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #483. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | (11200) all_57_13 = e3 & op(e0, e2) = e3 % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (11181), (11200), (function-axioms) are % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #556. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | (11201) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8991), (11168), (11201), (function-axioms) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #6. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11202) ~ (all_54_9 = e3) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | REDUCE: (257), (11202) imply: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | (11203) ~ (all_52_6 = e3) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (11176), (11203), (function-axioms) are % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #654. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | (11204) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 135.30/19.83 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 135.30/19.83 | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (10702), (10753), (11204), % 135.30/19.83 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.30/19.83 | | | | | | | | | | | | | | | | | | | #3. % 135.30/19.83 | | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | (11205) all_57_7 = e1 & op(e1, e2) = e1 % 135.30/19.83 | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | ALPHA: (11205) implies: % 135.30/19.83 | | | | | | | | | | | | | | | | | | (11206) op(e1, e2) = e1 % 135.30/19.83 | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (11071), (11206), (function-axioms) are % 135.30/19.83 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #65. % 135.30/19.83 | | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | (11207) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = % 135.30/19.83 | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1) % 135.30/19.83 | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (8984), (10711), (11207), % 135.30/19.83 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 135.30/19.83 | | | | | | | | | | | | | | | | | #1. % 135.30/19.83 | | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | | % 135.30/19.83 | | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | | % 135.30/19.83 | | | | | | | | | End of split % 135.30/19.83 | | | | | | | | | % 135.30/19.83 | | | | | | | | End of split % 135.30/19.83 | | | | | | | | % 135.30/19.83 | | | | | | | Case 2: % 135.30/19.83 | | | | | | | | % 135.30/19.83 | | | | | | | | (11208) all_57_11 = e2 & op(e1, e0) = e2 % 135.30/19.83 | | | | | | | | % 135.30/19.83 | | | | | | | | REF_CLOSE: (160), (10701), (11208), (function-axioms) are % 135.30/19.83 | | | | | | | | inconsistent by sub-proof #514. % 135.30/19.83 | | | | | | | | % 135.30/19.83 | | | | | | | End of split % 135.30/19.83 | | | | | | | % 135.30/19.83 | | | | | | End of split % 135.30/19.83 | | | | | | % 135.30/19.83 | | | | | Case 2: % 135.30/19.83 | | | | | | % 135.30/19.83 | | | | | | (11209) ~ (all_4_1 = e2) & op(e1, e1) = all_4_1 & $i(all_4_1) % 135.30/19.83 | | | | | | % 135.30/19.83 | | | | | | ALPHA: (11209) implies: % 135.30/19.83 | | | | | | (11210) ~ (all_4_1 = e2) % 135.30/19.83 | | | | | | (11211) op(e1, e1) = all_4_1 % 135.30/19.83 | | | | | | % 135.30/19.83 | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_4_1, e1, % 135.30/19.83 | | | | | | e1, simplifying with (10702), (11211) gives: % 135.30/19.83 | | | | | | (11212) all_4_1 = e2 % 135.30/19.83 | | | | | | % 135.30/19.83 | | | | | | REDUCE: (11210), (11212) imply: % 135.30/19.83 | | | | | | (11213) $false % 135.30/19.83 | | | | | | % 135.30/19.83 | | | | | | CLOSE: (11213) is inconsistent. % 135.30/19.83 | | | | | | % 135.30/19.83 | | | | | End of split % 135.30/19.83 | | | | | % 135.30/19.83 | | | | End of split % 135.30/19.83 | | | | % 135.30/19.83 | | | End of split % 135.30/19.83 | | | % 135.30/19.83 | | End of split % 135.30/19.83 | | % 135.30/19.83 | End of split % 135.30/19.83 | % 135.30/19.83 End of proof % 135.30/19.83 % 135.30/19.83 Sub-proof #1 shows that the following formulas are inconsistent: % 135.30/19.83 ---------------------------------------------------------------- % 135.30/19.84 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.30/19.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.30/19.84 (2) ~ (e2 = e1) % 135.30/19.84 (3) all_57_8 = e2 % 135.30/19.84 (4) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 135.30/19.84 (5) ~ (all_52_14 = e1) % 135.30/19.84 (6) op(e1, e0) = all_52_14 % 135.30/19.84 % 135.30/19.84 Begin of proof % 135.30/19.84 | % 135.30/19.84 | BETA: splitting (4) gives: % 135.30/19.84 | % 135.30/19.84 | Case 1: % 135.30/19.84 | | % 135.30/19.84 | | (7) all_57_8 = e1 & op(e1, e1) = e1 % 135.30/19.84 | | % 135.30/19.84 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #574. % 135.30/19.84 | | % 135.30/19.84 | Case 2: % 135.30/19.84 | | % 135.30/19.84 | | (8) all_57_11 = e1 & op(e1, e0) = e1 % 135.30/19.84 | | % 135.30/19.84 | | ALPHA: (8) implies: % 135.30/19.84 | | (9) op(e1, e0) = e1 % 135.30/19.84 | | % 135.30/19.84 | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #327. % 135.30/19.84 | | % 135.30/19.84 | End of split % 135.30/19.84 | % 135.30/19.84 End of proof % 135.30/19.84 % 135.30/19.84 Sub-proof #2 shows that the following formulas are inconsistent: % 135.30/19.84 ---------------------------------------------------------------- % 135.30/19.84 (1) ~ (all_52_3 = all_52_7) % 135.30/19.84 (2) ~ (all_52_4 = e0) % 135.30/19.84 (3) op(e2, e0) = all_52_13 % 135.30/19.84 (4) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 135.30/19.84 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 135.30/19.84 (5) ~ (all_52_11 = e2) % 135.30/19.84 (6) ~ (e2 = e0) % 135.30/19.84 (7) ~ (all_52_2 = e2) % 135.30/19.84 (8) ~ (all_52_3 = all_52_11) % 135.30/19.84 (9) all_54_12 = all_52_3 % 135.30/19.84 (10) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 135.30/19.84 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 135.30/19.84 (11) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) % 135.30/19.84 | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = % 135.30/19.84 e3) % 135.30/19.84 (12) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 135.30/19.84 (13) ~ (all_52_13 = e1) % 135.30/19.84 (14) ~ (all_52_2 = all_52_3) % 135.30/19.84 (15) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 135.30/19.84 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 135.30/19.84 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.30/19.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.30/19.84 (17) ~ (e2 = e1) % 135.30/19.84 (18) ~ (all_52_6 = e2) % 135.30/19.84 (19) ~ (e3 = e0) % 135.30/19.84 (20) ~ (all_52_4 = all_52_6) % 135.30/19.84 (21) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) % 135.30/19.84 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = % 135.30/19.84 e2) % 135.30/19.84 (22) ~ (e3 = e2) % 135.30/19.84 (23) op(e0, e0) = e1 % 135.30/19.84 (24) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 135.30/19.84 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 135.30/19.84 (25) ~ (all_52_14 = e2) % 135.30/19.84 (26) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 135.30/19.84 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) % 135.30/19.84 (27) op(e0, e1) = all_52_11 % 135.30/19.84 (28) op(e0, e2) = all_52_7 % 135.30/19.84 (29) op(e1, e1) = e2 % 135.30/19.84 (30) ~ (all_52_6 = e0) % 135.30/19.84 (31) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 135.30/19.84 (32) all_54_9 = all_52_6 % 135.30/19.84 (33) ~ (all_52_2 = e0) % 135.30/19.84 (34) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.30/19.84 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.30/19.84 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.30/19.84 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.30/19.84 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 135.30/19.84 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.30/19.84 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) % 135.30/19.84 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.30/19.84 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.84 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 135.30/19.84 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.84 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 135.30/19.84 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 135.30/19.84 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.30/19.84 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) % 135.30/19.84 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 135.30/19.84 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 135.30/19.84 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 135.30/19.84 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.30/19.84 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.30/19.84 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.30/19.84 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 135.30/19.84 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & % 135.30/19.84 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & % 135.30/19.84 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.30/19.84 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.30/19.84 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.30/19.84 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.84 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ % 135.30/19.84 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.84 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 135.30/19.84 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 135.30/19.84 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.30/19.84 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) % 135.30/19.84 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.30/19.84 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.30/19.84 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 % 135.30/19.84 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.84 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = % 135.30/19.84 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.30/19.84 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 135.30/19.84 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.30/19.84 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.30/19.84 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 135.30/19.84 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.30/19.84 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.30/19.84 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.30/19.84 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.84 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.30/19.84 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.30/19.84 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.30/19.84 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.30/19.84 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.30/19.84 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.30/19.84 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.30/19.84 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.30/19.84 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.30/19.84 $i(all_56_29)))) % 135.30/19.84 (35) op(e1, e2) = all_52_6 % 135.30/19.84 (36) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 135.30/19.84 (37) ~ (all_52_2 = all_52_6) % 135.30/19.84 (38) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 135.30/19.84 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 135.30/19.84 e1) % 135.30/19.84 (39) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 135.30/19.84 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 135.30/19.84 (40) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) | % 135.30/19.84 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2) % 135.30/19.84 (41) ~ (all_52_3 = e1) % 135.30/19.84 (42) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 135.30/19.84 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 135.30/19.84 (43) ~ (all_52_7 = e1) % 135.30/19.84 (44) op(e1, e3) = all_52_2 % 135.30/19.84 (45) ( ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 & $i(all_10_0)) | ( ~ % 135.30/19.84 (all_10_1 = e1) & op(e0, e0) = all_10_1 & $i(all_10_1)) % 135.30/19.84 (46) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 135.30/19.84 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 135.30/19.84 (47) op(e3, e2) = all_52_4 % 135.30/19.84 (48) op(e0, e3) = all_52_3 % 135.30/19.84 (49) op(e3, e0) = all_52_12 % 135.30/19.84 (50) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) | % 135.30/19.84 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2) % 135.30/19.84 (51) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 135.30/19.84 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 135.30/19.84 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 135.30/19.84 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 135.30/19.84 (52) ~ (all_52_14 = e1) % 135.30/19.84 (53) all_57_11 = e0 % 135.30/19.84 (54) op(e3, e3) = e0 % 135.30/19.84 (55) ~ (e3 = e1) % 135.30/19.84 (56) ~ (e1 = e0) % 135.30/19.84 (57) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 135.30/19.84 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 135.30/19.84 (58) all_54_8 = all_52_2 % 135.30/19.84 (59) ~ (all_52_3 = e0) % 135.30/19.84 (60) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 135.30/19.84 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 135.30/19.84 (61) op(e1, e0) = all_52_14 % 135.30/19.84 (62) op(e1, e0) = e0 % 135.30/19.84 % 135.30/19.84 Begin of proof % 135.30/19.84 | % 135.30/19.84 | BETA: splitting (45) gives: % 135.30/19.84 | % 135.30/19.84 | Case 1: % 135.30/19.84 | | % 135.30/19.84 | | (63) ~ (all_10_0 = e2) & op(e0, e3) = all_10_0 & $i(all_10_0) % 135.30/19.84 | | % 135.30/19.84 | | ALPHA: (63) implies: % 135.30/19.84 | | (64) ~ (all_10_0 = e2) % 135.30/19.84 | | (65) op(e0, e3) = all_10_0 % 135.30/19.84 | | % 135.30/19.84 | | GROUND_INST: instantiating (16) with all_52_3, all_10_0, e3, e0, simplifying % 135.30/19.84 | | with (48), (65) gives: % 135.30/19.84 | | (66) all_52_3 = all_10_0 % 135.30/19.84 | | % 135.30/19.84 | | COMBINE_EQS: (9), (66) imply: % 135.30/19.84 | | (67) all_54_12 = all_10_0 % 135.30/19.84 | | % 135.30/19.84 | | REDUCE: (14), (66) imply: % 135.30/19.84 | | (68) ~ (all_52_2 = all_10_0) % 135.30/19.84 | | % 135.30/19.84 | | REDUCE: (1), (66) imply: % 135.30/19.84 | | (69) ~ (all_52_7 = all_10_0) % 135.30/19.84 | | % 135.30/19.84 | | SIMP: (69) implies: % 135.30/19.84 | | (70) ~ (all_52_7 = all_10_0) % 135.30/19.84 | | % 135.30/19.84 | | REDUCE: (8), (66) imply: % 135.30/19.84 | | (71) ~ (all_52_11 = all_10_0) % 135.30/19.84 | | % 135.30/19.84 | | SIMP: (71) implies: % 135.30/19.84 | | (72) ~ (all_52_11 = all_10_0) % 135.30/19.84 | | % 135.30/19.84 | | REDUCE: (41), (66) imply: % 135.30/19.84 | | (73) ~ (all_10_0 = e1) % 135.30/19.84 | | % 135.30/19.84 | | REDUCE: (59), (66) imply: % 135.30/19.84 | | (74) ~ (all_10_0 = e0) % 135.30/19.84 | | % 135.30/19.84 | | BETA: splitting (21) gives: % 135.30/19.84 | | % 135.30/19.84 | | Case 1: % 135.30/19.84 | | | % 135.30/19.84 | | | (75) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) % 135.30/19.84 | | | = e2) % 135.30/19.84 | | | % 135.30/19.84 | | | BETA: splitting (75) gives: % 135.30/19.84 | | | % 135.30/19.84 | | | Case 1: % 135.30/19.84 | | | | % 135.30/19.84 | | | | (76) all_57_12 = e2 & op(e0, e3) = e2 % 135.30/19.84 | | | | % 135.30/19.84 | | | | ALPHA: (76) implies: % 135.30/19.84 | | | | (77) all_57_12 = e2 % 135.30/19.84 | | | | % 135.30/19.84 | | | | REF_CLOSE: (11), (16), (23), (27), (28), (31), (64), (67), (70), (72), % 135.30/19.84 | | | | (73), (74), (77) are inconsistent by sub-proof #23. % 135.30/19.84 | | | | % 135.30/19.84 | | | Case 2: % 135.30/19.84 | | | | % 135.30/19.84 | | | | (78) all_57_13 = e2 & op(e0, e2) = e2 % 135.30/19.84 | | | | % 135.30/19.84 | | | | ALPHA: (78) implies: % 135.30/19.84 | | | | (79) all_57_13 = e2 % 135.30/19.84 | | | | % 135.30/19.84 | | | | BETA: splitting (50) gives: % 135.30/19.84 | | | | % 135.30/19.84 | | | | Case 1: % 135.30/19.84 | | | | | % 135.30/19.84 | | | | | (80) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, % 135.30/19.84 | | | | | e3) = e2) % 135.30/19.84 | | | | | % 135.30/19.84 | | | | | BETA: splitting (80) gives: % 135.30/19.84 | | | | | % 135.30/19.84 | | | | | Case 1: % 135.30/19.84 | | | | | | % 135.30/19.84 | | | | | | (81) all_57_0 = e2 & op(e3, e3) = e2 % 135.30/19.84 | | | | | | % 135.30/19.84 | | | | | | ALPHA: (81) implies: % 135.30/19.84 | | | | | | (82) op(e3, e3) = e2 % 135.30/19.84 | | | | | | % 135.30/19.84 | | | | | | REF_CLOSE: (6), (16), (54), (82) are inconsistent by sub-proof #495. % 135.30/19.84 | | | | | | % 135.30/19.84 | | | | | Case 2: % 135.30/19.84 | | | | | | % 135.30/19.84 | | | | | | (83) all_57_2 = e2 & op(e2, e3) = e2 % 135.30/19.84 | | | | | | % 135.30/19.84 | | | | | | ALPHA: (83) implies: % 135.30/19.84 | | | | | | (84) all_57_2 = e2 % 135.30/19.84 | | | | | | (85) op(e2, e3) = e2 % 135.30/19.84 | | | | | | % 135.30/19.84 | | | | | | BETA: splitting (15) gives: % 135.30/19.84 | | | | | | % 135.30/19.84 | | | | | | Case 1: % 135.30/19.84 | | | | | | | % 135.30/19.84 | | | | | | | (86) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & % 135.30/19.84 | | | | | | | op(e2, e3) = e1) % 135.30/19.84 | | | | | | | % 135.30/19.84 | | | | | | | REF_CLOSE: (16), (17), (54), (56), (85), (86) are inconsistent by % 135.30/19.84 | | | | | | | sub-proof #69. % 135.30/19.84 | | | | | | | % 135.30/19.84 | | | | | | Case 2: % 135.30/19.84 | | | | | | | % 135.30/19.84 | | | | | | | (87) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & % 135.30/19.84 | | | | | | | op(e0, e3) = e1) % 135.30/19.84 | | | | | | | % 135.30/19.84 | | | | | | | BETA: splitting (87) gives: % 135.30/19.84 | | | | | | | % 135.30/19.84 | | | | | | | Case 1: % 135.30/19.84 | | | | | | | | % 135.30/19.84 | | | | | | | | (88) all_57_6 = e1 & op(e1, e3) = e1 % 135.30/19.84 | | | | | | | | % 135.30/19.84 | | | | | | | | ALPHA: (88) implies: % 135.30/19.84 | | | | | | | | (89) all_57_6 = e1 % 135.30/19.84 | | | | | | | | % 135.30/19.84 | | | | | | | | BETA: splitting (46) gives: % 135.30/19.84 | | | | | | | | % 135.30/19.84 | | | | | | | | Case 1: % 135.30/19.84 | | | | | | | | | % 135.30/19.84 | | | | | | | | | (90) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & % 135.30/19.84 | | | | | | | | | op(e1, e2) = e3) % 135.30/19.84 | | | | | | | | | % 135.30/19.84 | | | | | | | | | BETA: splitting (90) gives: % 135.30/19.84 | | | | | | | | | % 135.30/19.84 | | | | | | | | | Case 1: % 135.30/19.84 | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | (91) all_57_6 = e3 & op(e1, e3) = e3 % 135.30/19.84 | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | REF_CLOSE: (55), (89), (91) are inconsistent by sub-proof % 135.30/19.84 | | | | | | | | | | #61. % 135.30/19.84 | | | | | | | | | | % 135.30/19.84 | | | | | | | | | Case 2: % 135.30/19.84 | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | (92) all_57_7 = e3 & op(e1, e2) = e3 % 135.30/19.84 | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | ALPHA: (92) implies: % 135.30/19.84 | | | | | | | | | | (93) all_57_7 = e3 % 135.30/19.84 | | | | | | | | | | (94) op(e1, e2) = e3 % 135.30/19.84 | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | BETA: splitting (4) gives: % 135.30/19.84 | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | Case 1: % 135.30/19.84 | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | (95) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 % 135.30/19.84 | | | | | | | | | | | & op(e2, e2) = e0) % 135.30/19.84 | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | BETA: splitting (95) gives: % 135.30/19.84 | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | Case 1: % 135.30/19.84 | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | (96) all_57_1 = e0 & op(e3, e2) = e0 % 135.30/19.84 | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | REF_CLOSE: (2), (16), (47), (96) are inconsistent by % 135.30/19.84 | | | | | | | | | | | | sub-proof #693. % 135.30/19.84 | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | Case 2: % 135.30/19.84 | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | (97) all_57_3 = e0 & op(e2, e2) = e0 % 135.30/19.84 | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | ALPHA: (97) implies: % 135.30/19.84 | | | | | | | | | | | | (98) op(e2, e2) = e0 % 135.30/19.84 | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | BETA: splitting (24) gives: % 135.30/19.84 | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | Case 1: % 135.30/19.84 | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | (99) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 135.30/19.84 | | | | | | | | | | | | | & op(e2, e3) = e3) % 135.30/19.84 | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | BETA: splitting (99) gives: % 135.30/19.84 | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | Case 1: % 135.30/19.84 | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | (100) all_57_0 = e3 & op(e3, e3) = e3 % 135.30/19.84 | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | ALPHA: (100) implies: % 135.30/19.84 | | | | | | | | | | | | | | (101) op(e3, e3) = e3 % 135.30/19.84 | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (54), (101) are inconsistent by % 135.30/19.84 | | | | | | | | | | | | | | sub-proof #773. % 135.30/19.84 | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | Case 2: % 135.30/19.84 | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | (102) all_57_2 = e3 & op(e2, e3) = e3 % 135.30/19.84 | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | REF_CLOSE: (22), (84), (102) are inconsistent by sub-proof % 135.30/19.84 | | | | | | | | | | | | | | #590. % 135.30/19.84 | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | End of split % 135.30/19.84 | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | Case 2: % 135.30/19.84 | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | (103) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 135.30/19.84 | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 135.30/19.84 | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | BETA: splitting (103) gives: % 135.30/19.84 | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | Case 1: % 135.30/19.84 | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | (104) all_57_6 = e3 & op(e1, e3) = e3 % 135.30/19.84 | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | ALPHA: (104) implies: % 135.30/19.84 | | | | | | | | | | | | | | (105) all_57_6 = e3 % 135.30/19.84 | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | REF_CLOSE: (55), (89), (105) are inconsistent by sub-proof % 135.30/19.84 | | | | | | | | | | | | | | #575. % 135.30/19.84 | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | Case 2: % 135.30/19.84 | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | (106) all_57_12 = e3 & op(e0, e3) = e3 % 135.30/19.84 | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | ALPHA: (106) implies: % 135.30/19.84 | | | | | | | | | | | | | | (107) all_57_12 = e3 % 135.30/19.84 | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | BETA: splitting (51) gives: % 135.30/19.84 | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | Case 1: % 135.30/19.84 | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | (108) all_57_15 = e0 & op(e0, e0) = e0 % 135.30/19.84 | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | ALPHA: (108) implies: % 135.30/19.84 | | | | | | | | | | | | | | | (109) op(e0, e0) = e0 % 135.30/19.84 | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | REF_CLOSE: (16), (23), (56), (109) are inconsistent by % 135.30/19.84 | | | | | | | | | | | | | | | sub-proof #220. % 135.30/19.84 | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | Case 2: % 135.30/19.84 | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | (110) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 135.30/19.84 | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 135.30/19.84 | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 135.30/19.84 | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 135.30/19.84 | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 135.30/19.84 | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | ALPHA: (110) implies: % 135.30/19.84 | | | | | | | | | | | | | | | (111) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 135.30/19.84 | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 135.30/19.84 | | | | | | | | | | | | | | | e1) = e0) % 135.30/19.84 | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | BETA: splitting (57) gives: % 135.30/19.84 | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | Case 1: % 135.30/19.84 | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | (112) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 135.30/19.84 | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 135.30/19.84 | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (56), (85), (98), (112) are % 135.30/19.84 | | | | | | | | | | | | | | | | inconsistent by sub-proof #93. % 135.30/19.84 | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | Case 2: % 135.30/19.84 | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | (113) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 135.30/19.84 | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 135.30/19.84 | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | BETA: splitting (113) gives: % 135.30/19.84 | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | Case 1: % 135.30/19.84 | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | (114) all_57_5 = e1 & op(e2, e1) = e1 % 135.30/19.84 | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | ALPHA: (114) implies: % 135.30/19.84 | | | | | | | | | | | | | | | | | (115) all_57_5 = e1 % 135.30/19.84 | | | | | | | | | | | | | | | | | (116) op(e2, e1) = e1 % 135.30/19.84 | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | BETA: splitting (26) gives: % 135.30/19.84 | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.84 | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | (117) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 % 135.30/19.84 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3) % 135.30/19.84 | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives: % 135.30/19.84 | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.84 | | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | | (118) all_57_2 = e3 & op(e2, e3) = e3 % 135.30/19.84 | | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | | ALPHA: (118) implies: % 135.30/19.84 | | | | | | | | | | | | | | | | | | | (119) all_57_2 = e3 % 135.30/19.84 | | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (119) imply: % 135.30/19.84 | | | | | | | | | | | | | | | | | | | (120) e3 = e2 % 135.30/19.84 | | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | | SIMP: (120) implies: % 135.30/19.84 | | | | | | | | | | | | | | | | | | | (121) e3 = e2 % 135.30/19.84 | | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (121) imply: % 135.30/19.84 | | | | | | | | | | | | | | | | | | | (122) all_57_12 = e2 % 135.30/19.84 | | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (16), (23), (27), (28), (31), (64), (67), % 135.30/19.84 | | | | | | | | | | | | | | | | | | | (70), (72), (73), (74), (122) are inconsistent by % 135.30/19.84 | | | | | | | | | | | | | | | | | | | sub-proof #23. % 135.30/19.84 | | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.84 | | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | | (123) all_57_3 = e3 & op(e2, e2) = e3 % 135.30/19.84 | | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | | ALPHA: (123) implies: % 135.30/19.84 | | | | | | | | | | | | | | | | | | | (124) op(e2, e2) = e3 % 135.30/19.84 | | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (98), (124) are inconsistent by % 135.30/19.84 | | | | | | | | | | | | | | | | | | | sub-proof #641. % 135.30/19.84 | | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | End of split % 135.30/19.84 | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.84 | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | (125) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = % 135.30/19.84 | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 135.30/19.84 | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives: % 135.30/19.84 | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.84 | | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | | (126) all_57_5 = e3 & op(e2, e1) = e3 % 135.30/19.84 | | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | | ALPHA: (126) implies: % 135.30/19.84 | | | | | | | | | | | | | | | | | | | (127) all_57_5 = e3 % 135.30/19.84 | | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (115), (127) imply: % 135.30/19.84 | | | | | | | | | | | | | | | | | | | (128) e3 = e1 % 135.30/19.84 | | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | | SIMP: (128) implies: % 135.30/19.84 | | | | | | | | | | | | | | | | | | | (129) e3 = e1 % 135.30/19.84 | | | | | | | | | | | | | | | | | | | % 135.30/19.84 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (129) imply: % 135.30/19.84 | | | | | | | | | | | | | | | | | | | (130) all_57_12 = e1 % 135.30/19.84 | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (16), (19), (22), (23), (55), (56), % 135.30/19.85 | | | | | | | | | | | | | | | | | | | (79), (111), (130) are inconsistent by sub-proof % 135.30/19.85 | | | | | | | | | | | | | | | | | | | #4. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | (131) all_57_10 = e3 & op(e2, e0) = e3 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | ALPHA: (131) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | (132) op(e2, e0) = e3 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | (133) all_54_12 = e3 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (133) imply: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | (134) all_10_0 = e3 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | SIMP: (134) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | (135) all_10_0 = e3 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (135) imply: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | (136) ~ (all_52_2 = e3) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | (137) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (138) all_57_1 = e1 & op(e3, e2) = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (138) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (139) op(e3, e2) = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | (140) all_54_8 = e3 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (136), (140) are inconsistent by sub-proof % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | #121. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | (141) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | (142) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (143) all_57_9 = e2 & op(e3, e0) = e2 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (144) all_57_9 = e2 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (145) op(e3, e0) = e2 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (146) all_54_8 = e2 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (58), (146) are inconsistent by sub-proof % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | #430. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | (147) all_54_8 = e1 | all_54_8 = e0 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (148) all_54_8 = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (148) imply: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (149) all_52_2 = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (149) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (150) all_52_2 = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (150) imply: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (151) ~ (all_52_6 = e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (151) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (152) ~ (all_52_6 = e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (153) all_54_9 = e3 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (153) imply: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (154) all_52_6 = e3 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (154) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (155) all_52_6 = e3 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (20), (155) imply: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (156) ~ (all_52_4 = e3) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (157) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (159) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160) op(e3, e3) = e2 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (19), (42), (56), (84), (89), (107), % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160) are inconsistent by sub-proof #491. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (162) op(e3, e3) = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (16), (19), (22), (47), (55), (56), % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (60), (139), (144), (156), (162) are inconsistent % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #611. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (22), (49), (98), (145), (163) are % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #13. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (22), (29), (62), (165) are inconsistent by % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #42. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (166) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (167) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (167) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168) op(e2, e0) = e2 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (16), (22), (132), (168) are inconsistent by % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #546. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_29)))) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (171) ~ (all_56_19 = e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (172) op(e2, e1) = all_56_19 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (116), (171), (172) are inconsistent by % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #106. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (173) op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_29))) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_25) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (176) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (177) op(e0, e3) = e0 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (48), (59), (177) are inconsistent by % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #219. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_27) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179) ~ (all_56_19 = e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180) op(e2, e1) = all_56_19 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (116), (179), (180) are inconsistent by % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #106. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (181) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (52), (61), (62), (181) are inconsistent by % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #40. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182) ~ (all_54_9 = e3) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (32), (182) imply: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (183) ~ (all_52_6 = e3) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (35), (94), (183) are inconsistent by % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #654. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (184) all_54_8 = e0 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (58), (184) are inconsistent by sub-proof % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | #475. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (185) all_57_10 = e2 & op(e2, e0) = e2 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (186) op(e2, e0) = e2 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (16), (22), (132), (186) are inconsistent by % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #546. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | (187) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (188) all_57_11 = e2 & op(e1, e0) = e2 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (25), (61), (188) are inconsistent by % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #514. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (189) all_57_15 = e2 & op(e0, e0) = e2 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (189) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (190) all_57_15 = e2 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17), (19), (38), (51), (55), (56), (79), % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (107), (190) are inconsistent by sub-proof #11. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (191) all_57_3 = e1 & op(e2, e2) = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (192) op(e2, e2) = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (56), (98), (192) are inconsistent by % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | sub-proof #675. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | (193) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1) % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | Case 1: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (194) all_57_7 = e1 & op(e1, e2) = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (195) all_57_7 = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (195) imply: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (196) e3 = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | SIMP: (196) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (197) e3 = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (197) imply: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (198) all_57_12 = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (16), (19), (22), (23), (55), (56), % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (79), (111), (198) are inconsistent by sub-proof % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | #4. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | (199) all_57_13 = e1 & op(e0, e2) = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (28), (43), (199) are inconsistent by % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | sub-proof #178. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | (200) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (67), (73), (74), (200) are inconsistent by % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | sub-proof #24. % 135.30/19.85 | | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | (201) all_57_10 = e1 & op(e2, e0) = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | ALPHA: (201) implies: % 135.30/19.85 | | | | | | | | | | | | | | | | | (202) op(e2, e0) = e1 % 135.30/19.85 | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (13), (16), (202) are inconsistent by % 135.30/19.85 | | | | | | | | | | | | | | | | | sub-proof #180. % 135.30/19.85 | | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | (203) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = % 135.30/19.85 | | | | | | | | | | | e0 & op(e0, e2) = e0) % 135.30/19.85 | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | | REF_CLOSE: (6), (16), (30), (35), (79), (203) are % 135.30/19.85 | | | | | | | | | | | inconsistent by sub-proof #170. % 135.30/19.85 | | | | | | | | | | | % 135.30/19.85 | | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | | % 135.30/19.85 | | | | | | | | | End of split % 135.30/19.85 | | | | | | | | | % 135.30/19.85 | | | | | | | | Case 2: % 135.30/19.85 | | | | | | | | | % 135.30/19.85 | | | | | | | | | (204) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & % 135.30/19.85 | | | | | | | | | op(e1, e0) = e3) % 135.30/19.85 | | | | | | | | | % 135.30/19.85 | | | | | | | | | REF_CLOSE: (16), (19), (22), (29), (53), (204) are % 135.30/19.85 | | | | | | | | | inconsistent by sub-proof #3. % 135.30/19.85 | | | | | | | | | % 135.30/19.85 | | | | | | | | End of split % 135.30/19.85 | | | | | | | | % 135.30/19.86 | | | | | | | Case 2: % 135.30/19.86 | | | | | | | | % 135.30/19.86 | | | | | | | | (205) all_57_12 = e1 & op(e0, e3) = e1 % 135.30/19.86 | | | | | | | | % 135.30/19.86 | | | | | | | | ALPHA: (205) implies: % 135.30/19.86 | | | | | | | | (206) all_57_12 = e1 % 135.30/19.86 | | | | | | | | % 135.30/19.86 | | | | | | | | BETA: splitting (51) gives: % 135.30/19.86 | | | | | | | | % 135.30/19.86 | | | | | | | | Case 1: % 135.30/19.86 | | | | | | | | | % 135.30/19.86 | | | | | | | | | (207) all_57_15 = e0 & op(e0, e0) = e0 % 135.30/19.86 | | | | | | | | | % 135.30/19.86 | | | | | | | | | ALPHA: (207) implies: % 135.30/19.86 | | | | | | | | | (208) op(e0, e0) = e0 % 135.30/19.86 | | | | | | | | | % 135.30/19.86 | | | | | | | | | REF_CLOSE: (16), (23), (56), (208) are inconsistent by % 135.30/19.86 | | | | | | | | | sub-proof #220. % 135.30/19.86 | | | | | | | | | % 135.30/19.86 | | | | | | | | Case 2: % 135.30/19.86 | | | | | | | | | % 135.30/19.86 | | | | | | | | | (209) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 % 135.30/19.86 | | | | | | | | | & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 135.30/19.86 | | | | | | | | | = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | % 135.30/19.86 | | | | | | | | | (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = % 135.30/19.86 | | | | | | | | | e0 & op(e0, e1) = e0)) % 135.30/19.86 | | | | | | | | | % 135.30/19.86 | | | | | | | | | ALPHA: (209) implies: % 135.30/19.86 | | | | | | | | | (210) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 % 135.30/19.86 | | | | | | | | | & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = % 135.30/19.86 | | | | | | | | | e0) % 135.30/19.86 | | | | | | | | | % 135.30/19.86 | | | | | | | | | REF_CLOSE: (6), (11), (16), (19), (22), (23), (55), (56), % 135.30/19.86 | | | | | | | | | (79), (206), (210) are inconsistent by sub-proof % 135.30/19.86 | | | | | | | | | #4. % 135.30/19.86 | | | | | | | | | % 135.30/19.86 | | | | | | | | End of split % 135.30/19.86 | | | | | | | | % 135.30/19.86 | | | | | | | End of split % 135.30/19.86 | | | | | | | % 135.30/19.86 | | | | | | End of split % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | End of split % 135.30/19.86 | | | | | % 135.30/19.86 | | | | Case 2: % 135.30/19.86 | | | | | % 135.30/19.86 | | | | | (211) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, % 135.30/19.86 | | | | | e3) = e2) % 135.30/19.86 | | | | | % 135.30/19.86 | | | | | BETA: splitting (211) gives: % 135.30/19.86 | | | | | % 135.30/19.86 | | | | | Case 1: % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | | (212) all_57_6 = e2 & op(e1, e3) = e2 % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | | REF_CLOSE: (7), (16), (44), (212) are inconsistent by sub-proof % 135.30/19.86 | | | | | | #341. % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | Case 2: % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | | (213) all_57_12 = e2 & op(e0, e3) = e2 % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | | ALPHA: (213) implies: % 135.30/19.86 | | | | | | (214) all_57_12 = e2 % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | | REF_CLOSE: (11), (16), (23), (27), (28), (31), (64), (67), (70), % 135.30/19.86 | | | | | | (72), (73), (74), (214) are inconsistent by sub-proof % 135.30/19.86 | | | | | | #23. % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | End of split % 135.30/19.86 | | | | | % 135.30/19.86 | | | | End of split % 135.30/19.86 | | | | % 135.30/19.86 | | | End of split % 135.30/19.86 | | | % 135.30/19.86 | | Case 2: % 135.30/19.86 | | | % 135.30/19.86 | | | (215) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) % 135.30/19.86 | | | = e2) % 135.30/19.86 | | | % 135.30/19.86 | | | REF_CLOSE: (5), (16), (17), (23), (27), (215) are inconsistent by % 135.30/19.86 | | | sub-proof #34. % 135.30/19.86 | | | % 135.30/19.86 | | End of split % 135.30/19.86 | | % 135.30/19.86 | Case 2: % 135.30/19.86 | | % 135.30/19.86 | | (216) ~ (all_10_1 = e1) & op(e0, e0) = all_10_1 & $i(all_10_1) % 135.30/19.86 | | % 135.30/19.86 | | ALPHA: (216) implies: % 135.30/19.86 | | (217) ~ (all_10_1 = e1) % 135.30/19.86 | | (218) op(e0, e0) = all_10_1 % 135.30/19.86 | | % 135.30/19.86 | | GROUND_INST: instantiating (16) with e1, all_10_1, e0, e0, simplifying with % 135.30/19.86 | | (23), (218) gives: % 135.30/19.86 | | (219) all_10_1 = e1 % 135.30/19.86 | | % 135.30/19.86 | | REDUCE: (217), (219) imply: % 135.30/19.86 | | (220) $false % 135.30/19.86 | | % 135.30/19.86 | | CLOSE: (220) is inconsistent. % 135.30/19.86 | | % 135.30/19.86 | End of split % 135.30/19.86 | % 135.30/19.86 End of proof % 135.30/19.86 % 135.30/19.86 Sub-proof #3 shows that the following formulas are inconsistent: % 135.30/19.86 ---------------------------------------------------------------- % 135.30/19.86 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.30/19.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.30/19.86 (2) ~ (e3 = e0) % 135.30/19.86 (3) ~ (e3 = e2) % 135.30/19.86 (4) op(e1, e1) = e2 % 135.30/19.86 (5) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 135.30/19.86 (6) all_57_11 = e0 % 135.30/19.86 % 135.30/19.86 Begin of proof % 135.30/19.86 | % 135.30/19.86 | BETA: splitting (5) gives: % 135.30/19.86 | % 135.30/19.86 | Case 1: % 135.30/19.86 | | % 135.30/19.86 | | (7) all_57_8 = e3 & op(e1, e1) = e3 % 135.30/19.86 | | % 135.30/19.86 | | ALPHA: (7) implies: % 135.30/19.86 | | (8) op(e1, e1) = e3 % 135.30/19.86 | | % 135.30/19.86 | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #109. % 135.30/19.86 | | % 135.30/19.86 | Case 2: % 135.30/19.86 | | % 135.30/19.86 | | (9) all_57_11 = e3 & op(e1, e0) = e3 % 135.30/19.86 | | % 135.30/19.86 | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #256. % 135.30/19.86 | | % 135.30/19.86 | End of split % 135.30/19.86 | % 135.30/19.86 End of proof % 135.30/19.86 % 135.30/19.86 Sub-proof #4 shows that the following formulas are inconsistent: % 135.30/19.86 ---------------------------------------------------------------- % 135.30/19.86 (1) ~ (e2 = e0) % 135.30/19.86 (2) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) | % 135.30/19.86 (all_57_14 = e0 & op(e0, e1) = e0) % 135.30/19.86 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 135.30/19.86 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 135.30/19.86 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.30/19.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.30/19.86 (5) ~ (e3 = e0) % 135.30/19.86 (6) ~ (e3 = e2) % 135.30/19.86 (7) op(e0, e0) = e1 % 135.30/19.86 (8) all_57_13 = e2 % 135.30/19.86 (9) ~ (e3 = e1) % 135.30/19.86 (10) ~ (e1 = e0) % 135.30/19.86 (11) all_57_12 = e1 % 135.30/19.86 % 135.30/19.86 Begin of proof % 135.30/19.86 | % 135.30/19.86 | BETA: splitting (3) gives: % 135.30/19.86 | % 135.30/19.86 | Case 1: % 135.30/19.86 | | % 135.30/19.86 | | (12) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = % 135.30/19.86 | | e3) % 135.30/19.86 | | % 135.30/19.86 | | BETA: splitting (12) gives: % 135.30/19.86 | | % 135.30/19.86 | | Case 1: % 135.30/19.86 | | | % 135.30/19.86 | | | (13) all_57_12 = e3 & op(e0, e3) = e3 % 135.30/19.86 | | | % 135.30/19.86 | | | REF_CLOSE: (9), (11), (13) are inconsistent by sub-proof #394. % 135.30/19.86 | | | % 135.30/19.86 | | Case 2: % 135.30/19.86 | | | % 135.30/19.86 | | | (14) all_57_13 = e3 & op(e0, e2) = e3 % 135.30/19.86 | | | % 135.30/19.86 | | | ALPHA: (14) implies: % 135.30/19.86 | | | (15) all_57_13 = e3 % 135.30/19.86 | | | % 135.30/19.86 | | | COMBINE_EQS: (8), (15) imply: % 135.30/19.86 | | | (16) e3 = e2 % 135.30/19.86 | | | % 135.30/19.86 | | | REDUCE: (6), (16) imply: % 135.30/19.86 | | | (17) $false % 135.30/19.86 | | | % 135.30/19.86 | | | CLOSE: (17) is inconsistent. % 135.30/19.86 | | | % 135.30/19.86 | | End of split % 135.30/19.86 | | % 135.30/19.86 | Case 2: % 135.30/19.86 | | % 135.30/19.86 | | (18) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = % 135.30/19.86 | | e3) % 135.30/19.86 | | % 135.30/19.86 | | BETA: splitting (18) gives: % 135.30/19.86 | | % 135.30/19.86 | | Case 1: % 135.30/19.86 | | | % 135.30/19.86 | | | (19) all_57_14 = e3 & op(e0, e1) = e3 % 135.30/19.86 | | | % 135.30/19.86 | | | ALPHA: (19) implies: % 135.30/19.86 | | | (20) all_57_14 = e3 % 135.30/19.86 | | | % 135.30/19.86 | | | REF_CLOSE: (1), (2), (5), (8), (10), (11), (20) are inconsistent by % 135.30/19.86 | | | sub-proof #399. % 135.30/19.86 | | | % 135.30/19.86 | | Case 2: % 135.30/19.86 | | | % 135.30/19.86 | | | (21) all_57_15 = e3 & op(e0, e0) = e3 % 135.30/19.86 | | | % 135.30/19.86 | | | ALPHA: (21) implies: % 135.30/19.86 | | | (22) op(e0, e0) = e3 % 135.30/19.86 | | | % 135.30/19.86 | | | REF_CLOSE: (4), (7), (9), (22) are inconsistent by sub-proof #606. % 135.30/19.86 | | | % 135.30/19.86 | | End of split % 135.30/19.86 | | % 135.30/19.86 | End of split % 135.30/19.86 | % 135.30/19.86 End of proof % 135.30/19.86 % 135.30/19.86 Sub-proof #5 shows that the following formulas are inconsistent: % 135.30/19.86 ---------------------------------------------------------------- % 135.30/19.86 (1) all_57_11 = e3 & op(e1, e0) = e3 % 135.30/19.86 (2) all_57_11 = e0 % 135.30/19.86 (3) ~ (e3 = e0) % 135.30/19.86 % 135.30/19.86 Begin of proof % 135.30/19.86 | % 135.30/19.86 | ALPHA: (1) implies: % 135.30/19.86 | (4) all_57_11 = e3 % 135.30/19.86 | % 135.30/19.86 | COMBINE_EQS: (2), (4) imply: % 135.30/19.86 | (5) e3 = e0 % 135.30/19.86 | % 135.30/19.86 | SIMP: (5) implies: % 135.30/19.86 | (6) e3 = e0 % 135.30/19.86 | % 135.30/19.86 | REDUCE: (3), (6) imply: % 135.30/19.86 | (7) $false % 135.30/19.86 | % 135.30/19.86 | CLOSE: (7) is inconsistent. % 135.30/19.86 | % 135.30/19.86 End of proof % 135.30/19.86 % 135.30/19.86 Sub-proof #6 shows that the following formulas are inconsistent: % 135.30/19.86 ---------------------------------------------------------------- % 135.30/19.86 (1) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 135.30/19.86 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.30/19.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.30/19.86 (3) op(e0, e0) = e1 % 135.30/19.86 (4) ~ (e3 = e1) % 135.30/19.86 (5) all_57_14 = e1 % 135.30/19.86 % 135.30/19.86 Begin of proof % 135.30/19.86 | % 135.30/19.86 | BETA: splitting (1) gives: % 135.30/19.86 | % 135.30/19.86 | Case 1: % 135.30/19.86 | | % 135.30/19.86 | | (6) all_57_14 = e3 & op(e0, e1) = e3 % 135.30/19.86 | | % 135.30/19.86 | | ALPHA: (6) implies: % 135.30/19.86 | | (7) all_57_14 = e3 % 135.30/19.86 | | % 135.30/19.86 | | COMBINE_EQS: (5), (7) imply: % 135.30/19.86 | | (8) e3 = e1 % 135.30/19.86 | | % 135.30/19.86 | | REDUCE: (4), (8) imply: % 135.30/19.86 | | (9) $false % 135.30/19.86 | | % 135.30/19.86 | | CLOSE: (9) is inconsistent. % 135.30/19.86 | | % 135.30/19.86 | Case 2: % 135.30/19.86 | | % 135.30/19.86 | | (10) all_57_15 = e3 & op(e0, e0) = e3 % 135.30/19.86 | | % 135.30/19.86 | | ALPHA: (10) implies: % 135.30/19.86 | | (11) op(e0, e0) = e3 % 135.30/19.86 | | % 135.30/19.86 | | REF_CLOSE: (2), (3), (4), (11) are inconsistent by sub-proof #606. % 135.30/19.86 | | % 135.30/19.86 | End of split % 135.30/19.86 | % 135.30/19.86 End of proof % 135.30/19.86 % 135.30/19.86 Sub-proof #7 shows that the following formulas are inconsistent: % 135.30/19.86 ---------------------------------------------------------------- % 135.30/19.86 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 135.30/19.86 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 135.30/19.86 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) | % 135.30/19.86 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 135.30/19.86 (3) ~ (all_52_13 = e0) % 135.30/19.86 (4) op(e2, e0) = all_52_13 % 135.30/19.86 (5) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 135.30/19.86 (6) ~ (all_52_11 = e2) % 135.30/19.86 (7) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 135.30/19.86 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 135.30/19.86 (8) ~ (all_52_13 = e1) % 135.30/19.86 (9) ~ (all_52_7 = e3) % 135.30/19.86 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.30/19.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.30/19.86 (11) ~ (e3 = e0) % 135.30/19.86 (12) ~ (all_52_1 = all_52_13) % 135.30/19.86 (13) op(e0, e0) = e1 % 135.30/19.86 (14) all_57_8 = e2 % 135.30/19.86 (15) op(e2, e2) = e3 % 135.30/19.86 (16) ~ (all_52_3 = e3) % 135.30/19.86 (17) ~ (all_52_1 = all_52_9) % 135.30/19.86 (18) op(e0, e1) = all_52_11 % 135.30/19.86 (19) op(e0, e2) = all_52_7 % 135.30/19.86 (20) op(e1, e1) = e2 % 135.30/19.86 (21) ~ (all_10_2 = e0) % 135.30/19.86 (22) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 135.30/19.86 (23) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.30/19.86 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.30/19.86 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.30/19.86 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.30/19.86 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 135.30/19.86 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.30/19.86 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) % 135.30/19.86 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.30/19.86 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.86 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 135.30/19.86 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.86 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 135.30/19.86 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 135.30/19.86 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.30/19.86 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) % 135.30/19.86 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 135.30/19.86 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 135.30/19.86 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 135.30/19.86 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.30/19.86 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.30/19.86 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.30/19.86 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 135.30/19.86 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & % 135.30/19.86 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & % 135.30/19.86 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.30/19.86 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.30/19.86 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.30/19.86 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.86 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ % 135.30/19.86 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.86 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 135.30/19.86 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 135.30/19.86 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.30/19.86 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) % 135.30/19.86 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.30/19.86 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.30/19.86 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 % 135.30/19.86 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.86 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = % 135.30/19.86 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.30/19.86 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 135.30/19.86 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.30/19.86 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.30/19.86 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 135.30/19.86 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.30/19.86 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.30/19.86 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.30/19.86 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.86 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.30/19.86 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.30/19.86 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.30/19.86 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.30/19.86 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.30/19.86 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.30/19.86 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.30/19.86 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.30/19.86 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.30/19.86 $i(all_56_29)))) % 135.30/19.86 (24) op(e3, e3) = all_10_2 % 135.30/19.86 (25) ~ (all_52_9 = e3) % 135.30/19.86 (26) op(e2, e1) = all_52_9 % 135.30/19.86 (27) ( ~ (all_6_0 = e0) & op(e2, e1) = all_6_0 & $i(all_6_0)) | ( ~ (all_6_1 % 135.30/19.86 = e3) & op(e2, e2) = all_6_1 & $i(all_6_1)) % 135.30/19.86 (28) op(e0, e3) = all_52_3 % 135.30/19.86 (29) ~ (all_52_13 = e3) % 135.30/19.86 (30) all_54_6 = all_52_9 % 135.30/19.86 (31) op(e2, e3) = all_52_1 % 135.30/19.86 (32) ~ (all_52_14 = e1) % 135.30/19.86 (33) all_54_7 = all_52_13 % 135.30/19.86 (34) op(e3, e1) = all_52_8 % 135.30/19.86 (35) ~ (e3 = e1) % 135.30/19.86 (36) ~ (e1 = e0) % 135.30/19.86 (37) ~ (all_52_9 = all_52_13) % 135.30/19.86 (38) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) | % 135.30/19.86 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) % 135.30/19.86 (39) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 135.30/19.86 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 135.30/19.86 (40) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 135.30/19.86 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 135.30/19.86 (41) op(e1, e0) = all_52_14 % 135.30/19.86 (42) op(e1, e0) = e0 % 135.30/19.86 % 135.30/19.86 Begin of proof % 135.30/19.86 | % 135.30/19.86 | BETA: splitting (27) gives: % 135.30/19.86 | % 135.30/19.86 | Case 1: % 135.30/19.86 | | % 135.30/19.86 | | (43) ~ (all_6_0 = e0) & op(e2, e1) = all_6_0 & $i(all_6_0) % 135.30/19.86 | | % 135.30/19.86 | | ALPHA: (43) implies: % 135.30/19.86 | | (44) ~ (all_6_0 = e0) % 135.30/19.86 | | (45) op(e2, e1) = all_6_0 % 135.30/19.86 | | % 135.30/19.86 | | BETA: splitting (5) gives: % 135.30/19.86 | | % 135.30/19.86 | | Case 1: % 135.30/19.86 | | | % 135.30/19.86 | | | (46) all_54_7 = e3 % 135.30/19.86 | | | % 135.30/19.86 | | | COMBINE_EQS: (33), (46) imply: % 135.30/19.86 | | | (47) all_52_13 = e3 % 135.30/19.86 | | | % 135.30/19.86 | | | REDUCE: (29), (47) imply: % 135.30/19.86 | | | (48) $false % 135.30/19.86 | | | % 135.30/19.86 | | | CLOSE: (48) is inconsistent. % 135.30/19.86 | | | % 135.30/19.86 | | Case 2: % 135.30/19.86 | | | % 135.30/19.86 | | | (49) ~ (all_54_7 = e3) % 135.30/19.86 | | | (50) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 135.30/19.86 | | | % 135.30/19.86 | | | BETA: splitting (50) gives: % 135.30/19.86 | | | % 135.30/19.86 | | | Case 1: % 135.30/19.86 | | | | % 135.30/19.86 | | | | (51) all_54_7 = e2 % 135.30/19.86 | | | | % 135.30/19.86 | | | | COMBINE_EQS: (33), (51) imply: % 135.30/19.86 | | | | (52) all_52_13 = e2 % 135.30/19.86 | | | | % 135.30/19.86 | | | | REDUCE: (12), (52) imply: % 135.30/19.86 | | | | (53) ~ (all_52_1 = e2) % 135.30/19.86 | | | | % 135.30/19.86 | | | | REDUCE: (37), (52) imply: % 135.30/19.86 | | | | (54) ~ (all_52_9 = e2) % 135.30/19.86 | | | | % 135.30/19.86 | | | | REDUCE: (29), (52) imply: % 135.30/19.86 | | | | (55) ~ (e3 = e2) % 135.30/19.86 | | | | % 135.30/19.86 | | | | SIMP: (55) implies: % 135.30/19.86 | | | | (56) ~ (e3 = e2) % 135.30/19.86 | | | | % 135.30/19.86 | | | | REDUCE: (3), (52) imply: % 135.30/19.86 | | | | (57) ~ (e2 = e0) % 135.30/19.86 | | | | % 135.30/19.86 | | | | BETA: splitting (7) gives: % 135.30/19.86 | | | | % 135.30/19.86 | | | | Case 1: % 135.30/19.86 | | | | | % 135.30/19.86 | | | | | (58) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, % 135.30/19.86 | | | | | e2) = e3) % 135.30/19.86 | | | | | % 135.30/19.86 | | | | | BETA: splitting (58) gives: % 135.30/19.86 | | | | | % 135.30/19.86 | | | | | Case 1: % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | | (59) all_57_12 = e3 & op(e0, e3) = e3 % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | | REF_CLOSE: (10), (16), (28), (59) are inconsistent by sub-proof % 135.30/19.86 | | | | | | #628. % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | Case 2: % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | | (60) all_57_13 = e3 & op(e0, e2) = e3 % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | | REF_CLOSE: (9), (10), (19), (60) are inconsistent by sub-proof #556. % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | End of split % 135.30/19.86 | | | | | % 135.30/19.86 | | | | Case 2: % 135.30/19.86 | | | | | % 135.30/19.86 | | | | | (61) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, % 135.30/19.86 | | | | | e0) = e3) % 135.30/19.86 | | | | | % 135.30/19.86 | | | | | BETA: splitting (61) gives: % 135.30/19.86 | | | | | % 135.30/19.86 | | | | | Case 1: % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | | (62) all_57_14 = e3 & op(e0, e1) = e3 % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | | ALPHA: (62) implies: % 135.30/19.86 | | | | | | (63) all_57_14 = e3 % 135.30/19.86 | | | | | | (64) op(e0, e1) = e3 % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | | BETA: splitting (23) gives: % 135.30/19.86 | | | | | | % 135.30/19.86 | | | | | | Case 1: % 135.30/19.86 | | | | | | | % 135.30/19.86 | | | | | | | (65) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ % 135.30/19.86 | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = % 135.30/19.86 | | | | | | | e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = % 135.30/19.86 | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.30/19.86 | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.30/19.86 | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.86 | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ % 135.30/19.86 | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = % 135.30/19.86 | | | | | | | e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = % 135.30/19.86 | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.30/19.86 | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.30/19.86 | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.30/19.86 | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ % 135.30/19.86 | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = % 135.30/19.86 | | | | | | | e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 135.30/19.86 | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 135.30/19.86 | | | | | | | all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.30/19.86 | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.30/19.86 | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ % 135.30/19.86 | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = % 135.30/19.86 | | | | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 135.30/19.86 | | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e2, % 135.30/19.86 | | | | | | | e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & % 135.30/19.86 | | | | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 135.30/19.86 | | | | | | | % 135.30/19.86 | | | | | | | BETA: splitting (65) gives: % 135.30/19.86 | | | | | | | % 135.30/19.86 | | | | | | | Case 1: % 135.30/19.86 | | | | | | | | % 135.30/19.86 | | | | | | | | (66) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ % 135.30/19.86 | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.30/19.86 | | | | | | | | = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, % 135.30/19.86 | | | | | | | | e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) % 135.30/19.86 | | | | | | | | = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.30/19.86 | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.86 | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & % 135.30/19.86 | | | | | | | | ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.30/19.86 | | | | | | | | (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & % 135.30/19.86 | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.30/19.86 | | | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.30/19.86 | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.30/19.86 | | | | | | | | $i(all_56_29)) % 135.30/19.86 | | | | | | | | % 135.30/19.86 | | | | | | | | BETA: splitting (66) gives: % 135.30/19.86 | | | | | | | | % 135.30/19.86 | | | | | | | | Case 1: % 135.30/19.86 | | | | | | | | | % 135.30/19.86 | | | | | | | | | (67) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & % 135.30/19.86 | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.30/19.86 | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & % 135.30/19.86 | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.30/19.86 | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.30/19.86 | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.30/19.86 | | | | | | | | | $i(all_56_27) % 135.30/19.86 | | | | | | | | | % 135.30/19.86 | | | | | | | | | ALPHA: (67) implies: % 135.30/19.86 | | | | | | | | | (68) ~ (all_56_27 = e0) % 135.30/19.86 | | | | | | | | | (69) ~ (all_56_19 = e1) % 135.30/19.86 | | | | | | | | | (70) op(e2, e0) = all_56_27 % 135.30/19.87 | | | | | | | | | (71) op(e2, e1) = all_56_19 % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | | REF_CLOSE: (4), (8), (10), (11), (15), (35), (36), (39), (40), % 135.30/19.87 | | | | | | | | | (44), (45), (68), (69), (70), (71) are inconsistent % 135.30/19.87 | | | | | | | | | by sub-proof #10. % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | Case 2: % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | | (72) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & % 135.30/19.87 | | | | | | | | | ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.30/19.87 | | | | | | | | | (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & % 135.30/19.87 | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.30/19.87 | | | | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.30/19.87 | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.30/19.87 | | | | | | | | | $i(all_56_29) % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | | ALPHA: (72) implies: % 135.30/19.87 | | | | | | | | | (73) op(e1, e0) = all_56_29 % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (8), (10), (11), (13), (14), % 135.30/19.87 | | | | | | | | | (15), (17), (18), (20), (21), (22), (23), (24), % 135.30/19.87 | | | | | | | | | (25), (26), (30), (31), (32), (34), (35), (36), % 135.30/19.87 | | | | | | | | | (38), (39), (40), (41), (42), (44), (45), (53), % 135.30/19.87 | | | | | | | | | (54), (56), (57), (63), (64), (73) are inconsistent % 135.30/19.87 | | | | | | | | | by sub-proof #8. % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | End of split % 135.30/19.87 | | | | | | | | % 135.30/19.87 | | | | | | | Case 2: % 135.30/19.87 | | | | | | | | % 135.30/19.87 | | | | | | | | (74) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & % 135.30/19.87 | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.87 | | | | | | | | (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & % 135.30/19.87 | | | | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.30/19.87 | | | | | | | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 135.30/19.87 | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.30/19.87 | | | | | | | | $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ % 135.30/19.87 | | | | | | | | (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.30/19.87 | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.30/19.87 | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.30/19.87 | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) % 135.30/19.87 | | | | | | | | = e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.30/19.87 | | | | | | | | $i(all_56_25)) % 135.30/19.87 | | | | | | | | % 135.30/19.87 | | | | | | | | REF_CLOSE: (10), (21), (24), (31), (53), (74) are inconsistent % 135.30/19.87 | | | | | | | | by sub-proof #533. % 135.30/19.87 | | | | | | | | % 135.30/19.87 | | | | | | | End of split % 135.30/19.87 | | | | | | | % 135.30/19.87 | | | | | | Case 2: % 135.30/19.87 | | | | | | | % 135.30/19.87 | | | | | | | (75) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ % 135.30/19.87 | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = % 135.30/19.87 | | | | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 135.30/19.87 | | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e1, % 135.30/19.87 | | | | | | | e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & % 135.30/19.87 | | | | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.30/19.87 | | | | | | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.30/19.87 | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = % 135.30/19.87 | | | | | | | e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = % 135.30/19.87 | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.30/19.87 | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.30/19.87 | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.30/19.87 | | | | | | | (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.30/19.87 | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = % 135.30/19.87 | | | | | | | e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 135.30/19.87 | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 135.30/19.87 | | | | | | | all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.30/19.87 | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.30/19.87 | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.30/19.87 | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = % 135.30/19.87 | | | | | | | e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.30/19.87 | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e1, % 135.30/19.87 | | | | | | | e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.30/19.87 | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, % 135.30/19.87 | | | | | | | e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.30/19.87 | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.30/19.87 | | | | | | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 135.30/19.87 | | | | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 135.30/19.87 | | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.30/19.87 | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.87 | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & % 135.30/19.87 | | | | | | | all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 135.30/19.87 | | | | | | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) % 135.30/19.87 | | | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.30/19.87 | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.30/19.87 | | | | | | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.30/19.87 | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & % 135.30/19.87 | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 % 135.30/19.87 | | | | | | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) % 135.30/19.87 | | | | | | | & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 135.30/19.87 | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 135.30/19.87 | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.30/19.87 | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & % 135.30/19.87 | | | | | | | ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.30/19.87 | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) % 135.30/19.87 | | | | | | | = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.30/19.87 | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 % 135.30/19.87 | | | | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.30/19.87 | | | | | | | $i(all_56_29)))) % 135.30/19.87 | | | | | | | % 135.30/19.87 | | | | | | | BETA: splitting (75) gives: % 135.30/19.87 | | | | | | | % 135.30/19.87 | | | | | | | Case 1: % 135.30/19.87 | | | | | | | | % 135.30/19.87 | | | | | | | | (76) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & % 135.30/19.87 | | | | | | | | ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.30/19.87 | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) % 135.30/19.87 | | | | | | | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = % 135.30/19.87 | | | | | | | | all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & % 135.30/19.87 | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.30/19.87 | | | | | | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ % 135.30/19.87 | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 % 135.30/19.87 | | | | | | | | = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & % 135.30/19.87 | | | | | | | | op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.30/19.87 | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.30/19.87 | | | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.87 | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.30/19.87 | | | | | | | | % 135.30/19.87 | | | | | | | | BETA: splitting (76) gives: % 135.30/19.87 | | | | | | | | % 135.30/19.87 | | | | | | | | Case 1: % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | | (77) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & % 135.30/19.87 | | | | | | | | | ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.30/19.87 | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) % 135.30/19.87 | | | | | | | | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = % 135.30/19.87 | | | | | | | | | all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & % 135.30/19.87 | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.30/19.87 | | | | | | | | | $i(all_56_25) % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | | ALPHA: (77) implies: % 135.30/19.87 | | | | | | | | | (78) op(e1, e1) = e3 % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | | REF_CLOSE: (10), (20), (56), (78) are inconsistent by % 135.30/19.87 | | | | | | | | | sub-proof #109. % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | Case 2: % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | | (79) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & % 135.30/19.87 | | | | | | | | | ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.30/19.87 | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & % 135.30/19.87 | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.30/19.87 | | | | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.30/19.87 | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.30/19.87 | | | | | | | | | $i(all_56_29) % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | | ALPHA: (79) implies: % 135.30/19.87 | | | | | | | | | (80) op(e1, e0) = all_56_29 % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (8), (10), (11), (13), (14), % 135.30/19.87 | | | | | | | | | (15), (17), (18), (20), (21), (22), (23), (24), % 135.30/19.87 | | | | | | | | | (25), (26), (30), (31), (32), (34), (35), (36), % 135.30/19.87 | | | | | | | | | (38), (39), (40), (41), (42), (44), (45), (53), % 135.30/19.87 | | | | | | | | | (54), (56), (57), (63), (64), (80) are inconsistent % 135.30/19.87 | | | | | | | | | by sub-proof #8. % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | End of split % 135.30/19.87 | | | | | | | | % 135.30/19.87 | | | | | | | Case 2: % 135.30/19.87 | | | | | | | | % 135.30/19.87 | | | | | | | | (81) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & % 135.30/19.87 | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.87 | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & % 135.30/19.87 | | | | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.30/19.87 | | | | | | | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 135.30/19.87 | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.30/19.87 | | | | | | | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ % 135.30/19.87 | | | | | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 % 135.30/19.87 | | | | | | | | = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 % 135.30/19.87 | | | | | | | | & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.30/19.87 | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) % 135.30/19.87 | | | | | | | | = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.30/19.87 | | | | | | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & % 135.30/19.87 | | | | | | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 135.30/19.87 | | | | | | | | (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 135.30/19.87 | | | | | | | | (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, % 135.30/19.87 | | | | | | | | e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.30/19.87 | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.30/19.87 | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.87 | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & % 135.30/19.87 | | | | | | | | all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.30/19.87 | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.30/19.87 | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, % 135.30/19.87 | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.30/19.87 | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.30/19.87 | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.30/19.87 | | | | | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 % 135.30/19.87 | | | | | | | | & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ % 135.30/19.87 | | | | | | | | (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, % 135.30/19.87 | | | | | | | | e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 135.30/19.87 | | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 135.30/19.87 | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.30/19.87 | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.30/19.87 | | | | | | | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.30/19.87 | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, % 135.30/19.87 | | | | | | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, % 135.30/19.87 | | | | | | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.30/19.87 | | | | | | | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.87 | | | | | | | | $i(all_56_21) & $i(all_56_29)))) % 135.30/19.87 | | | | | | | | % 135.30/19.87 | | | | | | | | BETA: splitting (81) gives: % 135.30/19.87 | | | | | | | | % 135.30/19.87 | | | | | | | | Case 1: % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | | (82) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & % 135.30/19.87 | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.87 | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & % 135.30/19.87 | | | | | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.30/19.87 | | | | | | | | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 135.30/19.87 | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.30/19.87 | | | | | | | | | $i(all_56_31) % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | | ALPHA: (82) implies: % 135.30/19.87 | | | | | | | | | (83) op(e2, e2) = e0 % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | | REF_CLOSE: (10), (11), (15), (83) are inconsistent by % 135.30/19.87 | | | | | | | | | sub-proof #641. % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | Case 2: % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | | (84) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) % 135.30/19.87 | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.30/19.87 | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, % 135.30/19.87 | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.30/19.87 | | | | | | | | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = % 135.30/19.87 | | | | | | | | | e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.30/19.87 | | | | | | | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & % 135.30/19.87 | | | | | | | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & % 135.30/19.87 | | | | | | | | | ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 135.30/19.87 | | | | | | | | | (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, % 135.30/19.87 | | | | | | | | | e3) = all_56_1 & op(e3, e2) = all_56_9 & % 135.30/19.87 | | | | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 135.30/19.87 | | | | | | | | | & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 135.30/19.87 | | | | | | | | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 135.30/19.87 | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.30/19.87 | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.30/19.87 | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.30/19.87 | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.30/19.87 | | | | | | | | | & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.30/19.87 | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.30/19.87 | | | | | | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = % 135.30/19.87 | | | | | | | | | e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & % 135.30/19.87 | | | | | | | | | ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.30/19.87 | | | | | | | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 135.30/19.87 | | | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 135.30/19.87 | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.30/19.87 | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = % 135.30/19.87 | | | | | | | | | e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & % 135.30/19.87 | | | | | | | | | ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.30/19.87 | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.30/19.87 | | | | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 % 135.30/19.87 | | | | | | | | | & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) % 135.30/19.87 | | | | | | | | | & $i(all_56_21) & $i(all_56_29)))) % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | | BETA: splitting (84) gives: % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | | Case 1: % 135.30/19.87 | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | (85) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) % 135.30/19.87 | | | | | | | | | | & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.30/19.87 | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, % 135.30/19.87 | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.30/19.87 | | | | | | | | | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = % 135.30/19.87 | | | | | | | | | | e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.30/19.87 | | | | | | | | | | $i(all_56_27) % 135.30/19.87 | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | ALPHA: (85) implies: % 135.30/19.87 | | | | | | | | | | (86) ~ (all_56_27 = e0) % 135.30/19.87 | | | | | | | | | | (87) ~ (all_56_19 = e1) % 135.30/19.87 | | | | | | | | | | (88) op(e2, e0) = all_56_27 % 135.30/19.87 | | | | | | | | | | (89) op(e2, e1) = all_56_19 % 135.30/19.87 | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | REF_CLOSE: (4), (8), (10), (11), (15), (35), (36), (39), % 135.30/19.87 | | | | | | | | | | (40), (44), (45), (86), (87), (88), (89) are % 135.30/19.87 | | | | | | | | | | inconsistent by sub-proof #10. % 135.30/19.87 | | | | | | | | | | % 135.30/19.87 | | | | | | | | | Case 2: % 135.30/19.87 | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | (90) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 % 135.30/19.87 | | | | | | | | | | = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.30/19.87 | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.30/19.87 | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.30/19.87 | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.30/19.87 | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.30/19.87 | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.30/19.87 | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.30/19.87 | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 135.30/19.87 | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.30/19.87 | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.30/19.87 | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 135.30/19.87 | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 135.30/19.87 | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.30/19.87 | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.30/19.87 | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.87 | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 135.30/19.87 | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.30/19.87 | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 135.30/19.87 | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.30/19.87 | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.30/19.87 | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.30/19.87 | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.30/19.87 | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.30/19.87 | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 135.30/19.87 | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.87 | | | | | | | | | | $i(all_56_21) & $i(all_56_29))) % 135.30/19.87 | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | ALPHA: (90) implies: % 135.30/19.87 | | | | | | | | | | (91) op(e0, e0) = all_56_31 % 135.30/19.87 | | | | | | | | | | (92) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) % 135.30/19.87 | | | | | | | | | | & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.30/19.87 | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 135.30/19.87 | | | | | | | | | | e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.30/19.87 | | | | | | | | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) % 135.30/19.87 | | | | | | | | | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.30/19.87 | | | | | | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 135.30/19.87 | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 135.30/19.87 | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.30/19.87 | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.30/19.87 | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.30/19.87 | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.30/19.87 | | | | | | | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 % 135.30/19.87 | | | | | | | | | | & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ % 135.30/19.87 | | | | | | | | | | (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, % 135.30/19.87 | | | | | | | | | | e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 135.30/19.87 | | | | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 135.30/19.87 | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.30/19.87 | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.30/19.87 | | | | | | | | | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.30/19.87 | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, % 135.30/19.87 | | | | | | | | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, % 135.30/19.87 | | | | | | | | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.30/19.87 | | | | | | | | | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.87 | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.30/19.87 | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | GROUND_INST: instantiating (10) with e1, all_56_31, e0, e0, % 135.30/19.87 | | | | | | | | | | simplifying with (13), (91) gives: % 135.30/19.87 | | | | | | | | | | (93) all_56_31 = e1 % 135.30/19.87 | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | GROUND_INST: instantiating (10) with all_52_11, e3, e1, e0, % 135.30/19.87 | | | | | | | | | | simplifying with (18), (64) gives: % 135.30/19.87 | | | | | | | | | | (94) all_52_11 = e3 % 135.30/19.87 | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | GROUND_INST: instantiating (10) with all_52_9, all_6_0, e1, e2, % 135.30/19.87 | | | | | | | | | | simplifying with (26), (45) gives: % 135.30/19.87 | | | | | | | | | | (95) all_52_9 = all_6_0 % 135.30/19.87 | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | COMBINE_EQS: (30), (95) imply: % 135.30/19.87 | | | | | | | | | | (96) all_54_6 = all_6_0 % 135.30/19.87 | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | REDUCE: (17), (95) imply: % 135.30/19.87 | | | | | | | | | | (97) ~ (all_52_1 = all_6_0) % 135.30/19.87 | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | REDUCE: (25), (95) imply: % 135.30/19.87 | | | | | | | | | | (98) ~ (all_6_0 = e3) % 135.30/19.87 | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | REDUCE: (54), (95) imply: % 135.30/19.87 | | | | | | | | | | (99) ~ (all_6_0 = e2) % 135.30/19.87 | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | BETA: splitting (22) gives: % 135.30/19.87 | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | Case 1: % 135.30/19.87 | | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | | (100) all_54_6 = e3 % 135.30/19.87 | | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | | COMBINE_EQS: (96), (100) imply: % 135.30/19.87 | | | | | | | | | | | (101) all_6_0 = e3 % 135.30/19.87 | | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | | REDUCE: (98), (101) imply: % 135.30/19.87 | | | | | | | | | | | (102) $false % 135.30/19.87 | | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | | CLOSE: (102) is inconsistent. % 135.30/19.87 | | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | Case 2: % 135.30/19.87 | | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | | (103) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 135.30/19.87 | | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (8), (10), (11), (14), (15), (20), % 135.30/19.87 | | | | | | | | | | | (25), (26), (31), (32), (34), (38), (39), (41), % 135.30/19.87 | | | | | | | | | | | (42), (44), (56), (57), (63), (92), (93), (96), % 135.30/19.87 | | | | | | | | | | | (97), (98), (99), (103) are inconsistent by % 135.30/19.87 | | | | | | | | | | | sub-proof #9. % 135.30/19.87 | | | | | | | | | | | % 135.30/19.87 | | | | | | | | | | End of split % 135.30/19.87 | | | | | | | | | | % 135.30/19.87 | | | | | | | | | End of split % 135.30/19.87 | | | | | | | | | % 135.30/19.87 | | | | | | | | End of split % 135.30/19.87 | | | | | | | | % 135.30/19.87 | | | | | | | End of split % 135.30/19.87 | | | | | | | % 135.30/19.87 | | | | | | End of split % 135.30/19.87 | | | | | | % 135.30/19.87 | | | | | Case 2: % 135.30/19.87 | | | | | | % 135.30/19.87 | | | | | | (104) all_57_15 = e3 & op(e0, e0) = e3 % 135.30/19.87 | | | | | | % 135.30/19.87 | | | | | | ALPHA: (104) implies: % 135.30/19.87 | | | | | | (105) op(e0, e0) = e3 % 135.30/19.87 | | | | | | % 135.30/19.87 | | | | | | REF_CLOSE: (10), (13), (35), (105) are inconsistent by sub-proof % 135.30/19.87 | | | | | | #606. % 135.30/19.87 | | | | | | % 135.30/19.87 | | | | | End of split % 135.30/19.87 | | | | | % 135.30/19.87 | | | | End of split % 135.30/19.87 | | | | % 135.30/19.87 | | | Case 2: % 135.30/19.87 | | | | % 135.30/19.87 | | | | (106) all_54_7 = e1 | all_54_7 = e0 % 135.30/19.87 | | | | % 135.30/19.87 | | | | REF_CLOSE: (3), (8), (33), (106) are inconsistent by sub-proof #313. % 135.30/19.87 | | | | % 135.30/19.87 | | | End of split % 135.30/19.87 | | | % 135.30/19.87 | | End of split % 135.30/19.87 | | % 135.30/19.87 | Case 2: % 135.30/19.87 | | % 135.30/19.87 | | (107) ~ (all_6_1 = e3) & op(e2, e2) = all_6_1 & $i(all_6_1) % 135.30/19.87 | | % 135.30/19.87 | | REF_CLOSE: (10), (15), (107) are inconsistent by sub-proof #74. % 135.30/19.87 | | % 135.30/19.87 | End of split % 135.30/19.87 | % 135.30/19.87 End of proof % 135.30/19.87 % 135.30/19.87 Sub-proof #8 shows that the following formulas are inconsistent: % 135.30/19.87 ---------------------------------------------------------------- % 135.30/19.87 (1) op(e1, e0) = all_56_29 % 135.30/19.87 (2) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 135.30/19.87 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 135.30/19.87 (3) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) | % 135.30/19.87 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 135.30/19.87 (4) op(e2, e0) = all_52_13 % 135.30/19.87 (5) ~ (all_52_11 = e2) % 135.30/19.87 (6) ~ (e2 = e0) % 135.30/19.87 (7) ~ (all_52_13 = e1) % 135.30/19.87 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.30/19.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.30/19.87 (9) ~ (e3 = e0) % 135.30/19.87 (10) ~ (e3 = e2) % 135.30/19.87 (11) op(e0, e0) = e1 % 135.30/19.87 (12) all_57_8 = e2 % 135.30/19.87 (13) op(e2, e2) = e3 % 135.30/19.87 (14) ~ (all_52_1 = all_52_9) % 135.30/19.87 (15) op(e0, e1) = all_52_11 % 135.30/19.87 (16) op(e1, e1) = e2 % 135.30/19.87 (17) ~ (all_10_2 = e0) % 135.30/19.87 (18) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 135.30/19.87 (19) ~ (all_52_9 = e2) % 135.30/19.87 (20) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.30/19.87 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.30/19.87 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.30/19.87 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.30/19.87 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 135.30/19.87 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.30/19.87 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) % 135.30/19.87 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.30/19.87 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.87 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 135.30/19.87 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.87 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 135.30/19.87 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 135.30/19.87 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.30/19.87 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) % 135.30/19.87 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 135.30/19.87 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 135.30/19.87 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 135.30/19.87 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.30/19.87 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.30/19.87 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.30/19.87 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 135.30/19.87 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & % 135.30/19.87 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & % 135.30/19.87 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.30/19.87 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.30/19.87 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.30/19.87 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.87 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ % 135.30/19.87 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.30/19.87 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 135.30/19.87 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 135.30/19.87 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.30/19.87 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) % 135.30/19.87 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.30/19.87 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.30/19.87 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 % 135.30/19.87 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.87 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = % 135.30/19.87 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.30/19.87 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 135.30/19.87 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.30/19.87 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.30/19.87 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 135.30/19.87 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.30/19.87 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.30/19.87 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.30/19.87 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.87 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.30/19.87 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.30/19.87 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.30/19.87 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.30/19.87 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.30/19.87 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.30/19.87 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.30/19.87 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.30/19.87 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.30/19.87 $i(all_56_29)))) % 135.30/19.87 (21) op(e3, e3) = all_10_2 % 135.30/19.87 (22) ~ (all_52_9 = e3) % 135.30/19.87 (23) op(e0, e1) = e3 % 135.30/19.87 (24) op(e2, e1) = all_52_9 % 135.30/19.87 (25) ~ (all_52_1 = e2) % 135.30/19.87 (26) op(e2, e1) = all_6_0 % 135.30/19.87 (27) all_57_14 = e3 % 135.30/19.87 (28) all_54_6 = all_52_9 % 135.30/19.87 (29) op(e2, e3) = all_52_1 % 135.30/19.87 (30) ~ (all_52_14 = e1) % 135.30/19.87 (31) op(e3, e1) = all_52_8 % 135.30/19.87 (32) ~ (e3 = e1) % 135.30/19.87 (33) ~ (e1 = e0) % 135.30/19.88 (34) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) | % 135.30/19.88 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) % 135.30/19.88 (35) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 135.30/19.88 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 135.30/19.88 (36) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 135.30/19.88 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 135.30/19.88 (37) op(e1, e0) = all_52_14 % 135.30/19.88 (38) ~ (all_6_0 = e0) % 135.30/19.88 (39) op(e1, e0) = e0 % 135.30/19.88 % 135.30/19.88 Begin of proof % 135.30/19.88 | % 135.30/19.88 | BETA: splitting (20) gives: % 135.30/19.88 | % 135.30/19.88 | Case 1: % 135.30/19.88 | | % 135.30/19.88 | | (40) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 % 135.30/19.88 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = % 135.30/19.88 | | e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.30/19.88 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.30/19.88 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.88 | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.30/19.88 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = % 135.30/19.88 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.30/19.88 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.30/19.88 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.30/19.88 | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 % 135.30/19.88 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = % 135.30/19.88 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.30/19.88 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 135.30/19.88 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.30/19.88 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.30/19.88 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.30/19.88 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.30/19.88 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 135.30/19.88 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 135.30/19.88 | | % 135.30/19.88 | | BETA: splitting (40) gives: % 135.30/19.88 | | % 135.30/19.88 | | Case 1: % 135.30/19.88 | | | % 135.30/19.88 | | | (41) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ % 135.30/19.88 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.30/19.88 | | | op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & % 135.30/19.88 | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 135.30/19.88 | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.30/19.88 | | | $i(all_56_27)) | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 % 135.30/19.88 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.30/19.88 | | | (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, % 135.30/19.88 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.30/19.88 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.30/19.88 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.30/19.88 | | | % 135.30/19.88 | | | BETA: splitting (41) gives: % 135.30/19.88 | | | % 135.30/19.88 | | | Case 1: % 135.30/19.88 | | | | % 135.30/19.88 | | | | (42) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ % 135.30/19.88 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.30/19.88 | | | | op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & % 135.30/19.88 | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 135.30/19.88 | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.30/19.88 | | | | $i(all_56_27) % 135.30/19.88 | | | | % 135.30/19.88 | | | | ALPHA: (42) implies: % 135.30/19.88 | | | | (43) ~ (all_56_27 = e0) % 135.30/19.88 | | | | (44) ~ (all_56_19 = e1) % 135.30/19.88 | | | | (45) op(e2, e0) = all_56_27 % 135.30/19.88 | | | | (46) op(e2, e1) = all_56_19 % 135.30/19.88 | | | | % 135.30/19.88 | | | | REF_CLOSE: (4), (7), (8), (9), (13), (26), (32), (33), (35), (36), (38), % 135.30/19.88 | | | | (43), (44), (45), (46) are inconsistent by sub-proof #10. % 135.30/19.88 | | | | % 135.30/19.88 | | | Case 2: % 135.30/19.88 | | | | % 135.30/19.88 | | | | (47) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ % 135.30/19.88 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.30/19.88 | | | | op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & % 135.30/19.88 | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.30/19.88 | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.30/19.88 | | | | $i(all_56_29) % 135.30/19.88 | | | | % 135.30/19.88 | | | | ALPHA: (47) implies: % 135.30/19.88 | | | | (48) ~ (all_56_29 = e0) % 135.30/19.88 | | | | % 135.30/19.88 | | | | REF_CLOSE: (1), (8), (39), (48) are inconsistent by sub-proof #45. % 135.30/19.88 | | | | % 135.30/19.88 | | | End of split % 135.30/19.88 | | | % 135.30/19.88 | | Case 2: % 135.30/19.88 | | | % 135.30/19.88 | | | (49) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ % 135.30/19.88 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.30/19.88 | | | op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & % 135.30/19.88 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.30/19.88 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.30/19.88 | | | $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 % 135.30/19.88 | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.30/19.88 | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 % 135.30/19.88 | | | & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e2, e3) = % 135.30/19.88 | | | e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.88 | | | $i(all_56_17) & $i(all_56_25)) % 135.30/19.88 | | | % 135.30/19.88 | | | REF_CLOSE: (8), (17), (21), (25), (29), (49) are inconsistent by sub-proof % 135.30/19.88 | | | #533. % 135.30/19.88 | | | % 135.30/19.88 | | End of split % 135.30/19.88 | | % 135.30/19.88 | Case 2: % 135.30/19.88 | | % 135.30/19.88 | | (50) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.30/19.88 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.30/19.88 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.30/19.88 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & % 135.30/19.88 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.30/19.88 | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.30/19.88 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.30/19.88 | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, % 135.30/19.88 | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.30/19.88 | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.30/19.88 | | $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.30/19.88 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 % 135.30/19.88 | | = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 135.30/19.88 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.30/19.88 | | op(e0, e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.30/19.88 | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 % 135.30/19.88 | | & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.30/19.88 | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.30/19.88 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.30/19.88 | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.30/19.88 | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 & % 135.30/19.88 | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.30/19.88 | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.30/19.88 | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 135.30/19.88 | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.30/19.88 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) % 135.30/19.88 | | & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 135.30/19.88 | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.30/19.88 | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.30/19.88 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.30/19.88 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.30/19.88 | | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 135.30/19.88 | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.30/19.88 | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & % 135.30/19.88 | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 135.30/19.88 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.30/19.88 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.30/19.88 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.30/19.88 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.30/19.88 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.30/19.88 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.30/19.88 | | $i(all_56_29)))) % 135.30/19.88 | | % 135.30/19.88 | | BETA: splitting (50) gives: % 135.30/19.88 | | % 135.30/19.88 | | Case 1: % 135.30/19.88 | | | % 135.30/19.88 | | | (51) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ % 135.30/19.88 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 135.30/19.88 | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 135.30/19.88 | | | all_56_17 & op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 135.30/19.88 | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.30/19.88 | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 % 135.30/19.88 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.30/19.88 | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, % 135.30/19.88 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.30/19.88 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.30/19.88 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.30/19.88 | | | % 135.30/19.88 | | | REF_CLOSE: (8), (10), (16), (39), (51) are inconsistent by sub-proof #42. % 135.30/19.88 | | | % 135.30/19.88 | | Case 2: % 135.30/19.88 | | | % 135.30/19.88 | | | (52) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.30/19.88 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.30/19.88 | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & % 135.30/19.88 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.30/19.88 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.30/19.88 | | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 % 135.30/19.88 | | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.30/19.88 | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.30/19.88 | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.30/19.88 | | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) % 135.30/19.88 | | | & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 & % 135.30/19.88 | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.30/19.88 | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.30/19.88 | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 135.30/19.88 | | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.30/19.88 | | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.88 | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.30/19.88 | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ % 135.30/19.88 | | | (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.30/19.88 | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.30/19.88 | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 135.30/19.88 | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 135.30/19.88 | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.30/19.88 | | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, % 135.30/19.88 | | | e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.30/19.88 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.30/19.88 | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = % 135.30/19.88 | | | e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.30/19.88 | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, % 135.30/19.88 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.30/19.88 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.30/19.88 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.30/19.88 | | | $i(all_56_29)))) % 135.30/19.88 | | | % 135.30/19.88 | | | BETA: splitting (52) gives: % 135.30/19.88 | | | % 135.30/19.88 | | | Case 1: % 135.30/19.88 | | | | % 135.30/19.88 | | | | (53) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.30/19.88 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.30/19.88 | | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & % 135.30/19.88 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.30/19.88 | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.30/19.88 | | | | $i(all_56_31) % 135.30/19.88 | | | | % 135.30/19.88 | | | | ALPHA: (53) implies: % 135.30/19.88 | | | | (54) op(e2, e2) = e0 % 135.30/19.88 | | | | % 135.30/19.88 | | | | REF_CLOSE: (8), (9), (13), (54) are inconsistent by sub-proof #641. % 135.30/19.88 | | | | % 135.30/19.88 | | | Case 2: % 135.30/19.88 | | | | % 135.30/19.88 | | | | (55) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.30/19.88 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.30/19.88 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.30/19.88 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.30/19.88 | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.30/19.88 | | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.30/19.88 | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.30/19.88 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = % 135.30/19.88 | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 135.30/19.88 | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.30/19.88 | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.30/19.88 | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 135.30/19.88 | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.30/19.88 | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.30/19.88 | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.30/19.88 | | | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 135.30/19.88 | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.88 | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.30/19.88 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = % 135.30/19.88 | | | | e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 135.30/19.88 | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 % 135.30/19.88 | | | | & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.30/19.88 | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.30/19.88 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = % 135.30/19.88 | | | | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.30/19.88 | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, % 135.30/19.88 | | | | e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.30/19.88 | | | | & $i(all_56_29)))) % 135.30/19.88 | | | | % 135.30/19.88 | | | | BETA: splitting (55) gives: % 135.30/19.88 | | | | % 135.30/19.88 | | | | Case 1: % 135.30/19.88 | | | | | % 135.30/19.88 | | | | | (56) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.30/19.88 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.30/19.88 | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.30/19.88 | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.30/19.88 | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.30/19.88 | | | | | $i(all_56_27) % 135.30/19.88 | | | | | % 135.30/19.88 | | | | | ALPHA: (56) implies: % 135.30/19.88 | | | | | (57) ~ (all_56_27 = e0) % 135.30/19.88 | | | | | (58) ~ (all_56_19 = e1) % 135.30/19.88 | | | | | (59) op(e2, e0) = all_56_27 % 135.30/19.88 | | | | | (60) op(e2, e1) = all_56_19 % 135.30/19.88 | | | | | % 135.30/19.88 | | | | | REF_CLOSE: (4), (7), (8), (9), (13), (26), (32), (33), (35), (36), % 135.30/19.88 | | | | | (38), (57), (58), (59), (60) are inconsistent by sub-proof % 135.30/19.88 | | | | | #10. % 135.30/19.88 | | | | | % 135.30/19.88 | | | | Case 2: % 135.30/19.88 | | | | | % 135.30/19.88 | | | | | (61) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.30/19.88 | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & % 135.30/19.88 | | | | | ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.30/19.88 | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 135.30/19.88 | | | | | & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) % 135.30/19.88 | | | | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.30/19.88 | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.30/19.88 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = % 135.30/19.88 | | | | | e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.30/19.88 | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.30/19.88 | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.30/19.88 | | | | | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 135.30/19.88 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.30/19.88 | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 135.30/19.88 | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.30/19.88 | | | | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.30/19.88 | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.30/19.88 | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.30/19.88 | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 135.30/19.88 | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 135.30/19.88 | | | | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 135.30/19.88 | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))) % 135.30/19.88 | | | | | % 135.30/19.88 | | | | | ALPHA: (61) implies: % 135.30/19.88 | | | | | (62) op(e0, e0) = all_56_31 % 135.30/19.88 | | | | | (63) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.30/19.88 | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) % 135.30/19.88 | | | | | & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 135.30/19.88 | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.30/19.88 | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 135.30/19.88 | | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.30/19.88 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) % 135.30/19.88 | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.30/19.88 | | | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 % 135.30/19.88 | | | | | & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.30/19.88 | | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 135.30/19.88 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.30/19.88 | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & % 135.30/19.88 | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) % 135.30/19.88 | | | | | = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.30/19.88 | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.30/19.88 | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) % 135.30/19.88 | | | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, % 135.30/19.88 | | | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 % 135.30/19.88 | | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.30/19.88 | | | | | $i(all_56_29)) % 135.30/19.88 | | | | | % 135.30/19.88 | | | | | GROUND_INST: instantiating (8) with e1, all_56_31, e0, e0, simplifying % 135.30/19.88 | | | | | with (11), (62) gives: % 135.30/19.88 | | | | | (64) all_56_31 = e1 % 135.30/19.88 | | | | | % 135.30/19.88 | | | | | GROUND_INST: instantiating (8) with all_52_11, e3, e1, e0, simplifying % 135.30/19.88 | | | | | with (15), (23) gives: % 135.30/19.88 | | | | | (65) all_52_11 = e3 % 135.30/19.88 | | | | | % 135.30/19.88 | | | | | GROUND_INST: instantiating (8) with e0, all_56_29, e0, e1, simplifying % 135.30/19.88 | | | | | with (1), (39) gives: % 135.30/19.88 | | | | | (66) all_56_29 = e0 % 135.30/19.88 | | | | | % 135.30/19.88 | | | | | GROUND_INST: instantiating (8) with all_52_9, all_6_0, e1, e2, % 135.30/19.88 | | | | | simplifying with (24), (26) gives: % 135.30/19.88 | | | | | (67) all_52_9 = all_6_0 % 135.30/19.88 | | | | | % 135.30/19.88 | | | | | COMBINE_EQS: (28), (67) imply: % 135.30/19.88 | | | | | (68) all_54_6 = all_6_0 % 135.30/19.88 | | | | | % 135.30/19.88 | | | | | REDUCE: (14), (67) imply: % 135.30/19.88 | | | | | (69) ~ (all_52_1 = all_6_0) % 135.30/19.88 | | | | | % 135.30/19.88 | | | | | REDUCE: (22), (67) imply: % 135.30/19.88 | | | | | (70) ~ (all_6_0 = e3) % 135.30/19.88 | | | | | % 135.30/19.88 | | | | | REDUCE: (19), (67) imply: % 135.30/19.88 | | | | | (71) ~ (all_6_0 = e2) % 135.30/19.88 | | | | | % 135.30/19.88 | | | | | BETA: splitting (18) gives: % 135.30/19.88 | | | | | % 135.30/19.88 | | | | | Case 1: % 135.30/19.88 | | | | | | % 135.30/19.88 | | | | | | (72) all_54_6 = e3 % 135.30/19.88 | | | | | | % 135.30/19.88 | | | | | | COMBINE_EQS: (68), (72) imply: % 135.30/19.88 | | | | | | (73) all_6_0 = e3 % 135.30/19.88 | | | | | | % 135.30/19.88 | | | | | | REDUCE: (70), (73) imply: % 135.30/19.88 | | | | | | (74) $false % 135.30/19.88 | | | | | | % 135.30/19.88 | | | | | | CLOSE: (74) is inconsistent. % 135.30/19.88 | | | | | | % 135.30/19.88 | | | | | Case 2: % 135.30/19.88 | | | | | | % 135.30/19.88 | | | | | | (75) ~ (all_54_6 = e3) % 135.30/19.88 | | | | | | (76) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 135.30/19.88 | | | | | | % 135.30/19.88 | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (12), (13), % 135.30/19.88 | | | | | | (16), (22), (24), (27), (29), (30), (31), (34), (35), % 135.30/19.88 | | | | | | (37), (38), (39), (63), (64), (68), (69), (70), (71), % 135.30/19.88 | | | | | | (76) are inconsistent by sub-proof #9. % 135.30/19.88 | | | | | | % 135.30/19.88 | | | | | End of split % 135.30/19.88 | | | | | % 135.30/19.88 | | | | End of split % 135.30/19.88 | | | | % 135.30/19.88 | | | End of split % 135.30/19.88 | | | % 135.30/19.88 | | End of split % 135.30/19.88 | | % 135.30/19.88 | End of split % 135.30/19.88 | % 135.30/19.88 End of proof % 135.30/19.88 % 135.30/19.88 Sub-proof #9 shows that the following formulas are inconsistent: % 135.30/19.88 ---------------------------------------------------------------- % 135.30/19.88 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 135.30/19.88 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 135.30/19.88 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) | % 135.30/19.88 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 135.30/19.88 (3) all_54_6 = all_6_0 % 135.30/19.88 (4) ~ (all_6_0 = e3) % 135.30/19.88 (5) op(e2, e0) = all_52_13 % 135.30/19.88 (6) ~ (e2 = e0) % 135.30/19.88 (7) ~ (all_52_13 = e1) % 135.30/19.88 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.30/19.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.30/19.88 (9) ~ (e3 = e0) % 135.30/19.88 (10) ~ (all_6_0 = e2) % 135.30/19.88 (11) ~ (e3 = e2) % 135.30/19.88 (12) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 135.30/19.88 (13) all_57_8 = e2 % 135.30/19.88 (14) op(e2, e2) = e3 % 135.30/19.88 (15) all_56_31 = e1 % 135.30/19.88 (16) op(e1, e1) = e2 % 135.30/19.88 (17) ~ (all_52_1 = all_6_0) % 135.30/19.88 (18) ~ (all_52_9 = e3) % 135.30/19.88 (19) op(e2, e1) = all_52_9 % 135.30/19.88 (20) all_57_14 = e3 % 135.30/19.88 (21) op(e2, e3) = all_52_1 % 135.30/19.88 (22) ~ (all_52_14 = e1) % 135.30/19.88 (23) op(e3, e1) = all_52_8 % 135.30/19.88 (24) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.30/19.88 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.30/19.88 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 135.30/19.88 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.30/19.88 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 135.30/19.88 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.30/19.88 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.30/19.88 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.30/19.88 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.30/19.88 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.30/19.88 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.30/19.88 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.30/19.88 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.30/19.88 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.30/19.88 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.30/19.88 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 135.30/19.88 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.30/19.88 $i(all_56_21) & $i(all_56_29)) % 135.30/19.88 (25) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) | % 135.30/19.88 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) % 135.30/19.88 (26) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 135.30/19.88 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 135.30/19.88 (27) op(e1, e0) = all_52_14 % 135.30/19.88 (28) ~ (all_6_0 = e0) % 135.30/19.88 (29) op(e1, e0) = e0 % 135.30/19.88 % 135.30/19.88 Begin of proof % 135.30/19.88 | % 135.30/19.88 | BETA: splitting (12) gives: % 135.30/19.88 | % 135.30/19.88 | Case 1: % 135.30/19.88 | | % 135.30/19.88 | | (30) all_54_6 = e2 % 135.30/19.88 | | % 135.30/19.88 | | COMBINE_EQS: (3), (30) imply: % 135.30/19.88 | | (31) all_6_0 = e2 % 135.30/19.88 | | % 135.30/19.88 | | REDUCE: (10), (31) imply: % 135.30/19.88 | | (32) $false % 135.30/19.88 | | % 135.30/19.88 | | CLOSE: (32) is inconsistent. % 135.30/19.88 | | % 135.30/19.88 | Case 2: % 135.30/19.88 | | % 135.30/19.88 | | (33) ~ (all_54_6 = e2) % 135.30/19.88 | | (34) all_54_6 = e1 | all_54_6 = e0 % 135.30/19.88 | | % 135.30/19.88 | | BETA: splitting (34) gives: % 135.30/19.88 | | % 135.30/19.88 | | Case 1: % 135.30/19.88 | | | % 135.30/19.88 | | | (35) all_54_6 = e1 % 135.30/19.88 | | | % 135.30/19.88 | | | COMBINE_EQS: (3), (35) imply: % 135.30/19.88 | | | (36) all_6_0 = e1 % 135.30/19.88 | | | % 135.30/19.88 | | | REDUCE: (17), (36) imply: % 135.30/19.88 | | | (37) ~ (all_52_1 = e1) % 135.30/19.88 | | | % 135.30/19.88 | | | REDUCE: (4), (36) imply: % 135.30/19.88 | | | (38) ~ (e3 = e1) % 135.30/19.88 | | | % 135.30/19.88 | | | SIMP: (38) implies: % 135.30/19.88 | | | (39) ~ (e3 = e1) % 135.30/19.88 | | | % 135.30/19.88 | | | REDUCE: (10), (36) imply: % 135.30/19.88 | | | (40) ~ (e2 = e1) % 135.30/19.88 | | | % 135.30/19.88 | | | SIMP: (40) implies: % 135.30/19.88 | | | (41) ~ (e2 = e1) % 135.30/19.88 | | | % 135.30/19.88 | | | REDUCE: (28), (36) imply: % 135.30/19.88 | | | (42) ~ (e1 = e0) % 135.30/19.88 | | | % 135.30/19.89 | | | BETA: splitting (26) gives: % 135.30/19.89 | | | % 135.30/19.89 | | | Case 1: % 135.30/19.89 | | | | % 135.30/19.89 | | | | (43) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) % 135.30/19.89 | | | | = e1) % 135.30/19.89 | | | | % 135.30/19.89 | | | | REF_CLOSE: (8), (14), (21), (37), (39), (43) are inconsistent by % 135.30/19.89 | | | | sub-proof #77. % 135.30/19.89 | | | | % 135.30/19.89 | | | Case 2: % 135.30/19.89 | | | | % 135.30/19.89 | | | | (44) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) % 135.30/19.89 | | | | = e1) % 135.30/19.89 | | | | % 135.30/19.89 | | | | BETA: splitting (44) gives: % 135.30/19.89 | | | | % 135.30/19.89 | | | | Case 1: % 135.30/19.89 | | | | | % 135.30/19.89 | | | | | (45) all_57_5 = e1 & op(e2, e1) = e1 % 135.30/19.89 | | | | | % 135.30/19.89 | | | | | ALPHA: (45) implies: % 135.30/19.89 | | | | | (46) all_57_5 = e1 % 135.30/19.89 | | | | | (47) op(e2, e1) = e1 % 135.30/19.89 | | | | | % 135.30/19.89 | | | | | BETA: splitting (24) gives: % 135.30/19.89 | | | | | % 135.30/19.89 | | | | | Case 1: % 135.30/19.89 | | | | | | % 135.30/19.89 | | | | | | (48) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.30/19.89 | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = % 135.30/19.89 | | | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 135.30/19.89 | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.30/19.89 | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.30/19.89 | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 135.30/19.89 | | | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.30/19.89 | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.30/19.89 | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.30/19.89 | | | | | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 135.30/19.89 | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 135.30/19.89 | | | | | | % 135.30/19.89 | | | | | | BETA: splitting (48) gives: % 135.30/19.89 | | | | | | % 135.30/19.89 | | | | | | Case 1: % 135.30/19.89 | | | | | | | % 135.30/19.89 | | | | | | | (49) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.30/19.89 | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = % 135.30/19.89 | | | | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 135.30/19.89 | | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.30/19.89 | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.30/19.89 | | | | | | | $i(all_56_25) % 135.30/19.89 | | | | | | | % 135.30/19.89 | | | | | | | ALPHA: (49) implies: % 135.30/19.89 | | | | | | | (50) all_56_31 = e3 % 135.30/19.89 | | | | | | | % 135.30/19.89 | | | | | | | COMBINE_EQS: (15), (50) imply: % 135.30/19.89 | | | | | | | (51) e3 = e1 % 135.30/19.89 | | | | | | | % 135.30/19.89 | | | | | | | COMBINE_EQS: (20), (51) imply: % 135.30/19.89 | | | | | | | (52) all_57_14 = e1 % 135.30/19.89 | | | | | | | % 135.48/19.89 | | | | | | | REF_CLOSE: (1), (2), (6), (8), (9), (11), (13), (16), (18), (19), % 135.48/19.89 | | | | | | | (23), (25), (39), (41), (42), (46), (52) are % 135.48/19.89 | | | | | | | inconsistent by sub-proof #76. % 135.48/19.89 | | | | | | | % 135.48/19.89 | | | | | | Case 2: % 135.48/19.89 | | | | | | | % 135.48/19.89 | | | | | | | (53) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.48/19.89 | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = % 135.48/19.89 | | | | | | | e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.48/19.89 | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.48/19.89 | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.48/19.89 | | | | | | | & $i(all_56_27) % 135.48/19.89 | | | | | | | % 135.48/19.89 | | | | | | | ALPHA: (53) implies: % 135.48/19.89 | | | | | | | (54) ~ (all_56_19 = e1) % 135.48/19.89 | | | | | | | (55) op(e2, e1) = all_56_19 % 135.48/19.89 | | | | | | | % 135.48/19.89 | | | | | | | REF_CLOSE: (8), (47), (54), (55) are inconsistent by sub-proof % 135.48/19.89 | | | | | | | #106. % 135.48/19.89 | | | | | | | % 135.48/19.89 | | | | | | End of split % 135.48/19.89 | | | | | | % 135.48/19.89 | | | | | Case 2: % 135.48/19.89 | | | | | | % 135.48/19.89 | | | | | | (56) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.48/19.89 | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = % 135.48/19.89 | | | | | | e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 135.48/19.89 | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 % 135.48/19.89 | | | | | | & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.48/19.89 | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.48/19.89 | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = % 135.48/19.89 | | | | | | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.48/19.89 | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, % 135.48/19.89 | | | | | | e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.48/19.89 | | | | | | & $i(all_56_29)) % 135.48/19.89 | | | | | | % 135.48/19.89 | | | | | | REF_CLOSE: (8), (22), (27), (29), (56) are inconsistent by sub-proof % 135.48/19.89 | | | | | | #40. % 135.48/19.89 | | | | | | % 135.48/19.89 | | | | | End of split % 135.48/19.89 | | | | | % 135.48/19.89 | | | | Case 2: % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | (57) all_57_10 = e1 & op(e2, e0) = e1 % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | ALPHA: (57) implies: % 135.48/19.89 | | | | | (58) op(e2, e0) = e1 % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | REF_CLOSE: (5), (7), (8), (58) are inconsistent by sub-proof #180. % 135.48/19.89 | | | | | % 135.48/19.89 | | | | End of split % 135.48/19.89 | | | | % 135.48/19.89 | | | End of split % 135.48/19.89 | | | % 135.48/19.89 | | Case 2: % 135.48/19.89 | | | % 135.48/19.89 | | | (59) all_54_6 = e0 % 135.48/19.89 | | | % 135.48/19.89 | | | COMBINE_EQS: (3), (59) imply: % 135.48/19.89 | | | (60) all_6_0 = e0 % 135.48/19.89 | | | % 135.48/19.89 | | | REDUCE: (28), (60) imply: % 135.48/19.89 | | | (61) $false % 135.48/19.89 | | | % 135.48/19.89 | | | CLOSE: (61) is inconsistent. % 135.48/19.89 | | | % 135.48/19.89 | | End of split % 135.48/19.89 | | % 135.48/19.89 | End of split % 135.48/19.89 | % 135.48/19.89 End of proof % 135.48/19.89 % 135.48/19.89 Sub-proof #10 shows that the following formulas are inconsistent: % 135.48/19.89 ---------------------------------------------------------------- % 135.48/19.89 (1) op(e2, e0) = all_52_13 % 135.48/19.89 (2) ~ (all_52_13 = e1) % 135.48/19.89 (3) op(e2, e1) = all_56_19 % 135.48/19.89 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.89 (5) ~ (e3 = e0) % 135.48/19.89 (6) ~ (all_56_19 = e1) % 135.48/19.89 (7) op(e2, e2) = e3 % 135.48/19.89 (8) op(e2, e1) = all_6_0 % 135.48/19.89 (9) ~ (all_56_27 = e0) % 135.48/19.89 (10) ~ (e3 = e1) % 135.48/19.89 (11) ~ (e1 = e0) % 135.48/19.89 (12) op(e2, e0) = all_56_27 % 135.48/19.89 (13) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 135.48/19.89 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 135.48/19.89 (14) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 135.48/19.89 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 135.48/19.89 (15) ~ (all_6_0 = e0) % 135.48/19.89 % 135.48/19.89 Begin of proof % 135.48/19.89 | % 135.48/19.89 | BETA: splitting (13) gives: % 135.48/19.89 | % 135.48/19.89 | Case 1: % 135.48/19.89 | | % 135.48/19.89 | | (16) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = % 135.48/19.89 | | e1) % 135.48/19.89 | | % 135.48/19.89 | | BETA: splitting (16) gives: % 135.48/19.89 | | % 135.48/19.89 | | Case 1: % 135.48/19.89 | | | % 135.48/19.89 | | | (17) all_57_2 = e1 & op(e2, e3) = e1 % 135.48/19.89 | | | % 135.48/19.89 | | | ALPHA: (17) implies: % 135.48/19.89 | | | (18) all_57_2 = e1 % 135.48/19.89 | | | % 135.48/19.89 | | | BETA: splitting (14) gives: % 135.48/19.89 | | | % 135.48/19.89 | | | Case 1: % 135.48/19.89 | | | | % 135.48/19.89 | | | | (19) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) % 135.48/19.89 | | | | = e0) % 135.48/19.89 | | | | % 135.48/19.89 | | | | BETA: splitting (19) gives: % 135.48/19.89 | | | | % 135.48/19.89 | | | | Case 1: % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | (20) all_57_2 = e0 & op(e2, e3) = e0 % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | REF_CLOSE: (11), (18), (20) are inconsistent by sub-proof #272. % 135.48/19.89 | | | | | % 135.48/19.89 | | | | Case 2: % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | (21) all_57_3 = e0 & op(e2, e2) = e0 % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | ALPHA: (21) implies: % 135.48/19.89 | | | | | (22) op(e2, e2) = e0 % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | REF_CLOSE: (4), (5), (7), (22) are inconsistent by sub-proof #641. % 135.48/19.89 | | | | | % 135.48/19.89 | | | | End of split % 135.48/19.89 | | | | % 135.48/19.89 | | | Case 2: % 135.48/19.89 | | | | % 135.48/19.89 | | | | (23) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) % 135.48/19.89 | | | | = e0) % 135.48/19.89 | | | | % 135.48/19.89 | | | | BETA: splitting (23) gives: % 135.48/19.89 | | | | % 135.48/19.89 | | | | Case 1: % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | (24) all_57_5 = e0 & op(e2, e1) = e0 % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | ALPHA: (24) implies: % 135.48/19.89 | | | | | (25) op(e2, e1) = e0 % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | GROUND_INST: instantiating (4) with e0, all_6_0, e1, e2, simplifying % 135.48/19.89 | | | | | with (8), (25) gives: % 135.48/19.89 | | | | | (26) all_6_0 = e0 % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | REDUCE: (15), (26) imply: % 135.48/19.89 | | | | | (27) $false % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | CLOSE: (27) is inconsistent. % 135.48/19.89 | | | | | % 135.48/19.89 | | | | Case 2: % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | (28) all_57_10 = e0 & op(e2, e0) = e0 % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | ALPHA: (28) implies: % 135.48/19.89 | | | | | (29) op(e2, e0) = e0 % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | REF_CLOSE: (4), (9), (12), (29) are inconsistent by sub-proof #275. % 135.48/19.89 | | | | | % 135.48/19.89 | | | | End of split % 135.48/19.89 | | | | % 135.48/19.89 | | | End of split % 135.48/19.89 | | | % 135.48/19.89 | | Case 2: % 135.48/19.89 | | | % 135.48/19.89 | | | (30) all_57_3 = e1 & op(e2, e2) = e1 % 135.48/19.89 | | | % 135.48/19.89 | | | ALPHA: (30) implies: % 135.48/19.89 | | | (31) op(e2, e2) = e1 % 135.48/19.89 | | | % 135.48/19.89 | | | REF_CLOSE: (4), (7), (10), (31) are inconsistent by sub-proof #325. % 135.48/19.89 | | | % 135.48/19.89 | | End of split % 135.48/19.89 | | % 135.48/19.89 | Case 2: % 135.48/19.89 | | % 135.48/19.89 | | (32) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = % 135.48/19.89 | | e1) % 135.48/19.89 | | % 135.48/19.89 | | BETA: splitting (32) gives: % 135.48/19.89 | | % 135.48/19.89 | | Case 1: % 135.48/19.89 | | | % 135.48/19.89 | | | (33) all_57_5 = e1 & op(e2, e1) = e1 % 135.48/19.89 | | | % 135.48/19.89 | | | ALPHA: (33) implies: % 135.48/19.89 | | | (34) op(e2, e1) = e1 % 135.48/19.89 | | | % 135.48/19.89 | | | REF_CLOSE: (3), (4), (6), (34) are inconsistent by sub-proof #106. % 135.48/19.89 | | | % 135.48/19.89 | | Case 2: % 135.48/19.89 | | | % 135.48/19.89 | | | (35) all_57_10 = e1 & op(e2, e0) = e1 % 135.48/19.89 | | | % 135.48/19.89 | | | ALPHA: (35) implies: % 135.48/19.89 | | | (36) op(e2, e0) = e1 % 135.48/19.89 | | | % 135.48/19.89 | | | REF_CLOSE: (1), (2), (4), (36) are inconsistent by sub-proof #180. % 135.48/19.89 | | | % 135.48/19.89 | | End of split % 135.48/19.89 | | % 135.48/19.89 | End of split % 135.48/19.89 | % 135.48/19.89 End of proof % 135.48/19.89 % 135.48/19.89 Sub-proof #11 shows that the following formulas are inconsistent: % 135.48/19.89 ---------------------------------------------------------------- % 135.48/19.89 (1) ~ (e2 = e0) % 135.48/19.89 (2) ~ (e2 = e1) % 135.48/19.89 (3) ~ (e3 = e0) % 135.48/19.89 (4) all_57_15 = e2 % 135.48/19.89 (5) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) | % 135.48/19.89 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 135.48/19.89 (6) all_57_13 = e2 % 135.48/19.89 (7) all_57_12 = e3 % 135.48/19.89 (8) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 135.48/19.89 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = % 135.48/19.89 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 135.48/19.89 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 135.48/19.89 (9) ~ (e3 = e1) % 135.48/19.89 (10) ~ (e1 = e0) % 135.48/19.89 % 135.48/19.89 Begin of proof % 135.48/19.89 | % 135.48/19.89 | BETA: splitting (8) gives: % 135.48/19.89 | % 135.48/19.89 | Case 1: % 135.48/19.89 | | % 135.48/19.89 | | (11) all_57_15 = e0 & op(e0, e0) = e0 % 135.48/19.89 | | % 135.48/19.89 | | REF_CLOSE: (1), (4), (11) are inconsistent by sub-proof #437. % 135.48/19.89 | | % 135.48/19.89 | Case 2: % 135.48/19.89 | | % 135.48/19.89 | | (12) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = % 135.48/19.89 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 & % 135.48/19.89 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) | % 135.48/19.89 | | (all_57_14 = e0 & op(e0, e1) = e0)) % 135.48/19.89 | | % 135.48/19.89 | | ALPHA: (12) implies: % 135.48/19.89 | | (13) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 135.48/19.89 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 135.48/19.89 | | % 135.48/19.89 | | BETA: splitting (13) gives: % 135.48/19.89 | | % 135.48/19.89 | | Case 1: % 135.48/19.89 | | | % 135.48/19.89 | | | (14) all_57_12 = e0 & op(e0, e3) = e0 % 135.48/19.89 | | | % 135.48/19.89 | | | ALPHA: (14) implies: % 135.48/19.89 | | | (15) all_57_12 = e0 % 135.48/19.89 | | | % 135.48/19.89 | | | REF_CLOSE: (3), (7), (15) are inconsistent by sub-proof #492. % 135.48/19.89 | | | % 135.48/19.89 | | Case 2: % 135.48/19.89 | | | % 135.48/19.89 | | | (16) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) % 135.48/19.89 | | | = e0) % 135.48/19.89 | | | % 135.48/19.89 | | | BETA: splitting (16) gives: % 135.48/19.89 | | | % 135.48/19.89 | | | Case 1: % 135.48/19.89 | | | | % 135.48/19.89 | | | | (17) all_57_13 = e0 & op(e0, e2) = e0 % 135.48/19.89 | | | | % 135.48/19.89 | | | | REF_CLOSE: (1), (6), (17) are inconsistent by sub-proof #411. % 135.48/19.89 | | | | % 135.48/19.89 | | | Case 2: % 135.48/19.89 | | | | % 135.48/19.89 | | | | (18) all_57_14 = e0 & op(e0, e1) = e0 % 135.48/19.89 | | | | % 135.48/19.89 | | | | ALPHA: (18) implies: % 135.48/19.89 | | | | (19) all_57_14 = e0 % 135.48/19.89 | | | | % 135.48/19.89 | | | | BETA: splitting (5) gives: % 135.48/19.89 | | | | % 135.48/19.89 | | | | Case 1: % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | (20) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, % 135.48/19.89 | | | | | e2) = e1) % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | REF_CLOSE: (2), (6), (7), (9), (20) are inconsistent by sub-proof % 135.48/19.89 | | | | | #245. % 135.48/19.89 | | | | | % 135.48/19.89 | | | | Case 2: % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | (21) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, % 135.48/19.89 | | | | | e0) = e1) % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | BETA: splitting (21) gives: % 135.48/19.89 | | | | | % 135.48/19.89 | | | | | Case 1: % 135.48/19.89 | | | | | | % 135.48/19.89 | | | | | | (22) all_57_14 = e1 & op(e0, e1) = e1 % 135.48/19.89 | | | | | | % 135.48/19.89 | | | | | | REF_CLOSE: (10), (19), (22) are inconsistent by sub-proof #231. % 135.48/19.89 | | | | | | % 135.48/19.89 | | | | | Case 2: % 135.48/19.89 | | | | | | % 135.48/19.89 | | | | | | (23) all_57_15 = e1 & op(e0, e0) = e1 % 135.48/19.89 | | | | | | % 135.48/19.89 | | | | | | REF_CLOSE: (2), (4), (23) are inconsistent by sub-proof #435. % 135.48/19.89 | | | | | | % 135.48/19.89 | | | | | End of split % 135.48/19.89 | | | | | % 135.48/19.89 | | | | End of split % 135.48/19.89 | | | | % 135.48/19.89 | | | End of split % 135.48/19.89 | | | % 135.48/19.89 | | End of split % 135.48/19.89 | | % 135.48/19.89 | End of split % 135.48/19.89 | % 135.48/19.89 End of proof % 135.48/19.89 % 135.48/19.89 Sub-proof #12 shows that the following formulas are inconsistent: % 135.48/19.89 ---------------------------------------------------------------- % 135.48/19.89 (1) op(e2, e2) = all_8_2 % 135.48/19.89 (2) op(e2, e1) = e1 % 135.48/19.89 (3) ~ (all_8_2 = e1) % 135.48/19.89 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.89 (5) op(e0, e0) = e1 % 135.48/19.89 (6) op(e0, e2) = all_52_7 % 135.48/19.89 (7) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 135.48/19.89 (8) all_54_5 = all_8_2 % 135.48/19.89 (9) ~ (all_52_14 = e1) % 135.48/19.89 (10) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.48/19.89 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.48/19.89 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.48/19.89 e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.48/19.89 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.48/19.89 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 135.48/19.89 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.48/19.89 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 135.48/19.89 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 % 135.48/19.89 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.48/19.89 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.48/19.89 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.48/19.89 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.48/19.89 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.48/19.89 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.48/19.89 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.48/19.89 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.48/19.89 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.48/19.89 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.48/19.89 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.48/19.89 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.48/19.89 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.48/19.89 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.48/19.89 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.89 $i(all_56_29)))) % 135.48/19.89 (11) ~ (e3 = e1) % 135.48/19.89 (12) ~ (all_52_7 = all_8_2) % 135.48/19.89 (13) ~ (all_8_2 = e3) % 135.48/19.89 (14) op(e1, e0) = all_52_14 % 135.48/19.89 (15) op(e1, e0) = e0 % 135.48/19.89 % 135.48/19.89 Begin of proof % 135.48/19.89 | % 135.48/19.89 | BETA: splitting (10) gives: % 135.48/19.89 | % 135.48/19.89 | Case 1: % 135.48/19.89 | | % 135.48/19.89 | | (16) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 135.48/19.89 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.48/19.89 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.48/19.89 | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) % 135.48/19.89 | | & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 135.48/19.89 | | % 135.48/19.89 | | ALPHA: (16) implies: % 135.48/19.89 | | (17) ~ (all_56_19 = e1) % 135.48/19.89 | | (18) op(e2, e1) = all_56_19 % 135.48/19.89 | | % 135.48/19.89 | | REF_CLOSE: (2), (4), (17), (18) are inconsistent by sub-proof #106. % 135.48/19.89 | | % 135.48/19.89 | Case 2: % 135.48/19.89 | | % 135.48/19.89 | | (19) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 % 135.48/19.89 | | = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.48/19.89 | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) % 135.48/19.89 | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.48/19.89 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.48/19.89 | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 % 135.48/19.89 | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.48/19.89 | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.48/19.89 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.48/19.89 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.48/19.89 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 % 135.48/19.89 | | = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.48/19.89 | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, % 135.48/19.89 | | e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 135.48/19.89 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.48/19.89 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.48/19.89 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.48/19.89 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.48/19.89 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.48/19.89 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29))) % 135.48/19.89 | | % 135.48/19.89 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14), % 135.48/19.89 | | (15), (19) are inconsistent by sub-proof #39. % 135.48/19.89 | | % 135.48/19.89 | End of split % 135.48/19.89 | % 135.48/19.89 End of proof % 135.48/19.89 % 135.48/19.89 Sub-proof #13 shows that the following formulas are inconsistent: % 135.48/19.89 ---------------------------------------------------------------- % 135.48/19.89 (1) op(e2, e2) = e0 % 135.48/19.89 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.89 (3) ~ (e3 = e0) % 135.48/19.89 (4) ~ (e3 = e2) % 135.48/19.89 (5) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.48/19.89 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.48/19.89 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.48/19.89 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.48/19.89 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 135.48/19.89 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 135.48/19.89 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 135.48/19.89 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.48/19.89 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.48/19.89 $i(all_56_17) & $i(all_56_25)) % 135.48/19.89 (6) op(e3, e0) = all_52_12 % 135.48/19.89 (7) op(e3, e0) = e2 % 135.48/19.89 % 135.48/19.89 Begin of proof % 135.48/19.89 | % 135.48/19.89 | BETA: splitting (5) gives: % 135.48/19.89 | % 135.48/19.89 | Case 1: % 135.48/19.89 | | % 135.48/19.89 | | (8) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.48/19.89 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.48/19.89 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.48/19.89 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.48/19.89 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 135.48/19.89 | | % 135.48/19.89 | | ALPHA: (8) implies: % 135.48/19.89 | | (9) op(e3, e0) = e3 % 135.48/19.89 | | % 135.48/19.89 | | REF_CLOSE: (2), (4), (6), (7), (9) are inconsistent by sub-proof #111. % 135.48/19.89 | | % 135.48/19.89 | Case 2: % 135.48/19.89 | | % 135.48/19.89 | | (10) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.48/19.89 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.89 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.89 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) % 135.48/19.89 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 135.48/19.89 | | % 135.48/19.89 | | ALPHA: (10) implies: % 135.48/19.89 | | (11) op(e2, e2) = e3 % 135.48/19.89 | | % 135.48/19.89 | | REF_CLOSE: (1), (2), (3), (11) are inconsistent by sub-proof #641. % 135.48/19.89 | | % 135.48/19.89 | End of split % 135.48/19.89 | % 135.48/19.89 End of proof % 135.48/19.89 % 135.48/19.89 Sub-proof #14 shows that the following formulas are inconsistent: % 135.48/19.89 ---------------------------------------------------------------- % 135.48/19.89 (1) ~ (e2 = e0) % 135.48/19.89 (2) op(e3, e3) = e1 % 135.48/19.89 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 135.48/19.89 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 135.48/19.89 (4) op(e3, e1) = e1 % 135.48/19.89 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.89 (6) ~ (e2 = e1) % 135.48/19.89 (7) ~ (e3 = e0) % 135.48/19.89 (8) ~ (e3 = e2) % 135.48/19.89 (9) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 135.48/19.89 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 135.48/19.89 (10) ~ (all_52_8 = e2) % 135.48/19.89 (11) all_57_4 = e1 % 135.48/19.89 (12) op(e3, e0) = all_52_12 % 135.48/19.89 (13) op(e3, e1) = all_52_8 % 135.48/19.89 (14) ~ (e3 = e1) % 135.48/19.89 (15) ~ (e1 = e0) % 135.48/19.89 (16) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 135.48/19.89 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 135.48/19.89 % 135.48/19.89 Begin of proof % 135.48/19.89 | % 135.48/19.89 | BETA: splitting (16) gives: % 135.48/19.89 | % 135.48/19.89 | Case 1: % 135.48/19.89 | | % 135.48/19.89 | | (17) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = % 135.48/19.89 | | e3) % 135.48/19.89 | | % 135.48/19.89 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (14), (15), (16), % 135.48/19.89 | | (17) are inconsistent by sub-proof #164. % 135.48/19.89 | | % 135.48/19.89 | Case 2: % 135.48/19.89 | | % 135.48/19.89 | | (18) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = % 135.48/19.89 | | e3) % 135.48/19.89 | | % 135.48/19.89 | | BETA: splitting (18) gives: % 135.48/19.89 | | % 135.48/19.89 | | Case 1: % 135.48/19.89 | | | % 135.48/19.89 | | | (19) all_57_4 = e3 & op(e3, e1) = e3 % 135.48/19.89 | | | % 135.48/19.89 | | | REF_CLOSE: (11), (14), (19) are inconsistent by sub-proof #438. % 135.48/19.89 | | | % 135.48/19.89 | | Case 2: % 135.48/19.89 | | | % 135.48/19.89 | | | (20) all_57_9 = e3 & op(e3, e0) = e3 % 135.48/19.89 | | | % 135.48/19.89 | | | ALPHA: (20) implies: % 135.48/19.89 | | | (21) op(e3, e0) = e3 % 135.48/19.89 | | | % 135.48/19.89 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 135.48/19.89 | | | (13), (14), (15), (16), (21) are inconsistent by sub-proof #18. % 135.48/19.89 | | | % 135.48/19.89 | | End of split % 135.48/19.89 | | % 135.48/19.89 | End of split % 135.48/19.89 | % 135.48/19.90 End of proof % 135.48/19.90 % 135.48/19.90 Sub-proof #15 shows that the following formulas are inconsistent: % 135.48/19.90 ---------------------------------------------------------------- % 135.48/19.90 (1) op(e3, e1) = e1 % 135.48/19.90 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.90 (3) ~ (e2 = e1) % 135.48/19.90 (4) op(e0, e0) = e1 % 135.48/19.90 (5) op(e0, e1) = all_52_11 % 135.48/19.90 (6) ~ (all_52_14 = e1) % 135.48/19.90 (7) ~ (all_52_11 = e0) % 135.48/19.90 (8) op(e1, e0) = all_52_14 % 135.48/19.90 (9) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 % 135.48/19.90 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.48/19.90 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 135.48/19.90 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.48/19.90 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.48/19.90 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.48/19.90 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.48/19.90 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.48/19.90 e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.48/19.90 $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & % 135.48/19.90 ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.48/19.90 (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 135.48/19.90 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.48/19.90 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & % 135.48/19.90 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.48/19.90 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 135.48/19.90 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.48/19.90 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.90 $i(all_56_21) & $i(all_56_29))) % 135.48/19.90 % 135.48/19.90 Begin of proof % 135.48/19.90 | % 135.48/19.90 | ALPHA: (9) implies: % 135.48/19.90 | (10) op(e0, e0) = all_56_31 % 135.48/19.90 | (11) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.48/19.90 | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.90 | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.90 | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.48/19.90 | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & % 135.48/19.90 | ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.48/19.90 | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.48/19.90 | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.48/19.90 | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.48/19.90 | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 % 135.48/19.90 | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = % 135.48/19.90 | e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.48/19.90 | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.48/19.90 | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.48/19.90 | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = % 135.48/19.90 | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) % 135.48/19.90 | = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.48/19.90 | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.48/19.90 | % 135.48/19.90 | BETA: splitting (11) gives: % 135.48/19.90 | % 135.48/19.90 | Case 1: % 135.48/19.90 | | % 135.48/19.90 | | (12) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.48/19.90 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.90 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.90 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 135.48/19.90 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.48/19.90 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.48/19.90 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.48/19.90 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.48/19.90 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.48/19.90 | | $i(all_56_27)) % 135.48/19.90 | | % 135.48/19.90 | | REF_CLOSE: (1), (2), (3), (4), (10), (12) are inconsistent by sub-proof #21. % 135.48/19.90 | | % 135.48/19.90 | Case 2: % 135.48/19.90 | | % 135.48/19.90 | | (13) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.48/19.90 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.48/19.90 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.48/19.90 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.48/19.90 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.48/19.90 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.48/19.90 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.48/19.90 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.48/19.90 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.90 | | $i(all_56_29)) % 135.48/19.90 | | % 135.48/19.90 | | BETA: splitting (13) gives: % 135.48/19.90 | | % 135.48/19.90 | | Case 1: % 135.48/19.90 | | | % 135.48/19.90 | | | (14) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.48/19.90 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.48/19.90 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.48/19.90 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.48/19.90 | | | $i(all_56_15) & $i(all_56_23) % 135.48/19.90 | | | % 135.48/19.90 | | | ALPHA: (14) implies: % 135.48/19.90 | | | (15) op(e1, e0) = e1 % 135.48/19.90 | | | % 135.48/19.90 | | | REF_CLOSE: (2), (6), (8), (15) are inconsistent by sub-proof #327. % 135.48/19.90 | | | % 135.48/19.90 | | Case 2: % 135.48/19.90 | | | % 135.48/19.90 | | | (16) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.48/19.90 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.48/19.90 | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.48/19.90 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.48/19.90 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 135.48/19.90 | | | % 135.48/19.90 | | | ALPHA: (16) implies: % 135.48/19.90 | | | (17) op(e0, e1) = e0 % 135.48/19.90 | | | % 135.48/19.90 | | | GROUND_INST: instantiating (2) with all_52_11, e0, e1, e0, simplifying % 135.48/19.90 | | | with (5), (17) gives: % 135.48/19.90 | | | (18) all_52_11 = e0 % 135.48/19.90 | | | % 135.48/19.90 | | | REDUCE: (7), (18) imply: % 135.48/19.90 | | | (19) $false % 135.48/19.90 | | | % 135.48/19.90 | | | CLOSE: (19) is inconsistent. % 135.48/19.90 | | | % 135.48/19.90 | | End of split % 135.48/19.90 | | % 135.48/19.90 | End of split % 135.48/19.90 | % 135.48/19.90 End of proof % 135.48/19.90 % 135.48/19.90 Sub-proof #16 shows that the following formulas are inconsistent: % 135.48/19.90 ---------------------------------------------------------------- % 135.48/19.90 (1) ~ (all_10_1 = e1) & op(e0, e0) = all_10_1 & $i(all_10_1) % 135.48/19.90 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.90 (3) op(e0, e0) = e1 % 135.48/19.90 % 135.48/19.90 Begin of proof % 135.48/19.90 | % 135.48/19.90 | ALPHA: (1) implies: % 135.48/19.90 | (4) ~ (all_10_1 = e1) % 135.48/19.90 | (5) op(e0, e0) = all_10_1 % 135.48/19.90 | % 135.48/19.90 | GROUND_INST: instantiating (2) with e1, all_10_1, e0, e0, simplifying with % 135.48/19.90 | (3), (5) gives: % 135.48/19.90 | (6) all_10_1 = e1 % 135.48/19.90 | % 135.48/19.90 | REDUCE: (4), (6) imply: % 135.48/19.90 | (7) $false % 135.48/19.90 | % 135.48/19.90 | CLOSE: (7) is inconsistent. % 135.48/19.90 | % 135.48/19.90 End of proof % 135.48/19.90 % 135.48/19.90 Sub-proof #17 shows that the following formulas are inconsistent: % 135.48/19.90 ---------------------------------------------------------------- % 135.48/19.90 (1) op(e3, e1) = e1 % 135.48/19.90 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.90 (3) op(e0, e0) = e1 % 135.48/19.90 (4) ~ (all_52_8 = e2) % 135.48/19.90 (5) ~ (all_52_14 = e1) % 135.48/19.90 (6) op(e3, e1) = all_52_8 % 135.48/19.90 (7) op(e1, e0) = all_52_14 % 135.48/19.90 (8) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 % 135.48/19.90 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.48/19.90 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 135.48/19.90 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.48/19.90 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.48/19.90 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.48/19.90 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.48/19.90 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.48/19.90 e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.48/19.90 $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & % 135.48/19.90 ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.48/19.90 (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 135.48/19.90 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.48/19.90 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & % 135.48/19.90 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.48/19.90 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 135.48/19.90 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.48/19.90 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.90 $i(all_56_21) & $i(all_56_29))) % 135.48/19.90 (9) op(e1, e0) = e0 % 135.48/19.90 % 135.48/19.90 Begin of proof % 135.48/19.90 | % 135.48/19.90 | ALPHA: (8) implies: % 135.48/19.90 | (10) op(e0, e0) = all_56_31 % 135.48/19.90 | (11) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.48/19.90 | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.90 | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.90 | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.48/19.90 | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & % 135.48/19.90 | ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.48/19.90 | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.48/19.90 | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.48/19.90 | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.48/19.90 | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 % 135.48/19.90 | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = % 135.48/19.90 | e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.48/19.90 | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.48/19.90 | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.48/19.90 | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = % 135.48/19.90 | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) % 135.48/19.90 | = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.48/19.90 | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.48/19.90 | % 135.48/19.90 | GROUND_INST: instantiating (2) with e1, all_56_31, e0, e0, simplifying with % 135.48/19.90 | (3), (10) gives: % 135.48/19.90 | (12) all_56_31 = e1 % 135.48/19.90 | % 135.48/19.90 | GROUND_INST: instantiating (2) with all_52_8, e1, e1, e3, simplifying with % 135.48/19.90 | (1), (6) gives: % 135.48/19.90 | (13) all_52_8 = e1 % 135.48/19.90 | % 135.48/19.90 | REDUCE: (4), (13) imply: % 135.48/19.90 | (14) ~ (e2 = e1) % 135.48/19.90 | % 135.48/19.90 | SIMP: (14) implies: % 135.48/19.90 | (15) ~ (e2 = e1) % 135.48/19.90 | % 135.48/19.90 | BETA: splitting (11) gives: % 135.48/19.90 | % 135.48/19.90 | Case 1: % 135.48/19.90 | | % 135.48/19.90 | | (16) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.48/19.90 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.90 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.90 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 135.48/19.90 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.48/19.90 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.48/19.90 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.48/19.90 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.48/19.90 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.48/19.90 | | $i(all_56_27)) % 135.48/19.90 | | % 135.48/19.90 | | BETA: splitting (16) gives: % 135.48/19.90 | | % 135.48/19.90 | | Case 1: % 135.48/19.90 | | | % 135.48/19.90 | | | (17) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.48/19.90 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.90 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.90 | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 135.48/19.90 | | | & $i(all_56_17) & $i(all_56_25) % 135.48/19.90 | | | % 135.48/19.90 | | | ALPHA: (17) implies: % 135.48/19.90 | | | (18) ~ (all_56_17 = e1) % 135.48/19.90 | | | (19) op(e3, e1) = all_56_17 % 135.48/19.90 | | | % 135.48/19.90 | | | REF_CLOSE: (1), (2), (18), (19) are inconsistent by sub-proof #349. % 135.48/19.90 | | | % 135.48/19.90 | | Case 2: % 135.48/19.90 | | | % 135.48/19.90 | | | (20) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.48/19.90 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.48/19.90 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.48/19.90 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.48/19.90 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 135.48/19.90 | | | % 135.48/19.90 | | | REF_CLOSE: (12), (15), (20) are inconsistent by sub-proof #33. % 135.48/19.90 | | | % 135.48/19.90 | | End of split % 135.48/19.90 | | % 135.48/19.90 | Case 2: % 135.48/19.90 | | % 135.48/19.90 | | (21) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.48/19.90 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.48/19.90 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.48/19.90 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.48/19.90 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.48/19.90 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.48/19.90 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.48/19.90 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.48/19.90 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.90 | | $i(all_56_29)) % 135.48/19.90 | | % 135.48/19.90 | | REF_CLOSE: (2), (5), (7), (9), (21) are inconsistent by sub-proof #40. % 135.48/19.90 | | % 135.48/19.90 | End of split % 135.48/19.90 | % 135.48/19.90 End of proof % 135.48/19.90 % 135.48/19.90 Sub-proof #18 shows that the following formulas are inconsistent: % 135.48/19.90 ---------------------------------------------------------------- % 135.48/19.90 (1) ~ (e2 = e0) % 135.48/19.90 (2) op(e3, e3) = e1 % 135.48/19.90 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 135.48/19.90 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 135.48/19.90 (4) op(e3, e1) = e1 % 135.48/19.90 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.90 (6) ~ (e2 = e1) % 135.48/19.90 (7) ~ (e3 = e0) % 135.48/19.90 (8) ~ (e3 = e2) % 135.48/19.90 (9) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 135.48/19.90 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 135.48/19.90 (10) ~ (all_52_8 = e2) % 135.48/19.90 (11) op(e3, e0) = e3 % 135.48/19.90 (12) all_57_4 = e1 % 135.48/19.90 (13) op(e3, e0) = all_52_12 % 135.48/19.90 (14) op(e3, e1) = all_52_8 % 135.48/19.90 (15) ~ (e3 = e1) % 135.48/19.90 (16) ~ (e1 = e0) % 135.48/19.90 (17) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 135.48/19.90 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 135.48/19.90 % 135.48/19.90 Begin of proof % 135.48/19.90 | % 135.48/19.90 | BETA: splitting (3) gives: % 135.48/19.90 | % 135.48/19.90 | Case 1: % 135.48/19.90 | | % 135.48/19.90 | | (18) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = % 135.48/19.90 | | e0) % 135.48/19.90 | | % 135.48/19.90 | | BETA: splitting (18) gives: % 135.48/19.90 | | % 135.48/19.90 | | Case 1: % 135.48/19.90 | | | % 135.48/19.90 | | | (19) all_57_0 = e0 & op(e3, e3) = e0 % 135.48/19.90 | | | % 135.48/19.90 | | | ALPHA: (19) implies: % 135.48/19.90 | | | (20) op(e3, e3) = e0 % 135.48/19.90 | | | % 135.48/19.90 | | | REF_CLOSE: (2), (5), (16), (20) are inconsistent by sub-proof #717. % 135.48/19.90 | | | % 135.48/19.90 | | Case 2: % 135.48/19.90 | | | % 135.48/19.90 | | | (21) all_57_1 = e0 & op(e3, e2) = e0 % 135.48/19.90 | | | % 135.48/19.90 | | | ALPHA: (21) implies: % 135.48/19.90 | | | (22) all_57_1 = e0 % 135.48/19.90 | | | % 135.48/19.90 | | | BETA: splitting (9) gives: % 135.48/19.90 | | | % 135.48/19.90 | | | Case 1: % 135.48/19.90 | | | | % 135.48/19.90 | | | | (23) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) % 135.48/19.90 | | | | = e2) % 135.48/19.90 | | | | % 135.48/19.90 | | | | REF_CLOSE: (1), (2), (5), (6), (22), (23) are inconsistent by sub-proof % 135.48/19.90 | | | | #148. % 135.48/19.90 | | | | % 135.48/19.90 | | | Case 2: % 135.48/19.90 | | | | % 135.48/19.90 | | | | (24) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) % 135.48/19.90 | | | | = e2) % 135.48/19.90 | | | | % 135.48/19.90 | | | | REF_CLOSE: (5), (8), (10), (11), (13), (14), (24) are inconsistent by % 135.48/19.90 | | | | sub-proof #19. % 135.48/19.90 | | | | % 135.48/19.90 | | | End of split % 135.48/19.90 | | | % 135.48/19.90 | | End of split % 135.48/19.90 | | % 135.48/19.90 | Case 2: % 135.48/19.90 | | % 135.48/19.90 | | (25) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = % 135.48/19.90 | | e0) % 135.48/19.90 | | % 135.48/19.90 | | BETA: splitting (25) gives: % 135.48/19.90 | | % 135.48/19.90 | | Case 1: % 135.48/19.90 | | | % 135.48/19.90 | | | (26) all_57_4 = e0 & op(e3, e1) = e0 % 135.48/19.90 | | | % 135.48/19.90 | | | ALPHA: (26) implies: % 135.48/19.90 | | | (27) op(e3, e1) = e0 % 135.48/19.90 | | | % 135.48/19.90 | | | REF_CLOSE: (4), (5), (16), (27) are inconsistent by sub-proof #343. % 135.48/19.90 | | | % 135.48/19.90 | | Case 2: % 135.48/19.90 | | | % 135.48/19.90 | | | (28) all_57_9 = e0 & op(e3, e0) = e0 % 135.48/19.90 | | | % 135.48/19.90 | | | ALPHA: (28) implies: % 135.48/19.90 | | | (29) all_57_9 = e0 % 135.48/19.90 | | | % 135.48/19.90 | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (12), (15), (17), (29) are % 135.48/19.90 | | | inconsistent by sub-proof #668. % 135.48/19.90 | | | % 135.48/19.90 | | End of split % 135.48/19.90 | | % 135.48/19.90 | End of split % 135.48/19.90 | % 135.48/19.90 End of proof % 135.48/19.90 % 135.48/19.90 Sub-proof #19 shows that the following formulas are inconsistent: % 135.48/19.90 ---------------------------------------------------------------- % 135.48/19.90 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.90 (2) ~ (e3 = e2) % 135.48/19.90 (3) ~ (all_52_8 = e2) % 135.48/19.90 (4) op(e3, e0) = e3 % 135.48/19.90 (5) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 135.48/19.90 (6) op(e3, e0) = all_52_12 % 135.48/19.90 (7) op(e3, e1) = all_52_8 % 135.48/19.90 % 135.48/19.90 Begin of proof % 135.48/19.90 | % 135.48/19.90 | BETA: splitting (5) gives: % 135.48/19.90 | % 135.48/19.90 | Case 1: % 135.48/19.90 | | % 135.48/19.90 | | (8) all_57_4 = e2 & op(e3, e1) = e2 % 135.48/19.90 | | % 135.48/19.90 | | REF_CLOSE: (1), (3), (7), (8) are inconsistent by sub-proof #442. % 135.48/19.90 | | % 135.48/19.90 | Case 2: % 135.48/19.90 | | % 135.48/19.90 | | (9) all_57_9 = e2 & op(e3, e0) = e2 % 135.48/19.90 | | % 135.48/19.90 | | ALPHA: (9) implies: % 135.48/19.90 | | (10) op(e3, e0) = e2 % 135.48/19.90 | | % 135.48/19.90 | | REF_CLOSE: (1), (2), (4), (6), (10) are inconsistent by sub-proof #111. % 135.48/19.90 | | % 135.48/19.90 | End of split % 135.48/19.90 | % 135.48/19.90 End of proof % 135.48/19.90 % 135.48/19.90 Sub-proof #20 shows that the following formulas are inconsistent: % 135.48/19.90 ---------------------------------------------------------------- % 135.48/19.90 (1) op(e3, e1) = e1 % 135.48/19.90 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.90 (3) ~ (e2 = e1) % 135.48/19.90 (4) op(e0, e0) = e1 % 135.48/19.90 (5) ~ (all_52_14 = e1) % 135.48/19.90 (6) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 135.48/19.90 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.48/19.90 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 135.48/19.90 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.48/19.90 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) % 135.48/19.90 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.48/19.90 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.48/19.90 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 135.48/19.90 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & % 135.48/19.90 all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ % 135.48/19.90 (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = % 135.48/19.90 e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 135.48/19.90 all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 % 135.48/19.90 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.48/19.90 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, % 135.48/19.90 e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.48/19.90 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.90 $i(all_56_29)) % 135.48/19.90 (7) op(e1, e0) = all_52_14 % 135.48/19.90 (8) op(e0, e0) = all_56_31 % 135.48/19.90 (9) op(e1, e0) = e0 % 135.48/19.90 % 135.48/19.90 Begin of proof % 135.48/19.90 | % 135.48/19.90 | BETA: splitting (6) gives: % 135.48/19.90 | % 135.48/19.90 | Case 1: % 135.48/19.90 | | % 135.48/19.90 | | (10) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.48/19.90 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.90 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.90 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 135.48/19.90 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.48/19.90 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.48/19.90 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.48/19.90 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.48/19.90 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.48/19.90 | | $i(all_56_27)) % 135.48/19.90 | | % 135.48/19.90 | | REF_CLOSE: (1), (2), (3), (4), (8), (10) are inconsistent by sub-proof #21. % 135.48/19.90 | | % 135.48/19.90 | Case 2: % 135.48/19.90 | | % 135.48/19.90 | | (11) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.48/19.90 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.48/19.90 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.48/19.90 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.48/19.90 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.48/19.90 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.48/19.90 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.48/19.90 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.48/19.90 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.90 | | $i(all_56_29)) % 135.48/19.90 | | % 135.48/19.90 | | REF_CLOSE: (2), (5), (7), (9), (11) are inconsistent by sub-proof #40. % 135.48/19.90 | | % 135.48/19.90 | End of split % 135.48/19.90 | % 135.48/19.90 End of proof % 135.48/19.90 % 135.48/19.90 Sub-proof #21 shows that the following formulas are inconsistent: % 135.48/19.90 ---------------------------------------------------------------- % 135.48/19.90 (1) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 135.48/19.90 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.48/19.90 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 135.48/19.90 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.48/19.90 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) % 135.48/19.90 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.48/19.90 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.48/19.90 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 135.48/19.90 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 135.48/19.90 (2) op(e3, e1) = e1 % 135.48/19.90 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.90 (4) ~ (e2 = e1) % 135.48/19.90 (5) op(e0, e0) = e1 % 135.48/19.90 (6) op(e0, e0) = all_56_31 % 135.48/19.90 % 135.48/19.90 Begin of proof % 135.48/19.90 | % 135.48/19.90 | BETA: splitting (1) gives: % 135.48/19.90 | % 135.48/19.90 | Case 1: % 135.48/19.90 | | % 135.48/19.90 | | (7) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.48/19.90 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.90 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.90 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.48/19.90 | | $i(all_56_17) & $i(all_56_25) % 135.48/19.90 | | % 135.48/19.90 | | ALPHA: (7) implies: % 135.48/19.90 | | (8) ~ (all_56_17 = e1) % 135.48/19.90 | | (9) op(e3, e1) = all_56_17 % 135.48/19.90 | | % 135.48/19.90 | | REF_CLOSE: (2), (3), (8), (9) are inconsistent by sub-proof #349. % 135.48/19.90 | | % 135.48/19.90 | Case 2: % 135.48/19.90 | | % 135.48/19.90 | | (10) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 135.48/19.90 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.48/19.90 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.48/19.90 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.48/19.90 | | $i(all_56_19) & $i(all_56_27) % 135.48/19.90 | | % 135.48/19.90 | | ALPHA: (10) implies: % 135.48/19.90 | | (11) all_56_31 = e2 % 135.48/19.90 | | % 135.48/19.90 | | REDUCE: (6), (11) imply: % 135.48/19.91 | | (12) op(e0, e0) = e2 % 135.48/19.91 | | % 135.48/19.91 | | REF_CLOSE: (3), (4), (5), (12) are inconsistent by sub-proof #636. % 135.48/19.91 | | % 135.48/19.91 | End of split % 135.48/19.91 | % 135.48/19.91 End of proof % 135.48/19.91 % 135.48/19.91 Sub-proof #22 shows that the following formulas are inconsistent: % 135.48/19.91 ---------------------------------------------------------------- % 135.48/19.91 (1) all_57_2 = e1 % 135.48/19.91 (2) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 135.48/19.91 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 135.48/19.91 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.48/19.91 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.48/19.91 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 135.48/19.91 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.48/19.91 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 135.48/19.91 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.48/19.91 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.91 $i(all_56_21) & $i(all_56_29)) % 135.48/19.91 (3) ~ (e2 = e0) % 135.48/19.91 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.91 (5) ~ (e2 = e1) % 135.48/19.91 (6) ~ (e3 = e0) % 135.48/19.91 (7) ~ (all_52_1 = e0) % 135.48/19.91 (8) ~ (e3 = e2) % 135.48/19.91 (9) ~ (all_52_2 = e0) % 135.48/19.91 (10) all_57_12 = e3 % 135.48/19.91 (11) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 135.48/19.91 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 135.48/19.91 (12) op(e1, e3) = all_52_2 % 135.48/19.91 (13) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) | % 135.48/19.91 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2) % 135.48/19.91 (14) op(e2, e3) = all_52_1 % 135.48/19.91 (15) ~ (e1 = e0) % 135.48/19.91 (16) op(e2, e3) = e1 % 135.48/19.91 % 135.48/19.91 Begin of proof % 135.48/19.91 | % 135.48/19.91 | BETA: splitting (2) gives: % 135.48/19.91 | % 135.48/19.91 | Case 1: % 135.48/19.91 | | % 135.48/19.91 | | (17) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.48/19.91 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 % 135.48/19.91 | | & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.48/19.91 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.48/19.91 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 135.48/19.91 | | % 135.48/19.91 | | ALPHA: (17) implies: % 135.48/19.91 | | (18) op(e3, e3) = e2 % 135.48/19.91 | | % 135.48/19.91 | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (11), (12), (14), (18) are % 135.48/19.91 | | inconsistent by sub-proof #25. % 135.48/19.91 | | % 135.48/19.91 | Case 2: % 135.48/19.91 | | % 135.48/19.91 | | (19) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.48/19.91 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = % 135.48/19.91 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.48/19.91 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.48/19.91 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 135.48/19.91 | | % 135.48/19.91 | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10), (11), (13), (15), (16), (19) % 135.48/19.91 | | are inconsistent by sub-proof #195. % 135.48/19.91 | | % 135.48/19.91 | End of split % 135.48/19.91 | % 135.48/19.91 End of proof % 135.48/19.91 % 135.48/19.91 Sub-proof #23 shows that the following formulas are inconsistent: % 135.48/19.91 ---------------------------------------------------------------- % 135.48/19.91 (1) ~ (all_10_0 = e1) % 135.48/19.91 (2) ~ (all_52_11 = all_10_0) % 135.48/19.91 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 135.48/19.91 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 135.48/19.91 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.91 (5) op(e0, e0) = e1 % 135.48/19.91 (6) op(e0, e1) = all_52_11 % 135.48/19.91 (7) op(e0, e2) = all_52_7 % 135.48/19.91 (8) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 135.48/19.91 (9) ~ (all_10_0 = e2) % 135.48/19.91 (10) ~ (all_52_7 = all_10_0) % 135.48/19.91 (11) ~ (all_10_0 = e0) % 135.48/19.91 (12) all_54_12 = all_10_0 % 135.48/19.91 (13) all_57_12 = e2 % 135.48/19.91 % 135.48/19.91 Begin of proof % 135.48/19.91 | % 135.48/19.91 | BETA: splitting (8) gives: % 135.48/19.91 | % 135.48/19.91 | Case 1: % 135.48/19.91 | | % 135.48/19.91 | | (14) all_54_12 = e3 % 135.48/19.91 | | % 135.48/19.91 | | COMBINE_EQS: (12), (14) imply: % 135.48/19.91 | | (15) all_10_0 = e3 % 135.48/19.91 | | % 135.48/19.91 | | SIMP: (15) implies: % 135.48/19.91 | | (16) all_10_0 = e3 % 135.48/19.91 | | % 135.48/19.91 | | REDUCE: (10), (16) imply: % 135.48/19.91 | | (17) ~ (all_52_7 = e3) % 135.48/19.91 | | % 135.48/19.91 | | REDUCE: (2), (16) imply: % 135.48/19.91 | | (18) ~ (all_52_11 = e3) % 135.48/19.91 | | % 135.48/19.91 | | REDUCE: (9), (16) imply: % 135.48/19.91 | | (19) ~ (e3 = e2) % 135.48/19.91 | | % 135.48/19.91 | | REDUCE: (1), (16) imply: % 135.48/19.91 | | (20) ~ (e3 = e1) % 135.48/19.91 | | % 135.48/19.91 | | REF_CLOSE: (3), (4), (5), (6), (7), (13), (17), (18), (19), (20) are % 135.48/19.91 | | inconsistent by sub-proof #29. % 135.48/19.91 | | % 135.48/19.91 | Case 2: % 135.48/19.91 | | % 135.48/19.91 | | (21) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 135.48/19.91 | | % 135.48/19.91 | | REF_CLOSE: (1), (9), (11), (12), (21) are inconsistent by sub-proof #24. % 135.48/19.91 | | % 135.48/19.91 | End of split % 135.48/19.91 | % 135.48/19.91 End of proof % 135.48/19.91 % 135.48/19.91 Sub-proof #24 shows that the following formulas are inconsistent: % 135.48/19.91 ---------------------------------------------------------------- % 135.48/19.91 (1) ~ (all_10_0 = e1) % 135.48/19.91 (2) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 135.48/19.91 (3) ~ (all_10_0 = e2) % 135.48/19.91 (4) ~ (all_10_0 = e0) % 135.48/19.91 (5) all_54_12 = all_10_0 % 135.48/19.91 % 135.48/19.91 Begin of proof % 135.48/19.91 | % 135.48/19.91 | BETA: splitting (2) gives: % 135.48/19.91 | % 135.48/19.91 | Case 1: % 135.48/19.91 | | % 135.48/19.91 | | (6) all_54_12 = e2 % 135.48/19.91 | | % 135.48/19.91 | | COMBINE_EQS: (5), (6) imply: % 135.48/19.91 | | (7) all_10_0 = e2 % 135.48/19.91 | | % 135.48/19.91 | | SIMP: (7) implies: % 135.48/19.91 | | (8) all_10_0 = e2 % 135.48/19.91 | | % 135.48/19.91 | | REDUCE: (3), (8) imply: % 135.48/19.91 | | (9) $false % 135.48/19.91 | | % 135.48/19.91 | | CLOSE: (9) is inconsistent. % 135.48/19.91 | | % 135.48/19.91 | Case 2: % 135.48/19.91 | | % 135.48/19.91 | | (10) all_54_12 = e1 | all_54_12 = e0 % 135.48/19.91 | | % 135.48/19.91 | | BETA: splitting (10) gives: % 135.48/19.91 | | % 135.48/19.91 | | Case 1: % 135.48/19.91 | | | % 135.48/19.91 | | | (11) all_54_12 = e1 % 135.48/19.91 | | | % 135.48/19.91 | | | COMBINE_EQS: (5), (11) imply: % 135.48/19.91 | | | (12) all_10_0 = e1 % 135.48/19.91 | | | % 135.48/19.91 | | | SIMP: (12) implies: % 135.48/19.91 | | | (13) all_10_0 = e1 % 135.48/19.91 | | | % 135.48/19.91 | | | REDUCE: (1), (13) imply: % 135.48/19.91 | | | (14) $false % 135.48/19.91 | | | % 135.48/19.91 | | | CLOSE: (14) is inconsistent. % 135.48/19.91 | | | % 135.48/19.91 | | Case 2: % 135.48/19.91 | | | % 135.48/19.91 | | | (15) all_54_12 = e0 % 135.48/19.91 | | | % 135.48/19.91 | | | COMBINE_EQS: (5), (15) imply: % 135.48/19.91 | | | (16) all_10_0 = e0 % 135.48/19.91 | | | % 135.48/19.91 | | | SIMP: (16) implies: % 135.48/19.91 | | | (17) all_10_0 = e0 % 135.48/19.91 | | | % 135.48/19.91 | | | REDUCE: (4), (17) imply: % 135.48/19.91 | | | (18) $false % 135.48/19.91 | | | % 135.48/19.91 | | | CLOSE: (18) is inconsistent. % 135.48/19.91 | | | % 135.48/19.91 | | End of split % 135.48/19.91 | | % 135.48/19.91 | End of split % 135.48/19.91 | % 135.48/19.91 End of proof % 135.48/19.91 % 135.48/19.91 Sub-proof #25 shows that the following formulas are inconsistent: % 135.48/19.91 ---------------------------------------------------------------- % 135.48/19.91 (1) op(e3, e3) = e2 % 135.48/19.91 (2) ~ (e2 = e0) % 135.48/19.91 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.91 (4) ~ (e3 = e0) % 135.48/19.91 (5) ~ (all_52_1 = e0) % 135.48/19.91 (6) ~ (all_52_2 = e0) % 135.48/19.91 (7) all_57_12 = e3 % 135.48/19.91 (8) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 135.48/19.91 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 135.48/19.91 (9) op(e1, e3) = all_52_2 % 135.48/19.91 (10) op(e2, e3) = all_52_1 % 135.48/19.91 % 135.48/19.91 Begin of proof % 135.48/19.91 | % 135.48/19.91 | BETA: splitting (8) gives: % 135.48/19.91 | % 135.48/19.91 | Case 1: % 135.48/19.91 | | % 135.48/19.91 | | (11) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = % 135.48/19.91 | | e0) % 135.48/19.91 | | % 135.48/19.91 | | REF_CLOSE: (1), (2), (3), (5), (10), (11) are inconsistent by sub-proof #89. % 135.48/19.91 | | % 135.48/19.91 | Case 2: % 135.48/19.91 | | % 135.48/19.91 | | (12) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = % 135.48/19.91 | | e0) % 135.48/19.91 | | % 135.48/19.91 | | REF_CLOSE: (3), (4), (6), (7), (9), (12) are inconsistent by sub-proof #27. % 135.48/19.91 | | % 135.48/19.91 | End of split % 135.48/19.91 | % 135.48/19.91 End of proof % 135.48/19.91 % 135.48/19.91 Sub-proof #26 shows that the following formulas are inconsistent: % 135.48/19.91 ---------------------------------------------------------------- % 135.48/19.91 (1) ~ (e2 = e0) % 135.48/19.91 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.91 (3) ~ (e3 = e0) % 135.48/19.91 (4) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 135.48/19.91 (5) all_57_9 = e3 % 135.48/19.91 (6) ~ (e3 = e2) % 135.48/19.91 (7) op(e1, e1) = e3 % 135.48/19.91 (8) all_57_15 = e1 % 135.48/19.91 (9) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 135.48/19.91 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = % 135.48/19.91 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 135.48/19.91 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 135.48/19.91 (10) ~ (e1 = e0) % 135.48/19.91 (11) all_57_10 = e2 % 135.48/19.91 % 135.48/19.91 Begin of proof % 135.48/19.91 | % 135.48/19.91 | BETA: splitting (4) gives: % 135.48/19.91 | % 135.48/19.91 | Case 1: % 135.48/19.91 | | % 135.48/19.91 | | (12) all_57_8 = e2 & op(e1, e1) = e2 % 135.48/19.91 | | % 135.48/19.91 | | ALPHA: (12) implies: % 135.48/19.91 | | (13) op(e1, e1) = e2 % 135.48/19.91 | | % 135.48/19.91 | | REF_CLOSE: (2), (6), (7), (13) are inconsistent by sub-proof #109. % 135.48/19.91 | | % 135.48/19.91 | Case 2: % 135.48/19.91 | | % 135.48/19.91 | | (14) all_57_11 = e2 & op(e1, e0) = e2 % 135.48/19.91 | | % 135.48/19.91 | | ALPHA: (14) implies: % 135.48/19.91 | | (15) all_57_11 = e2 % 135.48/19.91 | | % 135.48/19.91 | | BETA: splitting (9) gives: % 135.48/19.91 | | % 135.48/19.91 | | Case 1: % 135.48/19.91 | | | % 135.48/19.91 | | | (16) all_57_15 = e0 & op(e0, e0) = e0 % 135.48/19.91 | | | % 135.48/19.91 | | | REF_CLOSE: (8), (10), (16) are inconsistent by sub-proof #412. % 135.48/19.91 | | | % 135.48/19.91 | | Case 2: % 135.48/19.91 | | | % 135.48/19.91 | | | (17) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) % 135.48/19.91 | | | = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 % 135.48/19.91 | | | & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) | % 135.48/19.91 | | | (all_57_14 = e0 & op(e0, e1) = e0)) % 135.48/19.91 | | | % 135.48/19.91 | | | ALPHA: (17) implies: % 135.48/19.91 | | | (18) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = % 135.48/19.91 | | | e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 135.48/19.91 | | | % 135.48/19.91 | | | BETA: splitting (18) gives: % 135.48/19.91 | | | % 135.48/19.91 | | | Case 1: % 135.48/19.91 | | | | % 135.48/19.91 | | | | (19) all_57_9 = e0 & op(e3, e0) = e0 % 135.48/19.91 | | | | % 135.48/19.91 | | | | ALPHA: (19) implies: % 135.48/19.91 | | | | (20) all_57_9 = e0 % 135.48/19.91 | | | | % 135.48/19.91 | | | | REF_CLOSE: (3), (5), (20) are inconsistent by sub-proof #670. % 135.48/19.91 | | | | % 135.48/19.91 | | | Case 2: % 135.48/19.91 | | | | % 135.48/19.91 | | | | (21) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, % 135.48/19.91 | | | | e0) = e0) % 135.48/19.91 | | | | % 135.48/19.91 | | | | BETA: splitting (21) gives: % 135.48/19.91 | | | | % 135.48/19.91 | | | | Case 1: % 135.48/19.91 | | | | | % 135.48/19.91 | | | | | (22) all_57_10 = e0 & op(e2, e0) = e0 % 135.48/19.91 | | | | | % 135.48/19.91 | | | | | REF_CLOSE: (1), (11), (22) are inconsistent by sub-proof #363. % 135.48/19.91 | | | | | % 135.48/19.91 | | | | Case 2: % 135.48/19.91 | | | | | % 135.48/19.91 | | | | | (23) all_57_11 = e0 & op(e1, e0) = e0 % 135.48/19.91 | | | | | % 135.48/19.91 | | | | | ALPHA: (23) implies: % 135.48/19.91 | | | | | (24) all_57_11 = e0 % 135.48/19.91 | | | | | % 135.48/19.91 | | | | | REF_CLOSE: (1), (15), (24) are inconsistent by sub-proof #638. % 135.48/19.91 | | | | | % 135.48/19.91 | | | | End of split % 135.48/19.91 | | | | % 135.48/19.91 | | | End of split % 135.48/19.91 | | | % 135.48/19.91 | | End of split % 135.48/19.91 | | % 135.48/19.91 | End of split % 135.48/19.91 | % 135.48/19.91 End of proof % 135.48/19.91 % 135.48/19.91 Sub-proof #27 shows that the following formulas are inconsistent: % 135.48/19.91 ---------------------------------------------------------------- % 135.48/19.91 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.91 (2) ~ (e3 = e0) % 135.48/19.91 (3) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 135.48/19.91 (4) ~ (all_52_2 = e0) % 135.48/19.91 (5) all_57_12 = e3 % 135.48/19.91 (6) op(e1, e3) = all_52_2 % 135.48/19.91 % 135.48/19.91 Begin of proof % 135.48/19.91 | % 135.48/19.91 | BETA: splitting (3) gives: % 135.48/19.91 | % 135.48/19.91 | Case 1: % 135.48/19.91 | | % 135.48/19.91 | | (7) all_57_6 = e0 & op(e1, e3) = e0 % 135.48/19.91 | | % 135.48/19.91 | | REF_CLOSE: (1), (4), (6), (7) are inconsistent by sub-proof #73. % 135.48/19.91 | | % 135.48/19.91 | Case 2: % 135.48/19.91 | | % 135.48/19.91 | | (8) all_57_12 = e0 & op(e0, e3) = e0 % 135.48/19.91 | | % 135.48/19.91 | | ALPHA: (8) implies: % 135.48/19.91 | | (9) all_57_12 = e0 % 135.48/19.91 | | % 135.48/19.91 | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #492. % 135.48/19.91 | | % 135.48/19.91 | End of split % 135.48/19.91 | % 135.48/19.91 End of proof % 135.48/19.91 % 135.48/19.91 Sub-proof #28 shows that the following formulas are inconsistent: % 135.48/19.91 ---------------------------------------------------------------- % 135.48/19.91 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 135.48/19.91 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.48/19.91 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 135.48/19.91 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.48/19.91 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ % 135.48/19.91 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.48/19.91 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = % 135.48/19.91 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.48/19.91 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.91 $i(all_56_29)) % 135.48/19.91 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.91 (3) ~ (e2 = e1) % 135.48/19.91 (4) op(e1, e3) = e2 % 135.48/19.91 (5) op(e1, e3) = all_52_2 % 135.48/19.91 (6) op(e1, e0) = e0 % 135.48/19.91 % 135.48/19.91 Begin of proof % 135.48/19.91 | % 135.48/19.91 | BETA: splitting (1) gives: % 135.48/19.91 | % 135.48/19.91 | Case 1: % 135.48/19.91 | | % 135.48/19.91 | | (7) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.48/19.91 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.91 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.91 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) % 135.48/19.91 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 135.48/19.91 | | % 135.48/19.91 | | ALPHA: (7) implies: % 135.48/19.91 | | (8) op(e1, e3) = e1 % 135.48/19.91 | | % 135.48/19.91 | | REF_CLOSE: (2), (3), (4), (5), (8) are inconsistent by sub-proof #517. % 135.48/19.91 | | % 135.48/19.91 | Case 2: % 135.48/19.91 | | % 135.48/19.91 | | (9) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.48/19.91 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 % 135.48/19.91 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.48/19.91 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.48/19.91 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 135.48/19.91 | | % 135.48/19.91 | | ALPHA: (9) implies: % 135.48/19.91 | | (10) ~ (all_56_29 = e0) % 135.48/19.91 | | (11) op(e1, e0) = all_56_29 % 135.48/19.91 | | % 135.48/19.91 | | REF_CLOSE: (2), (6), (10), (11) are inconsistent by sub-proof #45. % 135.48/19.91 | | % 135.48/19.91 | End of split % 135.48/19.91 | % 135.48/19.91 End of proof % 135.48/19.91 % 135.48/19.91 Sub-proof #29 shows that the following formulas are inconsistent: % 135.48/19.91 ---------------------------------------------------------------- % 135.48/19.91 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 135.48/19.91 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 135.48/19.91 (2) ~ (all_52_7 = e3) % 135.48/19.91 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.91 (4) ~ (e3 = e2) % 135.48/19.91 (5) op(e0, e0) = e1 % 135.48/19.91 (6) op(e0, e1) = all_52_11 % 135.48/19.91 (7) op(e0, e2) = all_52_7 % 135.48/19.91 (8) ~ (all_52_11 = e3) % 135.48/19.91 (9) ~ (e3 = e1) % 135.48/19.91 (10) all_57_12 = e2 % 135.48/19.91 % 135.48/19.91 Begin of proof % 135.48/19.91 | % 135.48/19.91 | BETA: splitting (1) gives: % 135.48/19.91 | % 135.48/19.91 | Case 1: % 135.48/19.91 | | % 135.48/19.91 | | (11) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = % 135.48/19.91 | | e3) % 135.48/19.91 | | % 135.48/19.91 | | BETA: splitting (11) gives: % 135.48/19.91 | | % 135.48/19.91 | | Case 1: % 135.48/19.91 | | | % 135.48/19.91 | | | (12) all_57_12 = e3 & op(e0, e3) = e3 % 135.48/19.91 | | | % 135.48/19.91 | | | ALPHA: (12) implies: % 135.48/19.91 | | | (13) all_57_12 = e3 % 135.48/19.91 | | | % 135.48/19.91 | | | REF_CLOSE: (4), (10), (13) are inconsistent by sub-proof #518. % 135.48/19.91 | | | % 135.48/19.91 | | Case 2: % 135.48/19.91 | | | % 135.48/19.91 | | | (14) all_57_13 = e3 & op(e0, e2) = e3 % 135.48/19.91 | | | % 135.48/19.91 | | | REF_CLOSE: (2), (3), (7), (14) are inconsistent by sub-proof #556. % 135.48/19.91 | | | % 135.48/19.91 | | End of split % 135.48/19.91 | | % 135.48/19.91 | Case 2: % 135.48/19.91 | | % 135.48/19.91 | | (15) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = % 135.48/19.91 | | e3) % 135.48/19.91 | | % 135.48/19.91 | | REF_CLOSE: (3), (5), (6), (8), (9), (15) are inconsistent by sub-proof #37. % 135.48/19.91 | | % 135.48/19.91 | End of split % 135.48/19.91 | % 135.48/19.91 End of proof % 135.48/19.91 % 135.48/19.91 Sub-proof #30 shows that the following formulas are inconsistent: % 135.48/19.91 ---------------------------------------------------------------- % 135.48/19.91 (1) op(e1, e1) = all_6_2 % 135.48/19.91 (2) ~ (all_6_2 = e3) % 135.48/19.91 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.91 (4) ~ (e2 = e1) % 135.48/19.91 (5) op(e0, e0) = e1 % 135.48/19.91 (6) ~ (all_52_11 = all_6_2) % 135.48/19.91 (7) op(e0, e1) = all_52_11 % 135.48/19.91 (8) all_54_10 = all_6_2 % 135.48/19.91 (9) ~ (all_6_2 = e2) % 135.48/19.91 (10) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 135.48/19.91 (11) ~ (all_52_14 = e1) % 135.48/19.91 (12) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.48/19.91 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.48/19.91 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.48/19.91 e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.48/19.91 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.48/19.91 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 135.48/19.91 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.48/19.91 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 135.48/19.91 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 % 135.48/19.91 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.48/19.91 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.48/19.91 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.48/19.91 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.48/19.91 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.48/19.91 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.48/19.91 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.48/19.91 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.48/19.91 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.48/19.91 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.48/19.91 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.48/19.91 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.48/19.91 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.48/19.91 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.48/19.91 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.91 $i(all_56_29)))) % 135.48/19.91 (13) ~ (e3 = e1) % 135.48/19.91 (14) op(e1, e0) = all_52_14 % 135.48/19.91 % 135.48/19.91 Begin of proof % 135.48/19.91 | % 135.48/19.91 | BETA: splitting (12) gives: % 135.48/19.91 | % 135.48/19.91 | Case 1: % 135.48/19.91 | | % 135.48/19.91 | | (15) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 135.48/19.91 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.48/19.91 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.48/19.91 | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) % 135.48/19.91 | | & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 135.48/19.91 | | % 135.48/19.91 | | ALPHA: (15) implies: % 135.48/19.91 | | (16) op(e1, e1) = e2 % 135.48/19.91 | | % 135.48/19.91 | | REF_CLOSE: (1), (3), (9), (16) are inconsistent by sub-proof #767. % 135.48/19.91 | | % 135.48/19.91 | Case 2: % 135.48/19.91 | | % 135.48/19.91 | | (17) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 % 135.48/19.91 | | = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.48/19.91 | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) % 135.48/19.91 | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.48/19.91 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.48/19.91 | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 % 135.48/19.91 | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.48/19.91 | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.48/19.91 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.48/19.91 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.48/19.91 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 % 135.48/19.91 | | = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.48/19.91 | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, % 135.48/19.91 | | e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 135.48/19.91 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.48/19.91 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.48/19.91 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.48/19.91 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.48/19.91 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.48/19.91 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29))) % 135.48/19.91 | | % 135.48/19.91 | | ALPHA: (17) implies: % 135.48/19.91 | | (18) op(e0, e0) = all_56_31 % 135.48/19.91 | | (19) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.48/19.91 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.91 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.91 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 135.48/19.91 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.48/19.91 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.48/19.91 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.48/19.91 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.48/19.91 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.48/19.91 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 135.48/19.91 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 % 135.48/19.91 | | = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 135.48/19.91 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.48/19.91 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & % 135.48/19.91 | | all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.48/19.91 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 135.48/19.91 | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.48/19.91 | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.91 | | $i(all_56_21) & $i(all_56_29)) % 135.48/19.91 | | % 135.48/19.91 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), % 135.48/19.91 | | (14), (18), (19) are inconsistent by sub-proof #31. % 135.48/19.91 | | % 135.48/19.91 | End of split % 135.48/19.91 | % 135.48/19.91 End of proof % 135.48/19.91 % 135.48/19.91 Sub-proof #31 shows that the following formulas are inconsistent: % 135.48/19.91 ---------------------------------------------------------------- % 135.48/19.92 (1) op(e1, e1) = all_6_2 % 135.48/19.92 (2) ~ (all_6_2 = e3) % 135.48/19.92 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.92 (4) ~ (e2 = e1) % 135.48/19.92 (5) op(e0, e0) = e1 % 135.48/19.92 (6) ~ (all_52_11 = all_6_2) % 135.48/19.92 (7) op(e0, e1) = all_52_11 % 135.48/19.92 (8) all_54_10 = all_6_2 % 135.48/19.92 (9) ~ (all_6_2 = e2) % 135.48/19.92 (10) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 135.48/19.92 (11) ~ (all_52_14 = e1) % 135.48/19.92 (12) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.48/19.92 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.92 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 135.48/19.92 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.48/19.92 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 135.48/19.92 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.48/19.92 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.48/19.92 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.48/19.92 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.48/19.92 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.48/19.92 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.48/19.92 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.48/19.92 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.48/19.92 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.48/19.92 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.48/19.92 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 135.48/19.92 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.92 $i(all_56_21) & $i(all_56_29)) % 135.48/19.92 (13) ~ (e3 = e1) % 135.48/19.92 (14) op(e1, e0) = all_52_14 % 135.48/19.92 (15) op(e0, e0) = all_56_31 % 135.48/19.92 % 135.48/19.92 Begin of proof % 135.48/19.92 | % 135.48/19.92 | GROUND_INST: instantiating (3) with e1, all_56_31, e0, e0, simplifying with % 135.48/19.92 | (5), (15) gives: % 135.48/19.92 | (16) all_56_31 = e1 % 135.48/19.92 | % 135.48/19.92 | BETA: splitting (12) gives: % 135.48/19.92 | % 135.48/19.92 | Case 1: % 135.48/19.92 | | % 135.48/19.92 | | (17) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.48/19.92 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.92 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.92 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 135.48/19.92 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.48/19.92 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.48/19.92 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.48/19.92 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.48/19.92 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.48/19.92 | | $i(all_56_27)) % 135.48/19.92 | | % 135.48/19.92 | | REF_CLOSE: (4), (13), (16), (17) are inconsistent by sub-proof #32. % 135.48/19.92 | | % 135.48/19.92 | Case 2: % 135.48/19.92 | | % 135.48/19.92 | | (18) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.48/19.92 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.48/19.92 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.48/19.92 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.48/19.92 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.48/19.92 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.48/19.92 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.48/19.92 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.48/19.92 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.92 | | $i(all_56_29)) % 135.48/19.92 | | % 135.48/19.92 | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (14), (18) are % 135.48/19.92 | | inconsistent by sub-proof #59. % 135.48/19.92 | | % 135.48/19.92 | End of split % 135.48/19.92 | % 135.48/19.92 End of proof % 135.48/19.92 % 135.48/19.92 Sub-proof #32 shows that the following formulas are inconsistent: % 135.48/19.92 ---------------------------------------------------------------- % 135.48/19.92 (1) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 135.48/19.92 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.48/19.92 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 135.48/19.92 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.48/19.92 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) % 135.48/19.92 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.48/19.92 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.48/19.92 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 135.48/19.92 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 135.48/19.92 (2) all_56_31 = e1 % 135.48/19.92 (3) ~ (e3 = e1) % 135.48/19.92 (4) ~ (e2 = e1) % 135.48/19.92 % 135.48/19.92 Begin of proof % 135.48/19.92 | % 135.48/19.92 | BETA: splitting (1) gives: % 135.48/19.92 | % 135.48/19.92 | Case 1: % 135.48/19.92 | | % 135.48/19.92 | | (5) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.48/19.92 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.92 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.92 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.48/19.92 | | $i(all_56_17) & $i(all_56_25) % 135.48/19.92 | | % 135.48/19.92 | | ALPHA: (5) implies: % 135.48/19.92 | | (6) all_56_31 = e3 % 135.48/19.92 | | % 135.48/19.92 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #253. % 135.48/19.92 | | % 135.48/19.92 | Case 2: % 135.48/19.92 | | % 135.48/19.92 | | (7) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 135.48/19.92 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.48/19.92 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.48/19.92 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.48/19.92 | | $i(all_56_19) & $i(all_56_27) % 135.48/19.92 | | % 135.48/19.92 | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #33. % 135.48/19.92 | | % 135.48/19.92 | End of split % 135.48/19.92 | % 135.48/19.92 End of proof % 135.48/19.92 % 135.48/19.92 Sub-proof #33 shows that the following formulas are inconsistent: % 135.48/19.92 ---------------------------------------------------------------- % 135.48/19.92 (1) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.48/19.92 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 % 135.48/19.92 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 135.48/19.92 all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.48/19.92 $i(all_56_19) & $i(all_56_27) % 135.48/19.92 (2) all_56_31 = e1 % 135.48/19.92 (3) ~ (e2 = e1) % 135.48/19.92 % 135.48/19.92 Begin of proof % 135.48/19.92 | % 135.48/19.92 | ALPHA: (1) implies: % 135.48/19.92 | (4) all_56_31 = e2 % 135.48/19.92 | % 135.48/19.92 | COMBINE_EQS: (2), (4) imply: % 135.48/19.92 | (5) e2 = e1 % 135.48/19.92 | % 135.48/19.92 | SIMP: (5) implies: % 135.48/19.92 | (6) e2 = e1 % 135.48/19.92 | % 135.48/19.92 | REDUCE: (3), (6) imply: % 135.48/19.92 | (7) $false % 135.48/19.92 | % 135.48/19.92 | CLOSE: (7) is inconsistent. % 135.48/19.92 | % 135.48/19.92 End of proof % 135.48/19.92 % 135.48/19.92 Sub-proof #34 shows that the following formulas are inconsistent: % 135.48/19.92 ---------------------------------------------------------------- % 135.48/19.92 (1) ~ (all_52_11 = e2) % 135.48/19.92 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.92 (3) ~ (e2 = e1) % 135.48/19.92 (4) op(e0, e0) = e1 % 135.48/19.92 (5) op(e0, e1) = all_52_11 % 135.48/19.92 (6) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2) % 135.48/19.92 % 135.48/19.92 Begin of proof % 135.48/19.92 | % 135.48/19.92 | BETA: splitting (6) gives: % 135.48/19.92 | % 135.48/19.92 | Case 1: % 135.48/19.92 | | % 135.48/19.92 | | (7) all_57_14 = e2 & op(e0, e1) = e2 % 135.48/19.92 | | % 135.48/19.92 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #512. % 135.48/19.92 | | % 135.48/19.92 | Case 2: % 135.48/19.92 | | % 135.48/19.92 | | (8) all_57_15 = e2 & op(e0, e0) = e2 % 135.48/19.92 | | % 135.48/19.92 | | ALPHA: (8) implies: % 135.48/19.92 | | (9) op(e0, e0) = e2 % 135.48/19.92 | | % 135.48/19.92 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #636. % 135.48/19.92 | | % 135.48/19.92 | End of split % 135.48/19.92 | % 135.48/19.92 End of proof % 135.48/19.92 % 135.48/19.92 Sub-proof #35 shows that the following formulas are inconsistent: % 135.48/19.92 ---------------------------------------------------------------- % 135.48/19.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.92 (2) op(e1, e0) = all_12_0 % 135.48/19.92 (3) op(e1, e0) = e2 % 135.48/19.92 (4) ~ (all_12_0 = e2) % 135.48/19.92 % 135.48/19.92 Begin of proof % 135.48/19.92 | % 135.48/19.92 | GROUND_INST: instantiating (1) with e2, all_12_0, e0, e1, simplifying with % 135.48/19.92 | (2), (3) gives: % 135.48/19.92 | (5) all_12_0 = e2 % 135.48/19.92 | % 135.48/19.92 | REDUCE: (4), (5) imply: % 135.48/19.92 | (6) $false % 135.48/19.92 | % 135.48/19.92 | CLOSE: (6) is inconsistent. % 135.48/19.92 | % 135.48/19.92 End of proof % 135.48/19.92 % 135.48/19.92 Sub-proof #36 shows that the following formulas are inconsistent: % 135.48/19.92 ---------------------------------------------------------------- % 135.48/19.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.92 (2) op(e1, e1) = all_12_1 % 135.48/19.92 (3) op(e1, e1) = e3 % 135.48/19.92 (4) ~ (all_12_1 = e3) % 135.48/19.92 % 135.48/19.92 Begin of proof % 135.48/19.92 | % 135.48/19.92 | GROUND_INST: instantiating (1) with e3, all_12_1, e1, e1, simplifying with % 135.48/19.92 | (2), (3) gives: % 135.48/19.92 | (5) all_12_1 = e3 % 135.48/19.92 | % 135.48/19.92 | REDUCE: (4), (5) imply: % 135.48/19.92 | (6) $false % 135.48/19.92 | % 135.48/19.92 | CLOSE: (6) is inconsistent. % 135.48/19.92 | % 135.48/19.92 End of proof % 135.48/19.92 % 135.48/19.92 Sub-proof #37 shows that the following formulas are inconsistent: % 135.48/19.92 ---------------------------------------------------------------- % 135.48/19.92 (1) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 135.48/19.92 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.92 (3) op(e0, e0) = e1 % 135.48/19.92 (4) op(e0, e1) = all_52_11 % 135.48/19.92 (5) ~ (all_52_11 = e3) % 135.48/19.92 (6) ~ (e3 = e1) % 135.48/19.92 % 135.48/19.92 Begin of proof % 135.48/19.92 | % 135.48/19.92 | BETA: splitting (1) gives: % 135.48/19.92 | % 135.48/19.92 | Case 1: % 135.48/19.92 | | % 135.48/19.92 | | (7) all_57_14 = e3 & op(e0, e1) = e3 % 135.48/19.92 | | % 135.48/19.92 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #652. % 135.48/19.92 | | % 135.48/19.92 | Case 2: % 135.48/19.92 | | % 135.48/19.92 | | (8) all_57_15 = e3 & op(e0, e0) = e3 % 135.48/19.92 | | % 135.48/19.92 | | ALPHA: (8) implies: % 135.48/19.92 | | (9) op(e0, e0) = e3 % 135.48/19.92 | | % 135.48/19.92 | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #606. % 135.48/19.92 | | % 135.48/19.92 | End of split % 135.48/19.92 | % 135.48/19.92 End of proof % 135.48/19.92 % 135.48/19.92 Sub-proof #38 shows that the following formulas are inconsistent: % 135.48/19.92 ---------------------------------------------------------------- % 135.48/19.92 (1) op(e2, e2) = all_8_2 % 135.48/19.92 (2) op(e2, e0) = all_52_13 % 135.48/19.92 (3) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 135.48/19.92 (4) ~ (all_8_2 = e1) % 135.48/19.92 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.92 (6) ~ (e3 = e2) % 135.48/19.92 (7) op(e0, e0) = e1 % 135.48/19.92 (8) op(e0, e2) = all_52_7 % 135.48/19.92 (9) op(e1, e1) = e2 % 135.48/19.92 (10) ~ (all_10_2 = e0) % 135.48/19.92 (11) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.48/19.92 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.48/19.92 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.48/19.92 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.48/19.92 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 135.48/19.92 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.48/19.92 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) % 135.48/19.92 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.48/19.92 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.92 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 135.48/19.92 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.48/19.92 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 135.48/19.92 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 135.48/19.92 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.48/19.92 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) % 135.48/19.92 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 135.48/19.92 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 135.48/19.92 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 135.48/19.92 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.48/19.92 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.48/19.92 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.92 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 135.48/19.92 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & % 135.48/19.92 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & % 135.48/19.92 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.48/19.92 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.48/19.92 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.48/19.92 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.92 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ % 135.48/19.92 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.48/19.92 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 135.48/19.92 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 135.48/19.92 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.48/19.92 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) % 135.48/19.92 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.48/19.92 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.48/19.92 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 % 135.48/19.92 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.48/19.92 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = % 135.48/19.92 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.48/19.92 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 135.48/19.92 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.48/19.92 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.48/19.92 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 135.48/19.92 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.48/19.92 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.48/19.92 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.48/19.92 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.48/19.92 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.48/19.92 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.48/19.92 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.48/19.92 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.48/19.92 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.48/19.92 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.48/19.92 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.48/19.92 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.48/19.92 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.92 $i(all_56_29)))) % 135.48/19.92 (12) op(e3, e3) = all_10_2 % 135.48/19.92 (13) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 135.48/19.92 (14) all_54_5 = all_8_2 % 135.48/19.92 (15) ~ (all_8_2 = e0) % 135.48/19.92 (16) ~ (all_52_13 = all_8_2) % 135.48/19.92 (17) ~ (all_10_2 = e2) % 135.48/19.92 (18) ~ (all_52_14 = e1) % 135.48/19.92 (19) ~ (e3 = e1) % 135.48/19.92 (20) ~ (all_52_7 = all_8_2) % 135.48/19.92 (21) ~ (all_8_2 = e3) % 135.48/19.92 (22) op(e1, e0) = all_52_14 % 135.48/19.92 (23) op(e1, e0) = e0 % 135.48/19.92 % 135.48/19.92 Begin of proof % 135.48/19.92 | % 135.48/19.92 | BETA: splitting (11) gives: % 135.48/19.92 | % 135.48/19.92 | Case 1: % 135.48/19.92 | | % 135.48/19.92 | | (24) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 % 135.48/19.92 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = % 135.48/19.92 | | e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.48/19.92 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.48/19.92 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.48/19.92 | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.48/19.92 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = % 135.48/19.92 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.48/19.92 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.48/19.92 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 135.48/19.92 | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 % 135.48/19.92 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = % 135.48/19.92 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.48/19.92 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 135.48/19.92 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.48/19.92 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.48/19.92 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.92 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.92 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 135.48/19.92 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 135.48/19.92 | | % 135.48/19.92 | | REF_CLOSE: (1), (5), (10), (12), (17), (21), (23), (24) are inconsistent by % 135.48/19.92 | | sub-proof #43. % 135.48/19.92 | | % 135.48/19.92 | Case 2: % 135.48/19.92 | | % 135.48/19.92 | | (25) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.48/19.92 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.92 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.92 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & % 135.48/19.92 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.48/19.92 | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.48/19.92 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.48/19.92 | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, % 135.48/19.92 | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.48/19.92 | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.92 | | $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.48/19.92 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 % 135.48/19.92 | | = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 135.48/19.92 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.48/19.92 | | op(e0, e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.48/19.92 | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 % 135.48/19.92 | | & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.48/19.92 | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.48/19.92 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.48/19.92 | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.48/19.92 | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 & % 135.48/19.92 | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.48/19.92 | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.48/19.92 | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 135.48/19.92 | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.48/19.92 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) % 135.48/19.92 | | & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 135.48/19.92 | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.48/19.92 | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.48/19.92 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.48/19.92 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.48/19.92 | | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 135.48/19.92 | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.48/19.92 | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & % 135.48/19.92 | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 135.48/19.92 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.48/19.92 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.48/19.92 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.48/19.92 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.48/19.92 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.48/19.92 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.92 | | $i(all_56_29)))) % 135.48/19.92 | | % 135.48/19.92 | | BETA: splitting (25) gives: % 135.48/19.92 | | % 135.48/19.92 | | Case 1: % 135.48/19.92 | | | % 135.48/19.92 | | | (26) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ % 135.48/19.92 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 135.48/19.92 | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 135.48/19.92 | | | all_56_17 & op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 135.48/19.92 | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.48/19.92 | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 % 135.48/19.92 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.48/19.92 | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, % 135.48/19.92 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.48/19.92 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.48/19.92 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.48/19.92 | | | % 135.48/19.92 | | | REF_CLOSE: (5), (6), (9), (23), (26) are inconsistent by sub-proof #42. % 135.48/19.92 | | | % 135.48/19.92 | | Case 2: % 135.48/19.92 | | | % 135.48/19.92 | | | (27) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.48/19.92 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.48/19.92 | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & % 135.48/19.92 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.48/19.92 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.48/19.92 | | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 % 135.48/19.92 | | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.48/19.92 | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.48/19.92 | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.48/19.92 | | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) % 135.48/19.92 | | | & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 & % 135.48/19.92 | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 135.48/19.92 | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.48/19.92 | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 135.48/19.92 | | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.48/19.92 | | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.48/19.92 | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 135.48/19.92 | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ % 135.48/19.92 | | | (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.48/19.92 | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.48/19.92 | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 135.48/19.92 | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 135.48/19.92 | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.48/19.92 | | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, % 135.48/19.92 | | | e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.48/19.92 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.48/19.92 | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = % 135.48/19.92 | | | e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.48/19.92 | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, % 135.48/19.92 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.48/19.92 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.48/19.92 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.92 | | | $i(all_56_29)))) % 135.48/19.92 | | | % 135.48/19.92 | | | BETA: splitting (27) gives: % 135.48/19.92 | | | % 135.48/19.92 | | | Case 1: % 135.48/19.92 | | | | % 135.48/19.92 | | | | (28) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.48/19.92 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.48/19.92 | | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & % 135.48/19.92 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.48/19.92 | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.48/19.92 | | | | $i(all_56_31) % 135.48/19.92 | | | | % 135.48/19.92 | | | | ALPHA: (28) implies: % 135.48/19.92 | | | | (29) op(e2, e0) = e2 % 135.48/19.92 | | | | % 135.48/19.92 | | | | REF_CLOSE: (2), (3), (4), (5), (14), (15), (16), (29) are inconsistent % 135.48/19.92 | | | | by sub-proof #60. % 135.48/19.92 | | | | % 135.48/19.92 | | | Case 2: % 135.48/19.92 | | | | % 135.48/19.92 | | | | (30) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.48/19.92 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.48/19.92 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.48/19.92 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.48/19.92 | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.48/19.92 | | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.48/19.92 | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.48/19.92 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = % 135.48/19.92 | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 135.48/19.92 | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.48/19.92 | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.48/19.92 | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 135.48/19.92 | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.48/19.92 | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.48/19.92 | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.48/19.92 | | | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 135.48/19.92 | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.48/19.92 | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.48/19.92 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = % 135.48/19.92 | | | | e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 135.48/19.92 | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 % 135.48/19.92 | | | | & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.48/19.92 | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.48/19.92 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = % 135.48/19.92 | | | | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.48/19.92 | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, % 135.48/19.92 | | | | e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.48/19.92 | | | | & $i(all_56_29)))) % 135.48/19.92 | | | | % 135.48/19.92 | | | | BETA: splitting (30) gives: % 135.48/19.92 | | | | % 135.48/19.92 | | | | Case 1: % 135.48/19.92 | | | | | % 135.48/19.92 | | | | | (31) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.48/19.92 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.48/19.92 | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.48/19.92 | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.48/19.92 | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.48/19.92 | | | | | $i(all_56_27) % 135.48/19.92 | | | | | % 135.48/19.92 | | | | | ALPHA: (31) implies: % 135.48/19.92 | | | | | (32) ~ (all_56_11 = e2) % 135.48/19.92 | | | | | (33) op(e2, e2) = all_56_11 % 135.48/19.92 | | | | | % 135.48/19.92 | | | | | BETA: splitting (3) gives: % 135.48/19.92 | | | | | % 135.48/19.92 | | | | | Case 1: % 135.48/19.92 | | | | | | % 135.48/19.92 | | | | | | (34) all_54_5 = e2 % 135.48/19.92 | | | | | | % 135.48/19.92 | | | | | | COMBINE_EQS: (14), (34) imply: % 135.48/19.92 | | | | | | (35) all_8_2 = e2 % 135.48/19.93 | | | | | | % 135.48/19.93 | | | | | | SIMP: (35) implies: % 135.48/19.93 | | | | | | (36) all_8_2 = e2 % 135.48/19.93 | | | | | | % 135.48/19.93 | | | | | | REDUCE: (1), (36) imply: % 135.48/19.93 | | | | | | (37) op(e2, e2) = e2 % 135.48/19.93 | | | | | | % 135.48/19.93 | | | | | | REF_CLOSE: (5), (32), (33), (37) are inconsistent by sub-proof #531. % 135.48/19.93 | | | | | | % 135.48/19.93 | | | | | Case 2: % 135.48/19.93 | | | | | | % 135.48/19.93 | | | | | | (38) all_54_5 = e1 | all_54_5 = e0 % 135.48/19.93 | | | | | | % 135.48/19.93 | | | | | | REF_CLOSE: (4), (14), (15), (38) are inconsistent by sub-proof #624. % 135.48/19.93 | | | | | | % 135.48/19.93 | | | | | End of split % 135.48/19.93 | | | | | % 135.48/19.93 | | | | Case 2: % 135.48/19.93 | | | | | % 135.48/19.93 | | | | | (39) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.48/19.93 | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & % 135.48/19.93 | | | | | ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.93 | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 135.48/19.93 | | | | | & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) % 135.48/19.93 | | | | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.48/19.93 | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.48/19.93 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = % 135.48/19.93 | | | | | e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.48/19.93 | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.48/19.93 | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 135.48/19.93 | | | | | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 135.48/19.93 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.48/19.93 | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 135.48/19.93 | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.48/19.93 | | | | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.48/19.93 | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.48/19.93 | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.48/19.93 | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 135.48/19.93 | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 135.48/19.93 | | | | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 135.48/19.93 | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))) % 135.48/19.93 | | | | | % 135.48/19.93 | | | | | REF_CLOSE: (1), (4), (5), (7), (8), (13), (14), (18), (19), (20), % 135.48/19.93 | | | | | (21), (22), (23), (39) are inconsistent by sub-proof #39. % 135.48/19.93 | | | | | % 135.48/19.93 | | | | End of split % 135.48/19.93 | | | | % 135.48/19.93 | | | End of split % 135.48/19.93 | | | % 135.48/19.93 | | End of split % 135.48/19.93 | | % 135.48/19.93 | End of split % 135.48/19.93 | % 135.48/19.93 End of proof % 135.48/19.93 % 135.48/19.93 Sub-proof #39 shows that the following formulas are inconsistent: % 135.48/19.93 ---------------------------------------------------------------- % 135.48/19.93 (1) op(e2, e2) = all_8_2 % 135.48/19.93 (2) ~ (all_8_2 = e1) % 135.48/19.93 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.93 (4) op(e0, e0) = e1 % 135.48/19.93 (5) op(e0, e2) = all_52_7 % 135.48/19.93 (6) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 135.48/19.93 (7) all_54_5 = all_8_2 % 135.48/19.93 (8) ~ (all_52_14 = e1) % 135.48/19.93 (9) ~ (e3 = e1) % 135.48/19.93 (10) ~ (all_52_7 = all_8_2) % 135.48/19.93 (11) ~ (all_8_2 = e3) % 135.48/19.93 (12) op(e1, e0) = all_52_14 % 135.48/19.93 (13) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = % 135.48/19.93 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 135.48/19.93 ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 % 135.48/19.93 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 % 135.48/19.93 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.48/19.93 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 135.48/19.93 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.48/19.93 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.48/19.93 e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.48/19.93 $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & % 135.48/19.93 ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.48/19.93 (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 135.48/19.93 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.48/19.93 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & % 135.48/19.93 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.48/19.93 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 135.48/19.93 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.48/19.93 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.93 $i(all_56_21) & $i(all_56_29))) % 135.48/19.93 (14) op(e1, e0) = e0 % 135.48/19.93 % 135.48/19.93 Begin of proof % 135.48/19.93 | % 135.48/19.93 | ALPHA: (13) implies: % 135.48/19.93 | (15) op(e0, e0) = all_56_31 % 135.48/19.93 | (16) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.48/19.93 | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.93 | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.93 | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.48/19.93 | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & % 135.48/19.93 | ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.48/19.93 | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.48/19.93 | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.48/19.93 | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.48/19.93 | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 % 135.48/19.93 | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = % 135.48/19.93 | e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.48/19.93 | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.48/19.93 | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.48/19.93 | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = % 135.48/19.93 | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) % 135.48/19.93 | = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.48/19.93 | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.48/19.93 | % 135.48/19.93 | BETA: splitting (16) gives: % 135.48/19.93 | % 135.48/19.93 | Case 1: % 135.48/19.93 | | % 135.48/19.93 | | (17) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.48/19.93 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.93 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.93 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 135.48/19.93 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.48/19.93 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.48/19.93 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.48/19.93 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.48/19.93 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.48/19.93 | | $i(all_56_27)) % 135.48/19.93 | | % 135.48/19.93 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (15), (17) % 135.48/19.93 | | are inconsistent by sub-proof #41. % 135.48/19.93 | | % 135.48/19.93 | Case 2: % 135.48/19.93 | | % 135.48/19.93 | | (18) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.48/19.93 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.48/19.93 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.48/19.93 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.48/19.93 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.48/19.93 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.48/19.93 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.48/19.93 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.48/19.93 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.93 | | $i(all_56_29)) % 135.48/19.93 | | % 135.48/19.93 | | REF_CLOSE: (3), (8), (12), (14), (18) are inconsistent by sub-proof #40. % 135.48/19.93 | | % 135.48/19.93 | End of split % 135.48/19.93 | % 135.48/19.93 End of proof % 135.48/19.93 % 135.48/19.93 Sub-proof #40 shows that the following formulas are inconsistent: % 135.48/19.93 ---------------------------------------------------------------- % 135.48/19.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.93 (2) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.48/19.93 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.48/19.93 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.48/19.93 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.48/19.93 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.48/19.93 e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.48/19.93 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.48/19.93 = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.93 $i(all_56_21) & $i(all_56_29)) % 135.48/19.93 (3) ~ (all_52_14 = e1) % 135.48/19.93 (4) op(e1, e0) = all_52_14 % 135.48/19.93 (5) op(e1, e0) = e0 % 135.48/19.93 % 135.48/19.93 Begin of proof % 135.48/19.93 | % 135.48/19.93 | BETA: splitting (2) gives: % 135.48/19.93 | % 135.48/19.93 | Case 1: % 135.48/19.93 | | % 135.48/19.93 | | (6) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 % 135.48/19.93 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 % 135.48/19.93 | | & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.48/19.93 | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) % 135.48/19.93 | | % 135.48/19.93 | | ALPHA: (6) implies: % 135.48/19.93 | | (7) op(e1, e0) = e1 % 135.48/19.93 | | % 135.48/19.93 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #327. % 135.48/19.93 | | % 135.48/19.93 | Case 2: % 135.48/19.93 | | % 135.48/19.93 | | (8) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.48/19.93 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.48/19.93 | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 135.48/19.93 | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.93 | | $i(all_56_21) & $i(all_56_29) % 135.48/19.93 | | % 135.48/19.93 | | ALPHA: (8) implies: % 135.48/19.93 | | (9) ~ (all_56_29 = e0) % 135.48/19.93 | | (10) op(e1, e0) = all_56_29 % 135.48/19.93 | | % 135.48/19.93 | | REF_CLOSE: (1), (5), (9), (10) are inconsistent by sub-proof #45. % 135.48/19.93 | | % 135.48/19.93 | End of split % 135.48/19.93 | % 135.48/19.93 End of proof % 135.48/19.93 % 135.48/19.93 Sub-proof #41 shows that the following formulas are inconsistent: % 135.48/19.93 ---------------------------------------------------------------- % 135.48/19.93 (1) op(e2, e2) = all_8_2 % 135.48/19.93 (2) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 135.48/19.93 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.48/19.93 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 135.48/19.93 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.48/19.93 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) % 135.48/19.93 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.48/19.93 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.48/19.93 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 135.48/19.93 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 135.48/19.93 (3) ~ (all_8_2 = e1) % 135.48/19.93 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.93 (5) op(e0, e0) = e1 % 135.48/19.93 (6) op(e0, e2) = all_52_7 % 135.48/19.93 (7) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 135.48/19.93 (8) all_54_5 = all_8_2 % 135.48/19.93 (9) ~ (e3 = e1) % 135.48/19.93 (10) ~ (all_52_7 = all_8_2) % 135.48/19.93 (11) ~ (all_8_2 = e3) % 135.48/19.93 (12) op(e0, e0) = all_56_31 % 135.48/19.93 % 135.48/19.93 Begin of proof % 135.48/19.93 | % 135.48/19.93 | BETA: splitting (2) gives: % 135.48/19.93 | % 135.48/19.93 | Case 1: % 135.48/19.93 | | % 135.48/19.93 | | (13) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.48/19.93 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.93 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.93 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.48/19.93 | | $i(all_56_17) & $i(all_56_25) % 135.48/19.93 | | % 135.48/19.93 | | ALPHA: (13) implies: % 135.48/19.93 | | (14) all_56_31 = e3 % 135.48/19.93 | | % 135.48/19.93 | | REDUCE: (12), (14) imply: % 135.48/19.93 | | (15) op(e0, e0) = e3 % 135.48/19.93 | | % 135.48/19.93 | | REF_CLOSE: (4), (5), (9), (15) are inconsistent by sub-proof #606. % 135.48/19.93 | | % 135.48/19.93 | Case 2: % 135.48/19.93 | | % 135.48/19.93 | | (16) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 135.48/19.93 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.48/19.93 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.48/19.93 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.48/19.93 | | $i(all_56_19) & $i(all_56_27) % 135.48/19.93 | | % 135.48/19.93 | | ALPHA: (16) implies: % 135.48/19.93 | | (17) ~ (all_56_11 = e2) % 135.48/19.93 | | (18) op(e0, e2) = e0 % 135.48/19.93 | | (19) op(e2, e2) = all_56_11 % 135.48/19.93 | | % 135.48/19.93 | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (11), (17), (18), (19) are % 135.48/19.93 | | inconsistent by sub-proof #227. % 135.48/19.93 | | % 135.48/19.93 | End of split % 135.48/19.93 | % 135.48/19.93 End of proof % 135.48/19.93 % 135.48/19.93 Sub-proof #42 shows that the following formulas are inconsistent: % 135.48/19.93 ---------------------------------------------------------------- % 135.48/19.93 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 135.48/19.93 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.48/19.93 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 135.48/19.93 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.48/19.93 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ % 135.48/19.93 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.48/19.93 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = % 135.48/19.93 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.48/19.93 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.93 $i(all_56_29)) % 135.48/19.93 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.93 (3) ~ (e3 = e2) % 135.48/19.93 (4) op(e1, e1) = e2 % 135.48/19.93 (5) op(e1, e0) = e0 % 135.48/19.93 % 135.48/19.93 Begin of proof % 135.48/19.93 | % 135.48/19.93 | BETA: splitting (1) gives: % 135.48/19.93 | % 135.48/19.93 | Case 1: % 135.48/19.93 | | % 135.48/19.93 | | (6) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.48/19.93 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.93 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.93 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) % 135.48/19.93 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 135.48/19.93 | | % 135.48/19.93 | | ALPHA: (6) implies: % 135.48/19.93 | | (7) op(e1, e1) = e3 % 135.48/19.93 | | % 135.48/19.93 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #109. % 135.48/19.93 | | % 135.48/19.93 | Case 2: % 135.48/19.93 | | % 135.48/19.93 | | (8) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.48/19.93 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 % 135.48/19.93 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.48/19.93 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.48/19.93 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 135.48/19.93 | | % 135.48/19.93 | | ALPHA: (8) implies: % 135.48/19.93 | | (9) ~ (all_56_29 = e0) % 135.48/19.93 | | (10) op(e1, e0) = all_56_29 % 135.48/19.93 | | % 135.48/19.93 | | REF_CLOSE: (2), (5), (9), (10) are inconsistent by sub-proof #45. % 135.48/19.93 | | % 135.48/19.93 | End of split % 135.48/19.93 | % 135.48/19.93 End of proof % 135.48/19.93 % 135.48/19.93 Sub-proof #43 shows that the following formulas are inconsistent: % 135.48/19.93 ---------------------------------------------------------------- % 135.48/19.93 (1) op(e2, e2) = all_8_2 % 135.48/19.93 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.93 (3) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 135.48/19.93 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 135.48/19.93 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.48/19.93 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.48/19.93 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 135.48/19.93 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.48/19.93 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 135.48/19.93 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.48/19.93 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.93 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 135.48/19.93 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.48/19.93 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 135.48/19.93 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 135.48/19.93 = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.48/19.93 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & % 135.48/19.93 ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, % 135.48/19.93 e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.48/19.93 op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 135.48/19.93 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 135.48/19.93 (4) ~ (all_10_2 = e0) % 135.48/19.93 (5) op(e3, e3) = all_10_2 % 135.48/19.93 (6) ~ (all_10_2 = e2) % 135.48/19.93 (7) ~ (all_8_2 = e3) % 135.48/19.93 (8) op(e1, e0) = e0 % 135.48/19.93 % 135.48/19.93 Begin of proof % 135.48/19.93 | % 135.48/19.93 | BETA: splitting (3) gives: % 135.48/19.93 | % 135.48/19.93 | Case 1: % 135.48/19.93 | | % 135.48/19.93 | | (9) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.48/19.93 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 % 135.48/19.93 | | & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 % 135.48/19.93 | | & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.48/19.93 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 135.48/19.93 | | all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.48/19.93 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 135.48/19.93 | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.48/19.93 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.48/19.93 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.48/19.93 | | % 135.48/19.93 | | REF_CLOSE: (2), (5), (6), (8), (9) are inconsistent by sub-proof #44. % 135.48/19.93 | | % 135.48/19.93 | Case 2: % 135.48/19.93 | | % 135.48/19.93 | | (10) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 % 135.48/19.93 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = % 135.48/19.93 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.48/19.93 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 135.48/19.93 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.48/19.93 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.48/19.93 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.93 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.93 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 135.48/19.93 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 135.48/19.93 | | % 135.48/19.93 | | BETA: splitting (10) gives: % 135.48/19.93 | | % 135.48/19.93 | | Case 1: % 135.48/19.93 | | | % 135.48/19.93 | | | (11) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ % 135.48/19.93 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.48/19.93 | | | op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.48/19.93 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.48/19.93 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.48/19.93 | | | $i(all_56_31) % 135.48/19.93 | | | % 135.48/19.93 | | | ALPHA: (11) implies: % 135.48/19.93 | | | (12) op(e3, e3) = e0 % 135.48/19.93 | | | % 135.48/19.93 | | | REF_CLOSE: (2), (4), (5), (12) are inconsistent by sub-proof #534. % 135.48/19.93 | | | % 135.48/19.93 | | Case 2: % 135.48/19.93 | | | % 135.48/19.93 | | | (13) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.48/19.93 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.93 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.93 | | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 135.48/19.93 | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 135.48/19.93 | | | % 135.48/19.93 | | | ALPHA: (13) implies: % 135.48/19.93 | | | (14) op(e2, e2) = e3 % 135.48/19.93 | | | % 135.48/19.93 | | | REF_CLOSE: (1), (2), (7), (14) are inconsistent by sub-proof #228. % 135.48/19.93 | | | % 135.48/19.93 | | End of split % 135.48/19.93 | | % 135.48/19.93 | End of split % 135.48/19.93 | % 135.48/19.93 End of proof % 135.48/19.93 % 135.48/19.93 Sub-proof #44 shows that the following formulas are inconsistent: % 135.48/19.93 ---------------------------------------------------------------- % 135.48/19.93 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 135.48/19.93 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 135.48/19.93 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.48/19.93 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.48/19.93 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 135.48/19.93 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.48/19.93 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 135.48/19.93 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.48/19.93 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.93 $i(all_56_21) & $i(all_56_29)) % 135.48/19.93 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.93 (3) op(e3, e3) = all_10_2 % 135.48/19.93 (4) ~ (all_10_2 = e2) % 135.48/19.93 (5) op(e1, e0) = e0 % 135.48/19.93 % 135.48/19.93 Begin of proof % 135.48/19.93 | % 135.48/19.93 | BETA: splitting (1) gives: % 135.48/19.93 | % 135.48/19.93 | Case 1: % 135.48/19.93 | | % 135.48/19.93 | | (6) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.48/19.93 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.48/19.93 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.48/19.93 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.48/19.93 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 135.48/19.93 | | % 135.48/19.93 | | ALPHA: (6) implies: % 135.48/19.93 | | (7) op(e3, e3) = e2 % 135.48/19.93 | | % 135.48/19.93 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #536. % 135.48/19.93 | | % 135.48/19.93 | Case 2: % 135.48/19.93 | | % 135.48/19.93 | | (8) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.48/19.93 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 135.48/19.93 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.48/19.93 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.48/19.93 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 135.48/19.93 | | % 135.48/19.93 | | ALPHA: (8) implies: % 135.48/19.93 | | (9) ~ (all_56_29 = e0) % 135.48/19.93 | | (10) op(e1, e0) = all_56_29 % 135.48/19.93 | | % 135.48/19.93 | | REF_CLOSE: (2), (5), (9), (10) are inconsistent by sub-proof #45. % 135.48/19.93 | | % 135.48/19.93 | End of split % 135.48/19.93 | % 135.48/19.93 End of proof % 135.48/19.93 % 135.48/19.93 Sub-proof #45 shows that the following formulas are inconsistent: % 135.48/19.93 ---------------------------------------------------------------- % 135.48/19.93 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.93 (2) op(e1, e0) = all_56_29 % 135.48/19.93 (3) op(e1, e0) = e0 % 135.48/19.93 (4) ~ (all_56_29 = e0) % 135.48/19.93 % 135.48/19.93 Begin of proof % 135.48/19.93 | % 135.48/19.93 | GROUND_INST: instantiating (1) with e0, all_56_29, e0, e1, simplifying with % 135.48/19.93 | (2), (3) gives: % 135.48/19.93 | (5) all_56_29 = e0 % 135.48/19.93 | % 135.48/19.93 | REDUCE: (4), (5) imply: % 135.48/19.93 | (6) $false % 135.48/19.93 | % 135.48/19.93 | CLOSE: (6) is inconsistent. % 135.48/19.93 | % 135.48/19.93 End of proof % 135.48/19.93 % 135.48/19.93 Sub-proof #46 shows that the following formulas are inconsistent: % 135.48/19.93 ---------------------------------------------------------------- % 135.48/19.93 (1) ~ (all_52_14 = e3) % 135.48/19.93 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.93 (3) op(e0, e0) = e1 % 135.48/19.93 (4) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 135.48/19.93 (5) ~ (e3 = e1) % 135.48/19.93 (6) op(e1, e0) = all_52_14 % 135.48/19.93 % 135.48/19.93 Begin of proof % 135.48/19.93 | % 135.48/19.93 | BETA: splitting (4) gives: % 135.48/19.93 | % 135.48/19.93 | Case 1: % 135.48/19.93 | | % 135.48/19.93 | | (7) all_57_11 = e3 & op(e1, e0) = e3 % 135.48/19.93 | | % 135.48/19.93 | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #750. % 135.48/19.93 | | % 135.48/19.93 | Case 2: % 135.48/19.93 | | % 135.48/19.93 | | (8) all_57_15 = e3 & op(e0, e0) = e3 % 135.48/19.93 | | % 135.48/19.93 | | ALPHA: (8) implies: % 135.48/19.94 | | (9) op(e0, e0) = e3 % 135.48/19.94 | | % 135.48/19.94 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #606. % 135.48/19.94 | | % 135.48/19.94 | End of split % 135.48/19.94 | % 135.48/19.94 End of proof % 135.48/19.94 % 135.48/19.94 Sub-proof #47 shows that the following formulas are inconsistent: % 135.48/19.94 ---------------------------------------------------------------- % 135.48/19.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.94 (2) ~ (e2 = e1) % 135.48/19.94 (3) op(e1, e3) = e2 % 135.48/19.94 (4) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 135.48/19.94 (5) ~ (all_52_3 = e1) % 135.48/19.94 (6) op(e1, e3) = all_52_2 % 135.48/19.94 (7) op(e0, e3) = all_52_3 % 135.48/19.94 % 135.48/19.94 Begin of proof % 135.48/19.94 | % 135.48/19.94 | BETA: splitting (4) gives: % 135.48/19.94 | % 135.48/19.94 | Case 1: % 135.48/19.94 | | % 135.48/19.94 | | (8) all_57_6 = e1 & op(e1, e3) = e1 % 135.48/19.94 | | % 135.48/19.94 | | ALPHA: (8) implies: % 135.48/19.94 | | (9) op(e1, e3) = e1 % 135.48/19.94 | | % 135.48/19.94 | | REF_CLOSE: (1), (2), (3), (6), (9) are inconsistent by sub-proof #517. % 135.48/19.94 | | % 135.48/19.94 | Case 2: % 135.48/19.94 | | % 135.48/19.94 | | (10) all_57_12 = e1 & op(e0, e3) = e1 % 135.48/19.94 | | % 135.48/19.94 | | REF_CLOSE: (1), (5), (7), (10) are inconsistent by sub-proof #48. % 135.48/19.94 | | % 135.48/19.94 | End of split % 135.48/19.94 | % 135.48/19.94 End of proof % 135.48/19.94 % 135.48/19.94 Sub-proof #48 shows that the following formulas are inconsistent: % 135.48/19.94 ---------------------------------------------------------------- % 135.48/19.94 (1) all_57_12 = e1 & op(e0, e3) = e1 % 135.48/19.94 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.94 (3) op(e0, e3) = all_52_3 % 135.48/19.94 (4) ~ (all_52_3 = e1) % 135.48/19.94 % 135.48/19.94 Begin of proof % 135.48/19.94 | % 135.48/19.94 | ALPHA: (1) implies: % 135.48/19.94 | (5) op(e0, e3) = e1 % 135.48/19.94 | % 135.48/19.94 | GROUND_INST: instantiating (2) with all_52_3, e1, e3, e0, simplifying with % 135.48/19.94 | (3), (5) gives: % 135.48/19.94 | (6) all_52_3 = e1 % 135.48/19.94 | % 135.48/19.94 | REDUCE: (4), (6) imply: % 135.48/19.94 | (7) $false % 135.48/19.94 | % 135.48/19.94 | CLOSE: (7) is inconsistent. % 135.48/19.94 | % 135.48/19.94 End of proof % 135.48/19.94 % 135.48/19.94 Sub-proof #49 shows that the following formulas are inconsistent: % 135.48/19.94 ---------------------------------------------------------------- % 135.48/19.94 (1) all_57_6 = e0 % 135.48/19.94 (2) ~ (e2 = e0) % 135.48/19.94 (3) all_57_12 = e0 % 135.48/19.94 (4) op(e3, e3) = e1 % 135.48/19.94 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.94 (6) ~ (e2 = e1) % 135.48/19.94 (7) ~ (e3 = e2) % 135.48/19.94 (8) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) | % 135.48/19.94 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2) % 135.48/19.94 (9) all_57_2 = e3 % 135.48/19.94 % 135.48/19.94 Begin of proof % 135.48/19.94 | % 135.48/19.94 | BETA: splitting (8) gives: % 135.48/19.94 | % 135.48/19.94 | Case 1: % 135.48/19.94 | | % 135.48/19.94 | | (10) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = % 135.48/19.94 | | e2) % 135.48/19.94 | | % 135.48/19.94 | | BETA: splitting (10) gives: % 135.48/19.94 | | % 135.48/19.94 | | Case 1: % 135.48/19.94 | | | % 135.48/19.94 | | | (11) all_57_0 = e2 & op(e3, e3) = e2 % 135.48/19.94 | | | % 135.48/19.94 | | | ALPHA: (11) implies: % 135.48/19.94 | | | (12) op(e3, e3) = e2 % 135.48/19.94 | | | % 135.48/19.94 | | | REF_CLOSE: (4), (5), (6), (12) are inconsistent by sub-proof #743. % 135.48/19.94 | | | % 135.48/19.94 | | Case 2: % 135.48/19.94 | | | % 135.48/19.94 | | | (13) all_57_2 = e2 & op(e2, e3) = e2 % 135.48/19.94 | | | % 135.48/19.94 | | | REF_CLOSE: (7), (9), (13) are inconsistent by sub-proof #454. % 135.48/19.94 | | | % 135.48/19.94 | | End of split % 135.48/19.94 | | % 135.48/19.94 | Case 2: % 135.48/19.94 | | % 135.48/19.94 | | (14) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = % 135.48/19.94 | | e2) % 135.48/19.94 | | % 135.48/19.94 | | REF_CLOSE: (1), (2), (3), (14) are inconsistent by sub-proof #140. % 135.48/19.94 | | % 135.48/19.94 | End of split % 135.48/19.94 | % 135.48/19.94 End of proof % 135.48/19.94 % 135.48/19.94 Sub-proof #50 shows that the following formulas are inconsistent: % 135.48/19.94 ---------------------------------------------------------------- % 135.48/19.94 (1) all_54_11 = all_12_0 % 135.48/19.94 (2) all_54_11 = e1 % 135.48/19.94 (3) ~ (all_12_0 = e1) % 135.48/19.94 % 135.48/19.94 Begin of proof % 135.48/19.94 | % 135.48/19.94 | COMBINE_EQS: (1), (2) imply: % 135.48/19.94 | (4) all_12_0 = e1 % 135.48/19.94 | % 135.48/19.94 | SIMP: (4) implies: % 135.48/19.94 | (5) all_12_0 = e1 % 135.48/19.94 | % 135.48/19.94 | REDUCE: (3), (5) imply: % 135.48/19.94 | (6) $false % 135.48/19.94 | % 135.48/19.94 | CLOSE: (6) is inconsistent. % 135.48/19.94 | % 135.48/19.94 End of proof % 135.48/19.94 % 135.48/19.94 Sub-proof #51 shows that the following formulas are inconsistent: % 135.48/19.94 ---------------------------------------------------------------- % 135.48/19.94 (1) all_54_11 = all_12_0 % 135.48/19.94 (2) all_54_11 = e2 % 135.48/19.94 (3) ~ (all_12_0 = e2) % 135.48/19.94 % 135.48/19.94 Begin of proof % 135.48/19.94 | % 135.48/19.94 | COMBINE_EQS: (1), (2) imply: % 135.48/19.94 | (4) all_12_0 = e2 % 135.48/19.94 | % 135.48/19.94 | SIMP: (4) implies: % 135.48/19.94 | (5) all_12_0 = e2 % 135.48/19.94 | % 135.48/19.94 | REDUCE: (3), (5) imply: % 135.48/19.94 | (6) $false % 135.48/19.94 | % 135.48/19.94 | CLOSE: (6) is inconsistent. % 135.48/19.94 | % 135.48/19.94 End of proof % 135.48/19.94 % 135.48/19.94 Sub-proof #52 shows that the following formulas are inconsistent: % 135.48/19.94 ---------------------------------------------------------------- % 135.48/19.94 (1) all_54_11 = all_12_0 % 135.48/19.94 (2) all_54_11 = e3 % 135.48/19.94 (3) ~ (all_12_0 = e3) % 135.48/19.94 % 135.48/19.94 Begin of proof % 135.48/19.94 | % 135.48/19.94 | COMBINE_EQS: (1), (2) imply: % 135.48/19.94 | (4) all_12_0 = e3 % 135.48/19.94 | % 135.48/19.94 | SIMP: (4) implies: % 135.48/19.94 | (5) all_12_0 = e3 % 135.48/19.94 | % 135.48/19.94 | REDUCE: (3), (5) imply: % 135.48/19.94 | (6) $false % 135.48/19.94 | % 135.48/19.94 | CLOSE: (6) is inconsistent. % 135.48/19.94 | % 135.48/19.94 End of proof % 135.48/19.94 % 135.48/19.94 Sub-proof #53 shows that the following formulas are inconsistent: % 135.48/19.94 ---------------------------------------------------------------- % 135.48/19.94 (1) ~ (all_30_1 = e1) & op(e0, e0) = all_30_1 & $i(all_30_1) % 135.48/19.94 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.94 (3) op(e0, e0) = e1 % 135.48/19.94 % 135.48/19.94 Begin of proof % 135.48/19.94 | % 135.48/19.94 | ALPHA: (1) implies: % 135.48/19.94 | (4) ~ (all_30_1 = e1) % 135.48/19.94 | (5) op(e0, e0) = all_30_1 % 135.48/19.94 | % 135.48/19.94 | GROUND_INST: instantiating (2) with e1, all_30_1, e0, e0, simplifying with % 135.48/19.94 | (3), (5) gives: % 135.48/19.94 | (6) all_30_1 = e1 % 135.48/19.94 | % 135.48/19.94 | REDUCE: (4), (6) imply: % 135.48/19.94 | (7) $false % 135.48/19.94 | % 135.48/19.94 | CLOSE: (7) is inconsistent. % 135.48/19.94 | % 135.48/19.94 End of proof % 135.48/19.94 % 135.48/19.94 Sub-proof #54 shows that the following formulas are inconsistent: % 135.48/19.94 ---------------------------------------------------------------- % 135.48/19.94 (1) all_54_13 = all_30_0 % 135.48/19.94 (2) all_54_13 = e3 % 135.48/19.94 (3) ~ (all_30_0 = e3) % 135.48/19.94 % 135.48/19.94 Begin of proof % 135.48/19.94 | % 135.48/19.94 | COMBINE_EQS: (1), (2) imply: % 135.48/19.94 | (4) all_30_0 = e3 % 135.48/19.94 | % 135.48/19.94 | SIMP: (4) implies: % 135.48/19.94 | (5) all_30_0 = e3 % 135.48/19.94 | % 135.48/19.94 | REDUCE: (3), (5) imply: % 135.48/19.94 | (6) $false % 135.48/19.94 | % 135.48/19.94 | CLOSE: (6) is inconsistent. % 135.48/19.94 | % 135.48/19.94 End of proof % 135.48/19.94 % 135.48/19.94 Sub-proof #55 shows that the following formulas are inconsistent: % 135.48/19.94 ---------------------------------------------------------------- % 135.48/19.94 (1) op(e2, e1) = e1 % 135.48/19.94 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.94 (3) op(e0, e0) = e1 % 135.48/19.94 (4) op(e0, e1) = all_52_11 % 135.48/19.94 (5) ~ (all_52_14 = e1) % 135.48/19.94 (6) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 135.48/19.94 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.48/19.94 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 135.48/19.94 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.48/19.94 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) % 135.48/19.94 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.48/19.94 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.48/19.94 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 135.48/19.94 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & % 135.48/19.94 all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ % 135.48/19.94 (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = % 135.48/19.94 e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 135.48/19.94 all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 % 135.48/19.94 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.48/19.94 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, % 135.48/19.94 e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.48/19.94 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.94 $i(all_56_29)) % 135.48/19.94 (7) ~ (all_52_11 = e0) % 135.48/19.94 (8) ~ (e3 = e1) % 135.48/19.94 (9) op(e1, e0) = all_52_14 % 135.48/19.94 (10) op(e0, e0) = all_56_31 % 135.48/19.94 % 135.48/19.94 Begin of proof % 135.48/19.94 | % 135.48/19.94 | BETA: splitting (6) gives: % 135.48/19.94 | % 135.48/19.94 | Case 1: % 135.48/19.94 | | % 135.48/19.94 | | (11) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.48/19.94 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.94 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.94 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 135.48/19.94 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.48/19.94 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.48/19.94 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.48/19.94 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.48/19.94 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.48/19.94 | | $i(all_56_27)) % 135.48/19.94 | | % 135.48/19.94 | | REF_CLOSE: (1), (2), (3), (8), (10), (11) are inconsistent by sub-proof #56. % 135.48/19.94 | | % 135.48/19.94 | Case 2: % 135.48/19.94 | | % 135.48/19.94 | | (12) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.48/19.94 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.48/19.94 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.48/19.94 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.48/19.94 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.48/19.94 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.48/19.94 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.48/19.94 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.48/19.94 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.94 | | $i(all_56_29)) % 135.48/19.94 | | % 135.48/19.94 | | BETA: splitting (12) gives: % 135.48/19.94 | | % 135.48/19.94 | | Case 1: % 135.48/19.94 | | | % 135.48/19.94 | | | (13) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.48/19.94 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.48/19.94 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.48/19.94 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.48/19.94 | | | $i(all_56_15) & $i(all_56_23) % 135.48/19.94 | | | % 135.48/19.94 | | | ALPHA: (13) implies: % 135.48/19.94 | | | (14) op(e1, e0) = e1 % 135.48/19.94 | | | % 135.48/19.94 | | | REF_CLOSE: (2), (5), (9), (14) are inconsistent by sub-proof #327. % 135.48/19.94 | | | % 135.48/19.94 | | Case 2: % 135.48/19.94 | | | % 135.48/19.94 | | | (15) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.48/19.94 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.48/19.94 | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.48/19.94 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.48/19.94 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 135.48/19.94 | | | % 135.48/19.94 | | | ALPHA: (15) implies: % 135.48/19.94 | | | (16) op(e0, e1) = e0 % 135.48/19.94 | | | % 135.48/19.94 | | | GROUND_INST: instantiating (2) with all_52_11, e0, e1, e0, simplifying % 135.48/19.94 | | | with (4), (16) gives: % 135.48/19.94 | | | (17) all_52_11 = e0 % 135.48/19.94 | | | % 135.48/19.94 | | | REDUCE: (7), (17) imply: % 135.48/19.94 | | | (18) $false % 135.48/19.94 | | | % 135.48/19.94 | | | CLOSE: (18) is inconsistent. % 135.48/19.94 | | | % 135.48/19.94 | | End of split % 135.48/19.94 | | % 135.48/19.94 | End of split % 135.48/19.94 | % 135.48/19.94 End of proof % 135.48/19.94 % 135.48/19.94 Sub-proof #56 shows that the following formulas are inconsistent: % 135.48/19.94 ---------------------------------------------------------------- % 135.48/19.94 (1) op(e2, e1) = e1 % 135.48/19.94 (2) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 135.48/19.94 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.48/19.94 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 135.48/19.94 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.48/19.94 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) % 135.48/19.94 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.48/19.94 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.48/19.94 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 135.48/19.94 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 135.48/19.94 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.94 (4) op(e0, e0) = e1 % 135.48/19.94 (5) ~ (e3 = e1) % 135.48/19.94 (6) op(e0, e0) = all_56_31 % 135.48/19.94 % 135.48/19.94 Begin of proof % 135.48/19.94 | % 135.48/19.94 | BETA: splitting (2) gives: % 135.48/19.94 | % 135.48/19.94 | Case 1: % 135.48/19.94 | | % 135.48/19.94 | | (7) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.48/19.94 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.94 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.94 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.48/19.94 | | $i(all_56_17) & $i(all_56_25) % 135.48/19.94 | | % 135.48/19.94 | | ALPHA: (7) implies: % 135.48/19.94 | | (8) all_56_31 = e3 % 135.48/19.94 | | % 135.48/19.94 | | REDUCE: (6), (8) imply: % 135.48/19.94 | | (9) op(e0, e0) = e3 % 135.48/19.94 | | % 135.48/19.94 | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #606. % 135.48/19.94 | | % 135.48/19.94 | Case 2: % 135.48/19.94 | | % 135.48/19.94 | | (10) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 135.48/19.94 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.48/19.94 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.48/19.94 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.48/19.94 | | $i(all_56_19) & $i(all_56_27) % 135.48/19.94 | | % 135.48/19.94 | | ALPHA: (10) implies: % 135.48/19.94 | | (11) ~ (all_56_19 = e1) % 135.48/19.94 | | (12) op(e2, e1) = all_56_19 % 135.48/19.94 | | % 135.48/19.94 | | REF_CLOSE: (1), (3), (11), (12) are inconsistent by sub-proof #106. % 135.48/19.94 | | % 135.48/19.94 | End of split % 135.48/19.94 | % 135.48/19.94 End of proof % 135.48/19.94 % 135.48/19.94 Sub-proof #57 shows that the following formulas are inconsistent: % 135.48/19.94 ---------------------------------------------------------------- % 135.48/19.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.94 (2) op(e2, e2) = all_8_2 % 135.48/19.94 (3) op(e2, e2) = e1 % 135.48/19.94 (4) ~ (all_8_2 = e1) % 135.48/19.94 % 135.48/19.94 Begin of proof % 135.48/19.94 | % 135.48/19.94 | GROUND_INST: instantiating (1) with all_8_2, e1, e2, e2, simplifying with (2), % 135.48/19.94 | (3) gives: % 135.48/19.94 | (5) all_8_2 = e1 % 135.48/19.94 | % 135.48/19.94 | REDUCE: (4), (5) imply: % 135.48/19.94 | (6) $false % 135.48/19.94 | % 135.48/19.94 | CLOSE: (6) is inconsistent. % 135.48/19.94 | % 135.48/19.94 End of proof % 135.48/19.94 % 135.48/19.94 Sub-proof #58 shows that the following formulas are inconsistent: % 135.48/19.94 ---------------------------------------------------------------- % 135.48/19.94 (1) op(e2, e2) = all_8_2 % 135.48/19.94 (2) op(e1, e1) = all_6_2 % 135.48/19.94 (3) ~ (all_8_2 = e1) % 135.48/19.94 (4) ~ (all_6_2 = e3) % 135.48/19.94 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.94 (6) ~ (all_52_11 = all_6_2) % 135.48/19.94 (7) op(e0, e1) = all_52_11 % 135.48/19.94 (8) op(e0, e2) = all_52_7 % 135.48/19.94 (9) all_54_10 = all_6_2 % 135.48/19.94 (10) ~ (all_6_2 = e2) % 135.48/19.94 (11) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 135.48/19.94 (12) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 135.48/19.94 (13) all_54_5 = all_8_2 % 135.48/19.94 (14) op(e3, e3) = e3 % 135.48/19.94 (15) ~ (all_52_14 = e1) % 135.48/19.94 (16) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.48/19.94 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.94 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 135.48/19.94 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.48/19.94 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 135.48/19.94 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.48/19.94 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.48/19.94 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.48/19.94 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.48/19.94 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.48/19.94 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.48/19.94 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.48/19.94 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.48/19.94 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.48/19.94 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.48/19.94 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 135.48/19.94 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.94 $i(all_56_21) & $i(all_56_29)) % 135.48/19.94 (17) ~ (all_52_7 = all_8_2) % 135.48/19.94 (18) ~ (all_8_2 = e3) % 135.48/19.94 (19) op(e1, e0) = all_52_14 % 135.48/19.94 % 135.48/19.94 Begin of proof % 135.48/19.94 | % 135.48/19.94 | BETA: splitting (16) gives: % 135.48/19.94 | % 135.48/19.94 | Case 1: % 135.48/19.94 | | % 135.48/19.94 | | (20) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.48/19.94 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.94 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.94 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 135.48/19.94 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.48/19.94 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.48/19.94 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.48/19.94 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.48/19.94 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.48/19.94 | | $i(all_56_27)) % 135.48/19.94 | | % 135.48/19.94 | | BETA: splitting (20) gives: % 135.48/19.94 | | % 135.48/19.94 | | Case 1: % 135.48/19.94 | | | % 135.48/19.94 | | | (21) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.48/19.94 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.94 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.94 | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 135.48/19.94 | | | & $i(all_56_17) & $i(all_56_25) % 135.48/19.94 | | | % 135.48/19.94 | | | ALPHA: (21) implies: % 135.48/19.94 | | | (22) ~ (all_56_1 = e3) % 135.48/19.94 | | | (23) op(e3, e3) = all_56_1 % 135.48/19.94 | | | % 135.48/19.94 | | | REF_CLOSE: (5), (14), (22), (23) are inconsistent by sub-proof #766. % 135.48/19.94 | | | % 135.48/19.94 | | Case 2: % 135.48/19.94 | | | % 135.48/19.94 | | | (24) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.48/19.94 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.48/19.94 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.48/19.94 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.48/19.94 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 135.48/19.94 | | | % 135.48/19.94 | | | ALPHA: (24) implies: % 135.48/19.94 | | | (25) ~ (all_56_11 = e2) % 135.48/19.94 | | | (26) op(e0, e2) = e0 % 135.48/19.94 | | | (27) op(e2, e2) = all_56_11 % 135.48/19.94 | | | % 135.48/19.94 | | | REF_CLOSE: (1), (3), (5), (8), (11), (13), (17), (18), (25), (26), (27) % 135.48/19.94 | | | are inconsistent by sub-proof #227. % 135.48/19.94 | | | % 135.48/19.94 | | End of split % 135.48/19.94 | | % 135.48/19.94 | Case 2: % 135.48/19.94 | | % 135.48/19.94 | | (28) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.48/19.94 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.48/19.94 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.48/19.94 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.48/19.94 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.48/19.94 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.48/19.94 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.48/19.94 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.48/19.94 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.94 | | $i(all_56_29)) % 135.48/19.94 | | % 135.48/19.94 | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (10), (12), (15), (19), (28) are % 135.48/19.94 | | inconsistent by sub-proof #59. % 135.48/19.94 | | % 135.48/19.94 | End of split % 135.48/19.94 | % 135.48/19.94 End of proof % 135.48/19.94 % 135.48/19.94 Sub-proof #59 shows that the following formulas are inconsistent: % 135.48/19.94 ---------------------------------------------------------------- % 135.48/19.94 (1) op(e1, e1) = all_6_2 % 135.48/19.94 (2) ~ (all_6_2 = e3) % 135.48/19.94 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.94 (4) ~ (all_52_11 = all_6_2) % 135.48/19.94 (5) op(e0, e1) = all_52_11 % 135.48/19.94 (6) all_54_10 = all_6_2 % 135.48/19.94 (7) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.48/19.94 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.48/19.94 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.48/19.94 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.48/19.94 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.48/19.94 e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.48/19.94 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.48/19.94 = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.94 $i(all_56_21) & $i(all_56_29)) % 135.48/19.94 (8) ~ (all_6_2 = e2) % 135.48/19.94 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 135.48/19.94 (10) ~ (all_52_14 = e1) % 135.48/19.94 (11) op(e1, e0) = all_52_14 % 135.48/19.94 % 135.48/19.94 Begin of proof % 135.48/19.94 | % 135.48/19.94 | BETA: splitting (7) gives: % 135.48/19.94 | % 135.48/19.95 | Case 1: % 135.48/19.95 | | % 135.48/19.95 | | (12) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 % 135.48/19.95 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = % 135.48/19.95 | | e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.48/19.95 | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.48/19.95 | | $i(all_56_23) % 135.48/19.95 | | % 135.48/19.95 | | ALPHA: (12) implies: % 135.48/19.95 | | (13) op(e1, e0) = e1 % 135.48/19.95 | | % 135.48/19.95 | | REF_CLOSE: (3), (10), (11), (13) are inconsistent by sub-proof #327. % 135.48/19.95 | | % 135.48/19.95 | Case 2: % 135.48/19.95 | | % 135.48/19.95 | | (14) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.48/19.95 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.48/19.95 | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 135.48/19.95 | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.95 | | $i(all_56_21) & $i(all_56_29) % 135.48/19.95 | | % 135.48/19.95 | | ALPHA: (14) implies: % 135.48/19.95 | | (15) ~ (all_56_21 = e1) % 135.48/19.95 | | (16) op(e0, e1) = e0 % 135.48/19.95 | | (17) op(e1, e1) = all_56_21 % 135.48/19.95 | | % 135.48/19.95 | | GROUND_INST: instantiating (3) with all_52_11, e0, e1, e0, simplifying with % 135.48/19.95 | | (5), (16) gives: % 135.48/19.95 | | (18) all_52_11 = e0 % 135.48/19.95 | | % 135.48/19.95 | | GROUND_INST: instantiating (3) with all_6_2, all_56_21, e1, e1, simplifying % 135.48/19.95 | | with (1), (17) gives: % 135.48/19.95 | | (19) all_56_21 = all_6_2 % 135.48/19.95 | | % 135.48/19.95 | | REDUCE: (4), (18) imply: % 135.48/19.95 | | (20) ~ (all_6_2 = e0) % 135.48/19.95 | | % 135.48/19.95 | | SIMP: (20) implies: % 135.48/19.95 | | (21) ~ (all_6_2 = e0) % 135.48/19.95 | | % 135.48/19.95 | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (15), (17), (21) are inconsistent % 135.48/19.95 | | by sub-proof #124. % 135.48/19.95 | | % 135.48/19.95 | End of split % 135.48/19.95 | % 135.48/19.95 End of proof % 135.48/19.95 % 135.48/19.95 Sub-proof #60 shows that the following formulas are inconsistent: % 135.48/19.95 ---------------------------------------------------------------- % 135.48/19.95 (1) op(e2, e0) = all_52_13 % 135.48/19.95 (2) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 135.48/19.95 (3) ~ (all_8_2 = e1) % 135.48/19.95 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.95 (5) op(e2, e0) = e2 % 135.48/19.95 (6) all_54_5 = all_8_2 % 135.48/19.95 (7) ~ (all_8_2 = e0) % 135.48/19.95 (8) ~ (all_52_13 = all_8_2) % 135.48/19.95 % 135.48/19.95 Begin of proof % 135.48/19.95 | % 135.48/19.95 | BETA: splitting (2) gives: % 135.48/19.95 | % 135.48/19.95 | Case 1: % 135.48/19.95 | | % 135.48/19.95 | | (9) all_54_5 = e2 % 135.48/19.95 | | % 135.48/19.95 | | COMBINE_EQS: (6), (9) imply: % 135.48/19.95 | | (10) all_8_2 = e2 % 135.48/19.95 | | % 135.48/19.95 | | SIMP: (10) implies: % 135.48/19.95 | | (11) all_8_2 = e2 % 135.48/19.95 | | % 135.48/19.95 | | REDUCE: (8), (11) imply: % 135.48/19.95 | | (12) ~ (all_52_13 = e2) % 135.48/19.95 | | % 135.48/19.95 | | REF_CLOSE: (1), (4), (5), (12) are inconsistent by sub-proof #768. % 135.48/19.95 | | % 135.48/19.95 | Case 2: % 135.48/19.95 | | % 135.48/19.95 | | (13) all_54_5 = e1 | all_54_5 = e0 % 135.48/19.95 | | % 135.48/19.95 | | REF_CLOSE: (3), (6), (7), (13) are inconsistent by sub-proof #624. % 135.48/19.95 | | % 135.48/19.95 | End of split % 135.48/19.95 | % 135.48/19.95 End of proof % 135.48/19.95 % 135.48/19.95 Sub-proof #61 shows that the following formulas are inconsistent: % 135.48/19.95 ---------------------------------------------------------------- % 135.48/19.95 (1) all_57_6 = e3 & op(e1, e3) = e3 % 135.48/19.95 (2) all_57_6 = e1 % 135.48/19.95 (3) ~ (e3 = e1) % 135.48/19.95 % 135.48/19.95 Begin of proof % 135.48/19.95 | % 135.48/19.95 | ALPHA: (1) implies: % 135.48/19.95 | (4) all_57_6 = e3 % 135.48/19.95 | % 135.48/19.95 | COMBINE_EQS: (2), (4) imply: % 135.48/19.95 | (5) e3 = e1 % 135.48/19.95 | % 135.48/19.95 | REDUCE: (3), (5) imply: % 135.48/19.95 | (6) $false % 135.48/19.95 | % 135.48/19.95 | CLOSE: (6) is inconsistent. % 135.48/19.95 | % 135.48/19.95 End of proof % 135.48/19.95 % 135.48/19.95 Sub-proof #62 shows that the following formulas are inconsistent: % 135.48/19.95 ---------------------------------------------------------------- % 135.48/19.95 (1) all_54_7 = all_20_0 % 135.48/19.95 (2) all_54_7 = e1 % 135.48/19.95 (3) ~ (all_20_0 = e1) % 135.48/19.95 % 135.48/19.95 Begin of proof % 135.48/19.95 | % 135.48/19.95 | COMBINE_EQS: (1), (2) imply: % 135.48/19.95 | (4) all_20_0 = e1 % 135.48/19.95 | % 135.48/19.95 | SIMP: (4) implies: % 135.48/19.95 | (5) all_20_0 = e1 % 135.48/19.95 | % 135.48/19.95 | REDUCE: (3), (5) imply: % 135.48/19.95 | (6) $false % 135.48/19.95 | % 135.48/19.95 | CLOSE: (6) is inconsistent. % 135.48/19.95 | % 135.48/19.95 End of proof % 135.48/19.95 % 135.48/19.95 Sub-proof #63 shows that the following formulas are inconsistent: % 135.48/19.95 ---------------------------------------------------------------- % 135.48/19.95 (1) all_54_7 = all_20_0 % 135.48/19.95 (2) all_54_7 = e2 % 135.48/19.95 (3) ~ (all_20_0 = e2) % 135.48/19.95 % 135.48/19.95 Begin of proof % 135.48/19.95 | % 135.48/19.95 | COMBINE_EQS: (1), (2) imply: % 135.48/19.95 | (4) all_20_0 = e2 % 135.48/19.95 | % 135.48/19.95 | SIMP: (4) implies: % 135.48/19.95 | (5) all_20_0 = e2 % 135.48/19.95 | % 135.48/19.95 | REDUCE: (3), (5) imply: % 135.48/19.95 | (6) $false % 135.48/19.95 | % 135.48/19.95 | CLOSE: (6) is inconsistent. % 135.48/19.95 | % 135.48/19.95 End of proof % 135.48/19.95 % 135.48/19.95 Sub-proof #64 shows that the following formulas are inconsistent: % 135.48/19.95 ---------------------------------------------------------------- % 135.48/19.95 (1) all_54_9 = all_52_6 % 135.48/19.95 (2) all_54_9 = e3 % 135.48/19.95 (3) ~ (all_52_6 = e3) % 135.48/19.95 % 135.48/19.95 Begin of proof % 135.48/19.95 | % 135.48/19.95 | COMBINE_EQS: (1), (2) imply: % 135.48/19.95 | (4) all_52_6 = e3 % 135.48/19.95 | % 135.48/19.95 | SIMP: (4) implies: % 135.48/19.95 | (5) all_52_6 = e3 % 135.48/19.95 | % 135.48/19.95 | REDUCE: (3), (5) imply: % 135.48/19.95 | (6) $false % 135.48/19.95 | % 135.48/19.95 | CLOSE: (6) is inconsistent. % 135.48/19.95 | % 135.48/19.95 End of proof % 135.48/19.95 % 135.48/19.95 Sub-proof #65 shows that the following formulas are inconsistent: % 135.48/19.95 ---------------------------------------------------------------- % 135.48/19.95 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.95 (2) op(e1, e2) = all_52_6 % 135.48/19.95 (3) op(e1, e2) = e1 % 135.48/19.95 (4) ~ (all_52_6 = e1) % 135.48/19.95 % 135.48/19.95 Begin of proof % 135.48/19.95 | % 135.48/19.95 | GROUND_INST: instantiating (1) with all_52_6, e1, e2, e1, simplifying with % 135.48/19.95 | (2), (3) gives: % 135.48/19.95 | (5) all_52_6 = e1 % 135.48/19.95 | % 135.48/19.95 | REDUCE: (4), (5) imply: % 135.48/19.95 | (6) $false % 135.48/19.95 | % 135.48/19.95 | CLOSE: (6) is inconsistent. % 135.48/19.95 | % 135.48/19.95 End of proof % 135.48/19.95 % 135.48/19.95 Sub-proof #66 shows that the following formulas are inconsistent: % 135.48/19.95 ---------------------------------------------------------------- % 135.48/19.95 (1) all_54_0 = all_10_2 % 135.48/19.95 (2) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 135.48/19.95 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 135.48/19.95 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.48/19.95 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.48/19.95 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 135.48/19.95 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.48/19.95 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 135.48/19.95 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.48/19.95 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.95 $i(all_56_21) & $i(all_56_29)) % 135.48/19.95 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.95 (4) ~ (all_10_2 = e0) % 135.48/19.95 (5) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 135.48/19.95 (6) op(e3, e3) = all_10_2 % 135.48/19.95 (7) ~ (all_10_2 = e2) % 135.48/19.95 (8) ~ (all_10_2 = e1) % 135.48/19.95 % 135.48/19.95 Begin of proof % 135.48/19.95 | % 135.48/19.95 | BETA: splitting (2) gives: % 135.48/19.95 | % 135.48/19.95 | Case 1: % 135.48/19.95 | | % 135.48/19.95 | | (9) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.48/19.95 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.48/19.95 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.48/19.95 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.48/19.95 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 135.48/19.95 | | % 135.48/19.95 | | ALPHA: (9) implies: % 135.48/19.95 | | (10) op(e3, e3) = e2 % 135.48/19.95 | | % 135.48/19.95 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10) are inconsistent by % 135.48/19.95 | | sub-proof #776. % 135.48/19.95 | | % 135.48/19.95 | Case 2: % 135.48/19.95 | | % 135.48/19.95 | | (11) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.48/19.95 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = % 135.48/19.95 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.48/19.95 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.48/19.95 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 135.48/19.95 | | % 135.48/19.95 | | ALPHA: (11) implies: % 135.48/19.95 | | (12) op(e3, e3) = e1 % 135.48/19.95 | | % 135.48/19.95 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (12) are inconsistent by % 135.48/19.95 | | sub-proof #774. % 135.48/19.95 | | % 135.48/19.95 | End of split % 135.48/19.95 | % 135.48/19.95 End of proof % 135.48/19.95 % 135.48/19.95 Sub-proof #67 shows that the following formulas are inconsistent: % 135.48/19.95 ---------------------------------------------------------------- % 135.48/19.95 (1) op(e1, e1) = all_6_2 % 135.48/19.95 (2) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & % 135.48/19.95 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & % 135.48/19.95 $i(all_40_1)) % 135.48/19.95 (3) ~ (all_52_11 = e2) % 135.48/19.95 (4) all_40_2 = all_6_2 % 135.48/19.95 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.95 (6) ~ (e2 = e1) % 135.48/19.95 (7) ~ (e3 = e2) % 135.48/19.95 (8) ~ (all_52_11 = all_6_2) % 135.48/19.95 (9) op(e0, e1) = all_52_11 % 135.48/19.95 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 135.48/19.95 (11) op(e2, e0) = e0 % 135.48/19.95 (12) op(e0, e0) = e2 % 135.48/19.95 (13) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.48/19.95 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.48/19.95 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.48/19.95 e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.48/19.95 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.48/19.95 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 135.48/19.95 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.48/19.95 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 135.48/19.95 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 % 135.48/19.95 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.48/19.95 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.48/19.95 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.48/19.95 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.48/19.95 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.48/19.95 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.48/19.95 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.48/19.95 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.48/19.95 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.48/19.95 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.48/19.95 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.48/19.95 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.48/19.95 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.48/19.95 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.48/19.95 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.48/19.95 $i(all_56_29)))) % 135.48/19.95 (14) all_54_14 = all_52_11 % 135.48/19.95 % 135.48/19.95 Begin of proof % 135.48/19.95 | % 135.48/19.95 | BETA: splitting (13) gives: % 135.48/19.95 | % 135.48/19.95 | Case 1: % 135.48/19.95 | | % 135.48/19.95 | | (15) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 135.48/19.95 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.48/19.95 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.48/19.95 | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) % 135.48/19.95 | | & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 135.48/19.95 | | % 135.48/19.95 | | ALPHA: (15) implies: % 135.48/19.95 | | (16) ~ (all_56_27 = e0) % 135.48/19.95 | | (17) op(e2, e0) = all_56_27 % 135.48/19.95 | | % 135.48/19.95 | | REF_CLOSE: (5), (11), (16), (17) are inconsistent by sub-proof #275. % 135.48/19.95 | | % 135.48/19.95 | Case 2: % 135.48/19.95 | | % 135.48/19.95 | | (18) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 % 135.48/19.95 | | = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.48/19.95 | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) % 135.48/19.95 | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.48/19.95 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.48/19.95 | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 % 135.48/19.95 | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.48/19.95 | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.48/19.95 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.48/19.95 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.48/19.95 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 % 135.48/19.95 | | = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.48/19.95 | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, % 135.48/19.95 | | e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 135.48/19.95 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.48/19.95 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.48/19.95 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.48/19.95 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.48/19.95 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.48/19.95 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29))) % 135.48/19.95 | | % 135.48/19.95 | | ALPHA: (18) implies: % 135.48/19.95 | | (19) op(e0, e0) = all_56_31 % 135.48/19.95 | | (20) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.48/19.95 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.95 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.95 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 135.48/19.95 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.48/19.95 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.48/19.95 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.48/19.95 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.48/19.95 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.48/19.95 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 135.48/19.95 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 % 135.48/19.95 | | = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 135.48/19.95 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.48/19.95 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & % 135.48/19.95 | | all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.48/19.95 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 135.48/19.95 | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.48/19.95 | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.95 | | $i(all_56_21) & $i(all_56_29)) % 135.48/19.95 | | % 135.48/19.95 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 135.48/19.95 | | (14), (19), (20) are inconsistent by sub-proof #273. % 135.48/19.95 | | % 135.48/19.95 | End of split % 135.48/19.95 | % 135.48/19.95 End of proof % 135.48/19.95 % 135.48/19.95 Sub-proof #68 shows that the following formulas are inconsistent: % 135.48/19.95 ---------------------------------------------------------------- % 135.48/19.95 (1) op(e2, e2) = all_8_2 % 135.48/19.95 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.95 (3) op(e0, e3) = e3 % 135.48/19.95 (4) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.48/19.95 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.48/19.95 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.48/19.95 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.48/19.95 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 135.48/19.95 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 135.48/19.95 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 135.48/19.95 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.48/19.95 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.48/19.95 $i(all_56_17) & $i(all_56_25)) % 135.48/19.95 (5) ~ (all_8_2 = e3) % 135.48/19.95 % 135.48/19.95 Begin of proof % 135.48/19.95 | % 135.48/19.95 | BETA: splitting (4) gives: % 135.48/19.95 | % 135.48/19.95 | Case 1: % 135.48/19.95 | | % 135.48/19.95 | | (6) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.48/19.95 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.48/19.95 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.48/19.95 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.48/19.95 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 135.48/19.95 | | % 135.48/19.95 | | ALPHA: (6) implies: % 135.48/19.95 | | (7) ~ (all_56_7 = e3) % 135.48/19.95 | | (8) op(e0, e3) = all_56_7 % 135.48/19.95 | | % 135.48/19.95 | | REF_CLOSE: (2), (3), (7), (8) are inconsistent by sub-proof #209. % 135.48/19.95 | | % 135.48/19.95 | Case 2: % 135.48/19.95 | | % 135.48/19.95 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.48/19.95 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.95 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.95 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) % 135.48/19.95 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 135.48/19.95 | | % 135.48/19.95 | | ALPHA: (9) implies: % 135.48/19.95 | | (10) op(e2, e2) = e3 % 135.48/19.95 | | % 135.48/19.95 | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #228. % 135.48/19.95 | | % 135.48/19.95 | End of split % 135.48/19.95 | % 135.48/19.95 End of proof % 135.48/19.95 % 135.48/19.95 Sub-proof #69 shows that the following formulas are inconsistent: % 135.48/19.95 ---------------------------------------------------------------- % 135.48/19.95 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.95 (2) ~ (e2 = e1) % 135.48/19.95 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) % 135.48/19.95 (4) op(e3, e3) = e0 % 135.48/19.95 (5) ~ (e1 = e0) % 135.48/19.95 (6) op(e2, e3) = e2 % 135.48/19.95 % 135.48/19.95 Begin of proof % 135.48/19.95 | % 135.48/19.95 | BETA: splitting (3) gives: % 135.48/19.95 | % 135.48/19.95 | Case 1: % 135.48/19.95 | | % 135.48/19.95 | | (7) all_57_0 = e1 & op(e3, e3) = e1 % 135.48/19.95 | | % 135.48/19.95 | | ALPHA: (7) implies: % 135.48/19.95 | | (8) op(e3, e3) = e1 % 135.48/19.95 | | % 135.48/19.95 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #717. % 135.48/19.95 | | % 135.48/19.95 | Case 2: % 135.48/19.95 | | % 135.48/19.95 | | (9) all_57_2 = e1 & op(e2, e3) = e1 % 135.48/19.95 | | % 135.48/19.95 | | ALPHA: (9) implies: % 135.48/19.95 | | (10) op(e2, e3) = e1 % 135.48/19.95 | | % 135.48/19.95 | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #450. % 135.48/19.95 | | % 135.48/19.95 | End of split % 135.48/19.95 | % 135.48/19.95 End of proof % 135.48/19.95 % 135.48/19.95 Sub-proof #70 shows that the following formulas are inconsistent: % 135.48/19.95 ---------------------------------------------------------------- % 135.48/19.95 (1) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) % 135.48/19.95 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.95 (3) ~ (e3 = e0) % 135.48/19.95 (4) ~ (e3 = e2) % 135.48/19.95 (5) all_57_2 = e2 % 135.48/19.95 (6) op(e3, e3) = e0 % 135.48/19.95 % 135.48/19.95 Begin of proof % 135.48/19.95 | % 135.48/19.95 | BETA: splitting (1) gives: % 135.48/19.95 | % 135.48/19.95 | Case 1: % 135.48/19.95 | | % 135.48/19.95 | | (7) all_57_0 = e3 & op(e3, e3) = e3 % 135.48/19.95 | | % 135.48/19.95 | | ALPHA: (7) implies: % 135.48/19.95 | | (8) op(e3, e3) = e3 % 135.48/19.95 | | % 135.48/19.95 | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #773. % 135.48/19.95 | | % 135.48/19.95 | Case 2: % 135.48/19.95 | | % 135.48/19.95 | | (9) all_57_2 = e3 & op(e2, e3) = e3 % 135.48/19.95 | | % 135.48/19.95 | | ALPHA: (9) implies: % 135.48/19.95 | | (10) all_57_2 = e3 % 135.48/19.95 | | % 135.48/19.95 | | COMBINE_EQS: (5), (10) imply: % 135.48/19.95 | | (11) e3 = e2 % 135.48/19.95 | | % 135.48/19.95 | | REDUCE: (4), (11) imply: % 135.48/19.95 | | (12) $false % 135.48/19.95 | | % 135.48/19.95 | | CLOSE: (12) is inconsistent. % 135.48/19.95 | | % 135.48/19.95 | End of split % 135.48/19.95 | % 135.48/19.95 End of proof % 135.48/19.95 % 135.48/19.95 Sub-proof #71 shows that the following formulas are inconsistent: % 135.48/19.95 ---------------------------------------------------------------- % 135.48/19.95 (1) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 135.48/19.95 (2) ~ (all_52_8 = e0) % 135.48/19.95 (3) all_54_2 = all_52_8 % 135.48/19.95 (4) ~ (all_52_8 = e2) % 135.48/19.95 (5) ~ (all_52_8 = e1) % 135.48/19.95 % 135.48/19.95 Begin of proof % 135.48/19.95 | % 135.48/19.95 | BETA: splitting (1) gives: % 135.48/19.95 | % 135.48/19.95 | Case 1: % 135.48/19.95 | | % 135.48/19.95 | | (6) all_54_2 = e2 % 135.48/19.95 | | % 135.48/19.95 | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #317. % 135.48/19.95 | | % 135.48/19.95 | Case 2: % 135.48/19.95 | | % 135.48/19.95 | | (7) all_54_2 = e1 | all_54_2 = e0 % 135.48/19.95 | | % 135.48/19.95 | | BETA: splitting (7) gives: % 135.48/19.95 | | % 135.48/19.95 | | Case 1: % 135.48/19.95 | | | % 135.48/19.95 | | | (8) all_54_2 = e1 % 135.48/19.95 | | | % 135.48/19.95 | | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #316. % 135.48/19.95 | | | % 135.48/19.95 | | Case 2: % 135.48/19.95 | | | % 135.48/19.95 | | | (9) all_54_2 = e0 % 135.48/19.95 | | | % 135.48/19.95 | | | COMBINE_EQS: (3), (9) imply: % 135.48/19.95 | | | (10) all_52_8 = e0 % 135.48/19.95 | | | % 135.48/19.95 | | | SIMP: (10) implies: % 135.48/19.95 | | | (11) all_52_8 = e0 % 135.48/19.95 | | | % 135.48/19.95 | | | REDUCE: (2), (11) imply: % 135.48/19.95 | | | (12) $false % 135.48/19.95 | | | % 135.48/19.95 | | | CLOSE: (12) is inconsistent. % 135.48/19.95 | | | % 135.48/19.95 | | End of split % 135.48/19.95 | | % 135.48/19.95 | End of split % 135.48/19.95 | % 135.48/19.95 End of proof % 135.48/19.95 % 135.48/19.95 Sub-proof #72 shows that the following formulas are inconsistent: % 135.48/19.95 ---------------------------------------------------------------- % 135.48/19.95 (1) op(e2, e2) = e0 % 135.48/19.95 (2) ~ (all_52_13 = e0) % 135.48/19.95 (3) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 135.48/19.95 (4) ~ (all_42_0 = e1) % 135.48/19.95 (5) ~ (all_52_4 = all_52_12) % 135.48/19.95 (6) ~ (all_52_13 = e1) % 135.48/19.95 (7) ~ (all_52_7 = e3) % 135.48/19.95 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.95 (9) ~ (e3 = e0) % 135.48/19.95 (10) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 135.48/19.95 (11) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 135.48/19.95 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) % 135.48/19.95 (12) all_54_3 = all_52_12 % 135.48/19.95 (13) ~ (all_52_12 = e0) % 135.48/19.95 (14) op(e0, e2) = all_52_7 % 135.48/19.95 (15) ~ (all_52_4 = e3) % 135.48/19.95 (16) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 135.48/19.95 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 135.48/19.96 (17) ~ (all_52_12 = all_52_13) % 135.48/19.96 (18) op(e3, e2) = all_52_4 % 135.48/19.96 (19) op(e0, e2) = all_42_0 % 135.48/19.96 (20) ~ (all_52_13 = e3) % 135.48/19.96 (21) op(e0, e2) = all_56_15 % 135.48/19.96 (22) all_57_2 = e3 % 135.48/19.96 (23) all_54_7 = all_52_13 % 135.48/19.96 (24) ~ (e3 = e1) % 135.48/19.96 (25) ~ (e1 = e0) % 135.48/19.96 (26) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 135.48/19.96 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 135.48/19.96 (27) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 135.48/19.96 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 135.48/19.96 (28) all_57_10 = e2 % 135.48/19.96 (29) ~ (all_52_12 = e3) % 135.48/19.96 % 135.48/19.96 Begin of proof % 135.48/19.96 | % 135.48/19.96 | BETA: splitting (3) gives: % 135.48/19.96 | % 135.48/19.96 | Case 1: % 135.48/19.96 | | % 135.48/19.96 | | (30) all_54_7 = e3 % 135.48/19.96 | | % 135.48/19.96 | | REF_CLOSE: (20), (23), (30) are inconsistent by sub-proof #338. % 135.48/19.96 | | % 135.48/19.96 | Case 2: % 135.48/19.96 | | % 135.48/19.96 | | (31) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 135.48/19.96 | | % 135.48/19.96 | | BETA: splitting (31) gives: % 135.48/19.96 | | % 135.48/19.96 | | Case 1: % 135.48/19.96 | | | % 135.48/19.96 | | | (32) all_54_7 = e2 % 135.48/19.96 | | | % 135.48/19.96 | | | COMBINE_EQS: (23), (32) imply: % 135.48/19.96 | | | (33) all_52_13 = e2 % 135.48/19.96 | | | % 135.48/19.96 | | | SIMP: (33) implies: % 135.48/19.96 | | | (34) all_52_13 = e2 % 135.48/19.96 | | | % 135.48/19.96 | | | REDUCE: (17), (34) imply: % 135.48/19.96 | | | (35) ~ (all_52_12 = e2) % 135.48/19.96 | | | % 135.48/19.96 | | | REDUCE: (6), (34) imply: % 135.48/19.96 | | | (36) ~ (e2 = e1) % 135.48/19.96 | | | % 135.48/19.96 | | | REDUCE: (2), (34) imply: % 135.48/19.96 | | | (37) ~ (e2 = e0) % 135.48/19.96 | | | % 135.48/19.96 | | | BETA: splitting (10) gives: % 135.48/19.96 | | | % 135.48/19.96 | | | Case 1: % 135.48/19.96 | | | | % 135.48/19.96 | | | | (38) all_54_3 = e3 % 135.48/19.96 | | | | % 135.48/19.96 | | | | COMBINE_EQS: (12), (38) imply: % 135.48/19.96 | | | | (39) all_52_12 = e3 % 135.48/19.96 | | | | % 135.48/19.96 | | | | REDUCE: (29), (39) imply: % 135.48/19.96 | | | | (40) $false % 135.48/19.96 | | | | % 135.48/19.96 | | | | CLOSE: (40) is inconsistent. % 135.48/19.96 | | | | % 135.48/19.96 | | | Case 2: % 135.48/19.96 | | | | % 135.48/19.96 | | | | (41) ~ (all_54_3 = e3) % 135.48/19.96 | | | | (42) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 135.48/19.96 | | | | % 135.48/19.96 | | | | BETA: splitting (42) gives: % 135.48/19.96 | | | | % 135.48/19.96 | | | | Case 1: % 135.48/19.96 | | | | | % 135.48/19.96 | | | | | (43) all_54_3 = e2 % 135.48/19.96 | | | | | % 135.48/19.96 | | | | | COMBINE_EQS: (12), (43) imply: % 135.48/19.96 | | | | | (44) all_52_12 = e2 % 135.48/19.96 | | | | | % 135.48/19.96 | | | | | REDUCE: (35), (44) imply: % 135.48/19.96 | | | | | (45) $false % 135.48/19.96 | | | | | % 135.48/19.96 | | | | | CLOSE: (45) is inconsistent. % 135.48/19.96 | | | | | % 135.48/19.96 | | | | Case 2: % 135.48/19.96 | | | | | % 135.48/19.96 | | | | | (46) all_54_3 = e1 | all_54_3 = e0 % 135.48/19.96 | | | | | % 135.48/19.96 | | | | | BETA: splitting (11) gives: % 135.48/19.96 | | | | | % 135.48/19.96 | | | | | Case 1: % 135.48/19.96 | | | | | | % 135.48/19.96 | | | | | | (47) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, % 135.48/19.96 | | | | | | e2) = e3) % 135.48/19.96 | | | | | | % 135.48/19.96 | | | | | | BETA: splitting (47) gives: % 135.48/19.96 | | | | | | % 135.48/19.96 | | | | | | Case 1: % 135.48/19.96 | | | | | | | % 135.48/19.96 | | | | | | | (48) all_57_1 = e3 & op(e3, e2) = e3 % 135.48/19.96 | | | | | | | % 135.48/19.96 | | | | | | | ALPHA: (48) implies: % 135.48/19.96 | | | | | | | (49) op(e3, e2) = e3 % 135.48/19.96 | | | | | | | % 135.48/19.96 | | | | | | | REF_CLOSE: (8), (15), (18), (49) are inconsistent by sub-proof % 135.48/19.96 | | | | | | | #738. % 135.48/19.96 | | | | | | | % 135.48/19.96 | | | | | | Case 2: % 135.48/19.96 | | | | | | | % 135.48/19.96 | | | | | | | (50) all_57_3 = e3 & op(e2, e2) = e3 % 135.48/19.96 | | | | | | | % 135.48/19.96 | | | | | | | ALPHA: (50) implies: % 135.48/19.96 | | | | | | | (51) all_57_3 = e3 % 135.48/19.96 | | | | | | | % 135.48/19.96 | | | | | | | REF_CLOSE: (9), (22), (24), (25), (26), (27), (28), (36), (37), % 135.48/19.96 | | | | | | | (51) are inconsistent by sub-proof #362. % 135.48/19.96 | | | | | | | % 135.48/19.96 | | | | | | End of split % 135.48/19.96 | | | | | | % 135.48/19.96 | | | | | Case 2: % 135.48/19.96 | | | | | | % 135.48/19.96 | | | | | | (52) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, % 135.48/19.96 | | | | | | e2) = e3) % 135.48/19.96 | | | | | | % 135.48/19.96 | | | | | | BETA: splitting (52) gives: % 135.48/19.96 | | | | | | % 135.48/19.96 | | | | | | Case 1: % 135.48/19.96 | | | | | | | % 135.48/19.96 | | | | | | | (53) all_57_7 = e3 & op(e1, e2) = e3 % 135.48/19.96 | | | | | | | % 135.48/19.96 | | | | | | | ALPHA: (53) implies: % 135.48/19.96 | | | | | | | (54) all_57_7 = e3 % 135.48/19.96 | | | | | | | % 135.48/19.96 | | | | | | | BETA: splitting (46) gives: % 135.48/19.96 | | | | | | | % 135.48/19.96 | | | | | | | Case 1: % 135.48/19.96 | | | | | | | | % 135.48/19.96 | | | | | | | | (55) all_54_3 = e1 % 135.48/19.96 | | | | | | | | % 135.48/19.96 | | | | | | | | COMBINE_EQS: (12), (55) imply: % 135.48/19.96 | | | | | | | | (56) all_52_12 = e1 % 135.48/19.96 | | | | | | | | % 135.48/19.96 | | | | | | | | REDUCE: (5), (56) imply: % 135.48/19.96 | | | | | | | | (57) ~ (all_52_4 = e1) % 135.48/19.96 | | | | | | | | % 135.48/19.96 | | | | | | | | REDUCE: (29), (56) imply: % 135.48/19.96 | | | | | | | | (58) ~ (e3 = e1) % 135.48/19.96 | | | | | | | | % 135.48/19.96 | | | | | | | | BETA: splitting (16) gives: % 135.48/19.96 | | | | | | | | % 135.48/19.96 | | | | | | | | Case 1: % 135.48/19.96 | | | | | | | | | % 135.48/19.96 | | | | | | | | | (59) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & % 135.48/19.96 | | | | | | | | | op(e2, e2) = e1) % 135.48/19.96 | | | | | | | | | % 135.48/19.96 | | | | | | | | | REF_CLOSE: (1), (8), (18), (25), (57), (59) are inconsistent % 135.48/19.96 | | | | | | | | | by sub-proof #564. % 135.48/19.96 | | | | | | | | | % 135.48/19.96 | | | | | | | | Case 2: % 135.48/19.96 | | | | | | | | | % 135.48/19.96 | | | | | | | | | (60) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & % 135.48/19.96 | | | | | | | | | op(e0, e2) = e1) % 135.48/19.96 | | | | | | | | | % 135.48/19.96 | | | | | | | | | BETA: splitting (60) gives: % 135.48/19.96 | | | | | | | | | % 135.48/19.96 | | | | | | | | | Case 1: % 135.48/19.96 | | | | | | | | | | % 135.48/19.96 | | | | | | | | | | (61) all_57_7 = e1 & op(e1, e2) = e1 % 135.48/19.96 | | | | | | | | | | % 135.48/19.96 | | | | | | | | | | REF_CLOSE: (24), (54), (61) are inconsistent by sub-proof % 135.48/19.96 | | | | | | | | | | #603. % 135.48/19.96 | | | | | | | | | | % 135.48/19.96 | | | | | | | | | Case 2: % 135.48/19.96 | | | | | | | | | | % 135.48/19.96 | | | | | | | | | | (62) all_57_13 = e1 & op(e0, e2) = e1 % 135.48/19.96 | | | | | | | | | | % 135.48/19.96 | | | | | | | | | | ALPHA: (62) implies: % 135.48/19.96 | | | | | | | | | | (63) op(e0, e2) = e1 % 135.48/19.96 | | | | | | | | | | % 135.48/19.96 | | | | | | | | | | GROUND_INST: instantiating (8) with all_42_0, all_56_15, e2, % 135.48/19.96 | | | | | | | | | | e0, simplifying with (19), (21) gives: % 135.48/19.96 | | | | | | | | | | (64) all_56_15 = all_42_0 % 135.48/19.96 | | | | | | | | | | % 135.48/19.96 | | | | | | | | | | GROUND_INST: instantiating (8) with e1, all_56_15, e2, e0, % 135.48/19.96 | | | | | | | | | | simplifying with (21), (63) gives: % 135.48/19.96 | | | | | | | | | | (65) all_56_15 = e1 % 135.48/19.96 | | | | | | | | | | % 135.48/19.96 | | | | | | | | | | COMBINE_EQS: (64), (65) imply: % 135.48/19.96 | | | | | | | | | | (66) all_42_0 = e1 % 135.48/19.96 | | | | | | | | | | % 135.48/19.96 | | | | | | | | | | REDUCE: (4), (66) imply: % 135.48/19.96 | | | | | | | | | | (67) $false % 135.48/19.96 | | | | | | | | | | % 135.48/19.96 | | | | | | | | | | CLOSE: (67) is inconsistent. % 135.48/19.96 | | | | | | | | | | % 135.48/19.96 | | | | | | | | | End of split % 135.48/19.96 | | | | | | | | | % 135.48/19.96 | | | | | | | | End of split % 135.48/19.96 | | | | | | | | % 135.48/19.96 | | | | | | | Case 2: % 135.48/19.96 | | | | | | | | % 135.48/19.96 | | | | | | | | (68) all_54_3 = e0 % 135.48/19.96 | | | | | | | | % 135.48/19.96 | | | | | | | | COMBINE_EQS: (12), (68) imply: % 135.48/19.96 | | | | | | | | (69) all_52_12 = e0 % 135.48/19.96 | | | | | | | | % 135.48/19.96 | | | | | | | | REDUCE: (13), (69) imply: % 135.48/19.96 | | | | | | | | (70) $false % 135.48/19.96 | | | | | | | | % 135.48/19.96 | | | | | | | | CLOSE: (70) is inconsistent. % 135.48/19.96 | | | | | | | | % 135.48/19.96 | | | | | | | End of split % 135.48/19.96 | | | | | | | % 135.48/19.96 | | | | | | Case 2: % 135.48/19.96 | | | | | | | % 135.48/19.96 | | | | | | | (71) all_57_13 = e3 & op(e0, e2) = e3 % 135.48/19.96 | | | | | | | % 135.48/19.96 | | | | | | | REF_CLOSE: (7), (8), (14), (71) are inconsistent by sub-proof % 135.48/19.96 | | | | | | | #556. % 135.48/19.96 | | | | | | | % 135.48/19.96 | | | | | | End of split % 135.48/19.96 | | | | | | % 135.48/19.96 | | | | | End of split % 135.48/19.96 | | | | | % 135.48/19.96 | | | | End of split % 135.48/19.96 | | | | % 135.48/19.96 | | | End of split % 135.48/19.96 | | | % 135.48/19.96 | | Case 2: % 135.48/19.96 | | | % 135.48/19.96 | | | (72) all_54_7 = e1 | all_54_7 = e0 % 135.48/19.96 | | | % 135.48/19.96 | | | REF_CLOSE: (2), (6), (23), (72) are inconsistent by sub-proof #313. % 135.48/19.96 | | | % 135.48/19.96 | | End of split % 135.48/19.96 | | % 135.48/19.96 | End of split % 135.48/19.96 | % 135.48/19.96 End of proof % 135.48/19.96 % 135.48/19.96 Sub-proof #73 shows that the following formulas are inconsistent: % 135.48/19.96 ---------------------------------------------------------------- % 135.48/19.96 (1) all_57_6 = e0 & op(e1, e3) = e0 % 135.48/19.96 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.96 (3) op(e1, e3) = all_52_2 % 135.48/19.96 (4) ~ (all_52_2 = e0) % 135.48/19.96 % 135.48/19.96 Begin of proof % 135.48/19.96 | % 135.48/19.96 | ALPHA: (1) implies: % 135.48/19.96 | (5) op(e1, e3) = e0 % 135.48/19.96 | % 135.48/19.96 | GROUND_INST: instantiating (2) with all_52_2, e0, e3, e1, simplifying with % 135.48/19.96 | (3), (5) gives: % 135.48/19.96 | (6) all_52_2 = e0 % 135.48/19.96 | % 135.48/19.96 | REDUCE: (4), (6) imply: % 135.48/19.96 | (7) $false % 135.48/19.96 | % 135.48/19.96 | CLOSE: (7) is inconsistent. % 135.48/19.96 | % 135.48/19.96 End of proof % 135.48/19.96 % 135.48/19.96 Sub-proof #74 shows that the following formulas are inconsistent: % 135.48/19.96 ---------------------------------------------------------------- % 135.48/19.96 (1) ~ (all_6_1 = e3) & op(e2, e2) = all_6_1 & $i(all_6_1) % 135.48/19.96 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.96 (3) op(e2, e2) = e3 % 135.48/19.96 % 135.48/19.96 Begin of proof % 135.48/19.96 | % 135.48/19.96 | ALPHA: (1) implies: % 135.48/19.96 | (4) ~ (all_6_1 = e3) % 135.48/19.96 | (5) op(e2, e2) = all_6_1 % 135.48/19.96 | % 135.48/19.96 | GROUND_INST: instantiating (2) with e3, all_6_1, e2, e2, simplifying with (3), % 135.48/19.96 | (5) gives: % 135.48/19.96 | (6) all_6_1 = e3 % 135.48/19.96 | % 135.48/19.96 | REDUCE: (4), (6) imply: % 135.48/19.96 | (7) $false % 135.48/19.96 | % 135.48/19.96 | CLOSE: (7) is inconsistent. % 135.48/19.96 | % 135.48/19.96 End of proof % 135.48/19.96 % 135.48/19.96 Sub-proof #75 shows that the following formulas are inconsistent: % 135.48/19.96 ---------------------------------------------------------------- % 135.48/19.96 (1) all_54_6 = all_6_0 % 135.48/19.96 (2) all_54_6 = e0 % 135.48/19.96 (3) ~ (all_6_0 = e0) % 135.48/19.96 % 135.48/19.96 Begin of proof % 135.48/19.96 | % 135.48/19.96 | COMBINE_EQS: (1), (2) imply: % 135.48/19.96 | (4) all_6_0 = e0 % 135.48/19.96 | % 135.48/19.96 | SIMP: (4) implies: % 135.48/19.96 | (5) all_6_0 = e0 % 135.48/19.96 | % 135.48/19.96 | REDUCE: (3), (5) imply: % 135.48/19.96 | (6) $false % 135.48/19.96 | % 135.48/19.96 | CLOSE: (6) is inconsistent. % 135.48/19.96 | % 135.48/19.96 End of proof % 135.48/19.96 % 135.48/19.96 Sub-proof #76 shows that the following formulas are inconsistent: % 135.48/19.96 ---------------------------------------------------------------- % 135.48/19.96 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 135.48/19.96 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 135.48/19.96 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) | % 135.48/19.96 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 135.48/19.96 (3) all_57_5 = e1 % 135.48/19.96 (4) ~ (e2 = e0) % 135.48/19.96 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.96 (6) ~ (e2 = e1) % 135.48/19.96 (7) ~ (e3 = e0) % 135.48/19.96 (8) ~ (e3 = e2) % 135.48/19.96 (9) all_57_8 = e2 % 135.48/19.96 (10) op(e1, e1) = e2 % 135.48/19.96 (11) ~ (all_52_9 = e3) % 135.48/19.96 (12) op(e2, e1) = all_52_9 % 135.48/19.96 (13) op(e3, e1) = all_52_8 % 135.48/19.96 (14) ~ (e3 = e1) % 135.48/19.96 (15) ~ (e1 = e0) % 135.48/19.96 (16) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) | % 135.48/19.96 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) % 135.48/19.96 (17) all_57_14 = e1 % 135.48/19.96 % 135.48/19.96 Begin of proof % 135.48/19.96 | % 135.48/19.96 | BETA: splitting (16) gives: % 135.48/19.96 | % 135.48/19.96 | Case 1: % 135.48/19.96 | | % 135.48/19.96 | | (18) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = % 135.48/19.96 | | e3) % 135.48/19.96 | | % 135.48/19.96 | | BETA: splitting (18) gives: % 135.48/19.96 | | % 135.48/19.96 | | Case 1: % 135.48/19.96 | | | % 135.48/19.96 | | | (19) all_57_4 = e3 & op(e3, e1) = e3 % 135.48/19.96 | | | % 135.48/19.96 | | | ALPHA: (19) implies: % 135.48/19.96 | | | (20) all_57_4 = e3 % 135.48/19.96 | | | (21) op(e3, e1) = e3 % 135.48/19.96 | | | % 135.48/19.96 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (13), (14), (15), (17), % 135.48/19.96 | | | (20), (21) are inconsistent by sub-proof #82. % 135.48/19.96 | | | % 135.48/19.96 | | Case 2: % 135.48/19.96 | | | % 135.48/19.96 | | | (22) all_57_5 = e3 & op(e2, e1) = e3 % 135.48/19.96 | | | % 135.48/19.96 | | | REF_CLOSE: (5), (11), (12), (22) are inconsistent by sub-proof #547. % 135.48/19.96 | | | % 135.48/19.96 | | End of split % 135.48/19.96 | | % 135.48/19.96 | Case 2: % 135.48/19.96 | | % 135.48/19.96 | | (23) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = % 135.48/19.96 | | e3) % 135.48/19.96 | | % 135.48/19.96 | | REF_CLOSE: (5), (8), (10), (14), (17), (23) are inconsistent by sub-proof % 135.48/19.96 | | #81. % 135.48/19.96 | | % 135.48/19.96 | End of split % 135.48/19.96 | % 135.48/19.96 End of proof % 135.48/19.96 % 135.48/19.96 Sub-proof #77 shows that the following formulas are inconsistent: % 135.48/19.96 ---------------------------------------------------------------- % 135.48/19.96 (1) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) % 135.48/19.96 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.96 (3) op(e2, e2) = e3 % 135.48/19.96 (4) ~ (all_52_1 = e1) % 135.48/19.96 (5) op(e2, e3) = all_52_1 % 135.48/19.96 (6) ~ (e3 = e1) % 135.48/19.96 % 135.48/19.96 Begin of proof % 135.48/19.96 | % 135.48/19.96 | BETA: splitting (1) gives: % 135.48/19.96 | % 135.48/19.96 | Case 1: % 135.48/19.96 | | % 135.48/19.96 | | (7) all_57_2 = e1 & op(e2, e3) = e1 % 135.48/19.96 | | % 135.48/19.96 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #676. % 135.48/19.96 | | % 135.48/19.96 | Case 2: % 135.48/19.96 | | % 135.48/19.96 | | (8) all_57_3 = e1 & op(e2, e2) = e1 % 135.48/19.96 | | % 135.48/19.96 | | ALPHA: (8) implies: % 135.48/19.96 | | (9) op(e2, e2) = e1 % 135.48/19.96 | | % 135.48/19.96 | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #325. % 135.48/19.96 | | % 135.48/19.96 | End of split % 135.48/19.96 | % 135.48/19.96 End of proof % 135.48/19.96 % 135.48/19.96 Sub-proof #78 shows that the following formulas are inconsistent: % 135.48/19.96 ---------------------------------------------------------------- % 135.48/19.96 (1) all_54_6 = all_6_0 % 135.48/19.96 (2) all_54_6 = e2 % 135.48/19.96 (3) ~ (all_6_0 = e2) % 135.48/19.96 % 135.48/19.96 Begin of proof % 135.48/19.96 | % 135.48/19.96 | COMBINE_EQS: (1), (2) imply: % 135.48/19.96 | (4) all_6_0 = e2 % 135.48/19.96 | % 135.48/19.96 | SIMP: (4) implies: % 135.48/19.96 | (5) all_6_0 = e2 % 135.48/19.96 | % 135.48/19.96 | REDUCE: (3), (5) imply: % 135.48/19.96 | (6) $false % 135.48/19.96 | % 135.48/19.96 | CLOSE: (6) is inconsistent. % 135.48/19.96 | % 135.48/19.96 End of proof % 135.48/19.96 % 135.48/19.96 Sub-proof #79 shows that the following formulas are inconsistent: % 135.48/19.96 ---------------------------------------------------------------- % 135.48/19.96 (1) all_54_6 = all_6_0 % 135.48/19.96 (2) all_54_6 = e3 % 135.48/19.96 (3) ~ (all_6_0 = e3) % 135.48/19.96 % 135.48/19.96 Begin of proof % 135.48/19.96 | % 135.48/19.96 | COMBINE_EQS: (1), (2) imply: % 135.48/19.96 | (4) all_6_0 = e3 % 135.48/19.96 | % 135.48/19.96 | SIMP: (4) implies: % 135.48/19.96 | (5) all_6_0 = e3 % 135.48/19.96 | % 135.48/19.96 | REDUCE: (3), (5) imply: % 135.48/19.96 | (6) $false % 135.48/19.96 | % 135.48/19.96 | CLOSE: (6) is inconsistent. % 135.48/19.96 | % 135.48/19.96 End of proof % 135.48/19.96 % 135.48/19.96 Sub-proof #80 shows that the following formulas are inconsistent: % 135.48/19.96 ---------------------------------------------------------------- % 135.48/19.96 (1) op(e2, e2) = all_8_2 % 135.48/19.96 (2) op(e3, e3) = e2 % 135.48/19.96 (3) ~ (e2 = e0) % 135.48/19.96 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.96 (5) ~ (e2 = e1) % 135.48/19.96 (6) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 135.48/19.96 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 135.48/19.96 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.48/19.96 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.48/19.96 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 135.48/19.96 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.48/19.96 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 135.48/19.96 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.48/19.96 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.48/19.96 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 135.48/19.96 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.48/19.96 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 135.48/19.96 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 135.48/19.96 = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.48/19.96 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & % 135.48/19.96 ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, % 135.48/19.96 e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.48/19.96 op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 135.48/19.96 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 135.48/19.96 (7) op(e2, e2) = e2 % 135.48/19.96 (8) ~ (all_8_2 = e3) % 135.48/19.96 % 135.48/19.96 Begin of proof % 135.48/19.96 | % 135.48/19.96 | BETA: splitting (6) gives: % 135.48/19.96 | % 135.48/19.96 | Case 1: % 135.48/19.96 | | % 135.48/19.96 | | (9) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.48/19.96 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 % 135.48/19.96 | | & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 % 135.48/19.96 | | & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.48/19.96 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 135.48/19.96 | | all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.48/19.96 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 135.48/19.96 | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.48/19.96 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.48/19.96 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.48/19.96 | | % 135.48/19.96 | | REF_CLOSE: (2), (4), (5), (7), (9) are inconsistent by sub-proof #444. % 135.48/19.96 | | % 135.48/19.96 | Case 2: % 135.48/19.96 | | % 135.48/19.96 | | (10) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 % 135.48/19.96 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = % 135.48/19.96 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.48/19.96 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 135.48/19.96 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.48/19.96 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.48/19.96 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.96 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.96 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 135.48/19.96 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 135.48/19.96 | | % 135.48/19.96 | | BETA: splitting (10) gives: % 135.48/19.96 | | % 135.48/19.96 | | Case 1: % 135.48/19.96 | | | % 135.48/19.96 | | | (11) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ % 135.48/19.96 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.48/19.96 | | | op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 135.48/19.96 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.48/19.96 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.48/19.96 | | | $i(all_56_31) % 135.48/19.96 | | | % 135.48/19.96 | | | ALPHA: (11) implies: % 135.48/19.96 | | | (12) op(e3, e3) = e0 % 135.48/19.96 | | | % 135.48/19.96 | | | REF_CLOSE: (2), (3), (4), (12) are inconsistent by sub-proof #495. % 135.48/19.96 | | | % 135.48/19.96 | | Case 2: % 135.48/19.96 | | | % 135.48/19.96 | | | (13) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.48/19.96 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.48/19.96 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.48/19.96 | | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 135.48/19.96 | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 135.48/19.96 | | | % 135.48/19.96 | | | ALPHA: (13) implies: % 135.48/19.96 | | | (14) op(e2, e2) = e3 % 135.48/19.96 | | | % 135.48/19.96 | | | REF_CLOSE: (1), (4), (8), (14) are inconsistent by sub-proof #228. % 135.48/19.96 | | | % 135.48/19.96 | | End of split % 135.48/19.96 | | % 135.48/19.96 | End of split % 135.48/19.96 | % 135.48/19.96 End of proof % 135.48/19.96 % 135.48/19.96 Sub-proof #81 shows that the following formulas are inconsistent: % 135.48/19.96 ---------------------------------------------------------------- % 135.48/19.96 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.96 (2) ~ (e3 = e2) % 135.48/19.96 (3) op(e1, e1) = e2 % 135.48/19.96 (4) ~ (e3 = e1) % 135.48/19.96 (5) all_57_14 = e1 % 135.48/19.96 (6) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) % 135.48/19.96 % 135.48/19.96 Begin of proof % 135.48/19.96 | % 135.48/19.96 | BETA: splitting (6) gives: % 135.48/19.96 | % 135.48/19.96 | Case 1: % 135.48/19.96 | | % 135.48/19.96 | | (7) all_57_8 = e3 & op(e1, e1) = e3 % 135.48/19.96 | | % 135.48/19.96 | | ALPHA: (7) implies: % 135.48/19.96 | | (8) op(e1, e1) = e3 % 135.48/19.96 | | % 135.48/19.96 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #109. % 135.48/19.96 | | % 135.48/19.96 | Case 2: % 135.48/19.96 | | % 135.48/19.96 | | (9) all_57_14 = e3 & op(e0, e1) = e3 % 135.48/19.96 | | % 135.48/19.96 | | ALPHA: (9) implies: % 135.48/19.96 | | (10) all_57_14 = e3 % 135.48/19.96 | | % 135.48/19.96 | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #561. % 135.48/19.96 | | % 135.48/19.96 | End of split % 135.48/19.96 | % 135.48/19.96 End of proof % 135.48/19.96 % 135.48/19.96 Sub-proof #82 shows that the following formulas are inconsistent: % 135.48/19.96 ---------------------------------------------------------------- % 135.48/19.96 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 135.48/19.96 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 135.48/19.96 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) | % 135.48/19.96 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 135.48/19.96 (3) all_57_5 = e1 % 135.48/19.96 (4) ~ (e2 = e0) % 135.48/19.96 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.48/19.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.48/19.96 (6) ~ (e2 = e1) % 135.48/19.96 (7) ~ (e3 = e0) % 135.48/19.96 (8) all_57_8 = e2 % 135.48/19.96 (9) all_57_4 = e3 % 135.48/19.96 (10) op(e3, e1) = all_52_8 % 135.48/19.96 (11) ~ (e3 = e1) % 135.48/19.96 (12) ~ (e1 = e0) % 135.48/19.96 (13) all_57_14 = e1 % 135.48/19.96 (14) op(e3, e1) = e3 % 135.48/19.96 % 135.48/19.96 Begin of proof % 135.48/19.96 | % 135.48/19.96 | BETA: splitting (2) gives: % 135.48/19.96 | % 135.48/19.96 | Case 1: % 135.48/19.96 | | % 135.48/19.96 | | (15) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = % 135.48/19.96 | | e0) % 135.48/19.96 | | % 135.48/19.96 | | BETA: splitting (15) gives: % 135.48/19.96 | | % 135.48/19.96 | | Case 1: % 135.48/19.96 | | | % 135.48/19.96 | | | (16) all_57_4 = e0 & op(e3, e1) = e0 % 135.48/19.96 | | | % 135.48/19.96 | | | ALPHA: (16) implies: % 135.48/19.96 | | | (17) op(e3, e1) = e0 % 135.48/19.96 | | | % 135.48/19.96 | | | REF_CLOSE: (5), (7), (10), (14), (17) are inconsistent by sub-proof #600. % 135.48/19.96 | | | % 135.48/19.96 | | Case 2: % 135.48/19.96 | | | % 135.48/19.96 | | | (18) all_57_5 = e0 & op(e2, e1) = e0 % 135.48/19.96 | | | % 135.48/19.96 | | | ALPHA: (18) implies: % 135.48/19.96 | | | (19) all_57_5 = e0 % 135.48/19.96 | | | % 135.48/19.96 | | | COMBINE_EQS: (3), (19) imply: % 135.48/19.96 | | | (20) e1 = e0 % 135.48/19.96 | | | % 135.48/19.96 | | | COMBINE_EQS: (13), (20) imply: % 135.48/19.96 | | | (21) all_57_14 = e0 % 135.48/19.96 | | | % 135.48/19.96 | | | REF_CLOSE: (1), (6), (8), (9), (11), (12), (19), (21) are inconsistent by % 135.48/19.96 | | | sub-proof #84. % 135.48/19.96 | | | % 135.48/19.96 | | End of split % 135.48/19.96 | | % 135.48/19.96 | Case 2: % 135.48/19.96 | | % 135.48/19.96 | | (22) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = % 135.48/19.96 | | e0) % 135.48/19.96 | | % 135.48/19.96 | | BETA: splitting (22) gives: % 135.48/19.96 | | % 135.48/19.96 | | Case 1: % 135.48/19.96 | | | % 135.48/19.96 | | | (23) all_57_8 = e0 & op(e1, e1) = e0 % 135.48/19.96 | | | % 135.48/19.96 | | | REF_CLOSE: (4), (8), (23) are inconsistent by sub-proof #83. % 135.48/19.96 | | | % 135.48/19.96 | | Case 2: % 135.48/19.96 | | | % 135.48/19.96 | | | (24) all_57_14 = e0 & op(e0, e1) = e0 % 135.48/19.96 | | | % 135.48/19.96 | | | ALPHA: (24) implies: % 135.48/19.97 | | | (25) all_57_14 = e0 % 135.48/19.97 | | | % 135.48/19.97 | | | COMBINE_EQS: (13), (25) imply: % 135.48/19.97 | | | (26) e1 = e0 % 135.48/19.97 | | | % 135.48/19.97 | | | SIMP: (26) implies: % 135.48/19.97 | | | (27) e1 = e0 % 135.48/19.97 | | | % 135.48/19.97 | | | COMBINE_EQS: (3), (27) imply: % 135.48/19.97 | | | (28) all_57_5 = e0 % 135.48/19.97 | | | % 135.48/19.97 | | | REF_CLOSE: (1), (6), (8), (9), (11), (12), (25), (28) are inconsistent by % 135.48/19.97 | | | sub-proof #84. % 135.48/19.97 | | | % 135.48/19.97 | | End of split % 135.48/19.97 | | % 135.48/19.97 | End of split % 135.48/19.97 | % 135.80/19.97 End of proof % 135.80/19.97 % 135.80/19.97 Sub-proof #83 shows that the following formulas are inconsistent: % 135.80/19.97 ---------------------------------------------------------------- % 135.80/19.97 (1) all_57_8 = e0 & op(e1, e1) = e0 % 135.80/19.97 (2) all_57_8 = e2 % 135.80/19.97 (3) ~ (e2 = e0) % 135.80/19.97 % 135.80/19.97 Begin of proof % 135.80/19.97 | % 135.80/19.97 | ALPHA: (1) implies: % 135.80/19.97 | (4) all_57_8 = e0 % 135.80/19.97 | % 135.80/19.97 | COMBINE_EQS: (2), (4) imply: % 135.80/19.97 | (5) e2 = e0 % 135.80/19.97 | % 135.80/19.97 | REDUCE: (3), (5) imply: % 135.80/19.97 | (6) $false % 135.80/19.97 | % 135.80/19.97 | CLOSE: (6) is inconsistent. % 135.80/19.97 | % 135.80/19.97 End of proof % 135.80/19.97 % 135.80/19.97 Sub-proof #84 shows that the following formulas are inconsistent: % 135.80/19.97 ---------------------------------------------------------------- % 135.80/19.97 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 135.80/19.97 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 135.80/19.97 (2) ~ (e2 = e1) % 135.80/19.97 (3) all_57_8 = e2 % 135.80/19.97 (4) all_57_14 = e0 % 135.80/19.97 (5) all_57_4 = e3 % 135.80/19.97 (6) ~ (e3 = e1) % 135.80/19.97 (7) ~ (e1 = e0) % 135.80/19.97 (8) all_57_5 = e0 % 135.80/19.97 % 135.80/19.97 Begin of proof % 135.80/19.97 | % 135.80/19.97 | BETA: splitting (1) gives: % 135.80/19.97 | % 135.80/19.97 | Case 1: % 135.80/19.97 | | % 135.80/19.97 | | (9) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) % 135.80/19.97 | | % 135.80/19.97 | | BETA: splitting (9) gives: % 135.80/19.97 | | % 135.80/19.97 | | Case 1: % 135.80/19.97 | | | % 135.80/19.97 | | | (10) all_57_4 = e1 & op(e3, e1) = e1 % 135.80/19.97 | | | % 135.80/19.97 | | | ALPHA: (10) implies: % 135.80/19.97 | | | (11) all_57_4 = e1 % 135.80/19.97 | | | % 135.80/19.97 | | | REF_CLOSE: (5), (6), (11) are inconsistent by sub-proof #671. % 135.80/19.97 | | | % 135.80/19.97 | | Case 2: % 135.80/19.97 | | | % 135.80/19.97 | | | (12) all_57_5 = e1 & op(e2, e1) = e1 % 135.80/19.97 | | | % 135.80/19.97 | | | ALPHA: (12) implies: % 135.80/19.97 | | | (13) all_57_5 = e1 % 135.80/19.97 | | | % 135.80/19.97 | | | COMBINE_EQS: (8), (13) imply: % 135.80/19.97 | | | (14) e1 = e0 % 135.80/19.97 | | | % 135.80/19.97 | | | SIMP: (14) implies: % 135.80/19.97 | | | (15) e1 = e0 % 135.80/19.97 | | | % 135.80/19.97 | | | REDUCE: (7), (15) imply: % 135.80/19.97 | | | (16) $false % 135.80/19.97 | | | % 135.80/19.97 | | | CLOSE: (16) is inconsistent. % 135.80/19.97 | | | % 135.80/19.97 | | End of split % 135.80/19.97 | | % 135.80/19.97 | Case 2: % 135.80/19.97 | | % 135.80/19.97 | | (17) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = % 135.80/19.97 | | e1) % 135.80/19.97 | | % 135.80/19.97 | | BETA: splitting (17) gives: % 135.80/19.97 | | % 135.80/19.97 | | Case 1: % 135.80/19.97 | | | % 135.80/19.97 | | | (18) all_57_8 = e1 & op(e1, e1) = e1 % 135.80/19.97 | | | % 135.80/19.97 | | | REF_CLOSE: (2), (3), (18) are inconsistent by sub-proof #85. % 135.80/19.97 | | | % 135.80/19.97 | | Case 2: % 135.80/19.97 | | | % 135.80/19.97 | | | (19) all_57_14 = e1 & op(e0, e1) = e1 % 135.80/19.97 | | | % 135.80/19.97 | | | REF_CLOSE: (4), (7), (19) are inconsistent by sub-proof #231. % 135.80/19.97 | | | % 135.80/19.97 | | End of split % 135.80/19.97 | | % 135.80/19.97 | End of split % 135.80/19.97 | % 135.80/19.97 End of proof % 135.80/19.97 % 135.80/19.97 Sub-proof #85 shows that the following formulas are inconsistent: % 135.80/19.97 ---------------------------------------------------------------- % 135.80/19.97 (1) all_57_8 = e1 & op(e1, e1) = e1 % 135.80/19.97 (2) all_57_8 = e2 % 135.80/19.97 (3) ~ (e2 = e1) % 135.80/19.97 % 135.80/19.97 Begin of proof % 135.80/19.97 | % 135.80/19.97 | ALPHA: (1) implies: % 135.80/19.97 | (4) all_57_8 = e1 % 135.80/19.97 | % 135.80/19.97 | COMBINE_EQS: (2), (4) imply: % 135.80/19.97 | (5) e2 = e1 % 135.80/19.97 | % 135.80/19.97 | SIMP: (5) implies: % 135.80/19.97 | (6) e2 = e1 % 135.80/19.97 | % 135.80/19.97 | REDUCE: (3), (6) imply: % 135.80/19.97 | (7) $false % 135.80/19.97 | % 135.80/19.97 | CLOSE: (7) is inconsistent. % 135.80/19.97 | % 135.80/19.97 End of proof % 135.80/19.97 % 135.80/19.97 Sub-proof #86 shows that the following formulas are inconsistent: % 135.80/19.97 ---------------------------------------------------------------- % 135.80/19.97 (1) ~ (e2 = e0) % 135.80/19.97 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.80/19.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.80/19.97 (3) op(e1, e1) = e2 % 135.80/19.97 (4) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.80/19.97 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.80/19.97 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.80/19.97 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.80/19.97 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.80/19.97 e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.80/19.97 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.80/19.97 = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.80/19.97 $i(all_56_21) & $i(all_56_29)) % 135.80/19.97 (5) ~ (all_4_2 = e1) % 135.80/19.97 (6) all_56_31 = all_4_2 % 135.80/19.97 % 135.80/19.97 Begin of proof % 135.80/19.97 | % 135.80/19.97 | BETA: splitting (4) gives: % 135.80/19.97 | % 135.80/19.97 | Case 1: % 135.80/19.97 | | % 135.80/19.97 | | (7) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 % 135.80/19.97 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 % 135.80/19.97 | | & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.80/19.97 | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) % 135.80/19.97 | | % 135.80/19.97 | | ALPHA: (7) implies: % 135.80/19.97 | | (8) op(e1, e1) = e0 % 135.80/19.97 | | % 135.80/19.97 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #98. % 135.80/19.97 | | % 135.80/19.97 | Case 2: % 135.80/19.97 | | % 135.80/19.97 | | (9) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.80/19.97 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.80/19.97 | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 135.80/19.97 | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.80/19.97 | | $i(all_56_21) & $i(all_56_29) % 135.80/19.97 | | % 135.80/19.97 | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #745. % 135.80/19.97 | | % 135.80/19.97 | End of split % 135.80/19.97 | % 135.80/19.97 End of proof % 135.80/19.97 % 135.80/19.97 Sub-proof #87 shows that the following formulas are inconsistent: % 135.80/19.97 ---------------------------------------------------------------- % 135.80/19.97 (1) op(e2, e2) = e0 % 135.80/19.97 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.80/19.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.80/19.97 (3) ~ (e2 = e1) % 135.80/19.97 (4) all_57_5 = e3 & op(e2, e1) = e3 % 135.80/19.97 (5) all_57_2 = e3 % 135.80/19.97 (6) ~ (e3 = e1) % 135.80/19.97 (7) ~ (e1 = e0) % 135.80/19.97 (8) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 135.80/19.97 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 135.80/19.97 (9) all_57_10 = e2 % 135.80/19.97 % 135.80/19.97 Begin of proof % 135.80/19.97 | % 135.80/19.97 | ALPHA: (4) implies: % 135.80/19.97 | (10) all_57_5 = e3 % 135.80/19.97 | % 135.80/19.97 | BETA: splitting (8) gives: % 135.80/19.97 | % 135.80/19.97 | Case 1: % 135.80/19.97 | | % 135.80/19.97 | | (11) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = % 135.80/19.97 | | e1) % 135.80/19.97 | | % 135.80/19.97 | | BETA: splitting (11) gives: % 135.80/19.97 | | % 135.80/19.97 | | Case 1: % 135.80/19.97 | | | % 135.80/19.97 | | | (12) all_57_2 = e1 & op(e2, e3) = e1 % 135.80/19.97 | | | % 135.80/19.97 | | | REF_CLOSE: (5), (6), (12) are inconsistent by sub-proof #371. % 135.80/19.97 | | | % 135.80/19.97 | | Case 2: % 135.80/19.97 | | | % 135.80/19.97 | | | (13) all_57_3 = e1 & op(e2, e2) = e1 % 135.80/19.97 | | | % 135.80/19.97 | | | ALPHA: (13) implies: % 135.80/19.97 | | | (14) op(e2, e2) = e1 % 135.80/19.97 | | | % 135.80/19.97 | | | REF_CLOSE: (1), (2), (7), (14) are inconsistent by sub-proof #675. % 135.80/19.97 | | | % 135.80/19.97 | | End of split % 135.80/19.97 | | % 135.80/19.97 | Case 2: % 135.80/19.97 | | % 135.80/19.97 | | (15) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = % 135.80/19.97 | | e1) % 135.80/19.97 | | % 135.80/19.97 | | BETA: splitting (15) gives: % 135.80/19.97 | | % 135.80/19.97 | | Case 1: % 135.80/19.97 | | | % 135.80/19.97 | | | (16) all_57_5 = e1 & op(e2, e1) = e1 % 135.80/19.97 | | | % 135.80/19.97 | | | ALPHA: (16) implies: % 135.80/19.97 | | | (17) all_57_5 = e1 % 135.80/19.97 | | | % 135.80/19.97 | | | REF_CLOSE: (6), (10), (17) are inconsistent by sub-proof #88. % 135.80/19.97 | | | % 135.80/19.97 | | Case 2: % 135.80/19.97 | | | % 135.80/19.97 | | | (18) all_57_10 = e1 & op(e2, e0) = e1 % 135.80/19.97 | | | % 135.80/19.97 | | | ALPHA: (18) implies: % 135.80/19.97 | | | (19) all_57_10 = e1 % 135.80/19.97 | | | % 135.80/19.97 | | | REF_CLOSE: (3), (9), (19) are inconsistent by sub-proof #414. % 135.80/19.97 | | | % 135.80/19.97 | | End of split % 135.80/19.97 | | % 135.80/19.97 | End of split % 135.80/19.97 | % 135.80/19.97 End of proof % 135.80/19.97 % 135.80/19.97 Sub-proof #88 shows that the following formulas are inconsistent: % 135.80/19.97 ---------------------------------------------------------------- % 135.80/19.97 (1) all_57_5 = e3 % 135.80/19.97 (2) all_57_5 = e1 % 135.80/19.97 (3) ~ (e3 = e1) % 135.80/19.97 % 135.80/19.97 Begin of proof % 135.80/19.97 | % 135.80/19.97 | COMBINE_EQS: (1), (2) imply: % 135.80/19.97 | (4) e3 = e1 % 135.80/19.97 | % 135.80/19.97 | SIMP: (4) implies: % 135.80/19.97 | (5) e3 = e1 % 135.80/19.97 | % 135.80/19.97 | REDUCE: (3), (5) imply: % 135.80/19.97 | (6) $false % 135.80/19.97 | % 135.80/19.97 | CLOSE: (6) is inconsistent. % 135.80/19.97 | % 135.80/19.97 End of proof % 135.80/19.97 % 135.80/19.97 Sub-proof #89 shows that the following formulas are inconsistent: % 135.80/19.97 ---------------------------------------------------------------- % 135.80/19.97 (1) op(e3, e3) = e2 % 135.80/19.97 (2) ~ (e2 = e0) % 135.80/19.97 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.80/19.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.80/19.97 (4) ~ (all_52_1 = e0) % 135.80/19.97 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) % 135.80/19.97 (6) op(e2, e3) = all_52_1 % 135.80/19.97 % 135.80/19.97 Begin of proof % 135.80/19.97 | % 135.80/19.97 | BETA: splitting (5) gives: % 135.80/19.97 | % 135.80/19.97 | Case 1: % 135.80/19.97 | | % 135.80/19.97 | | (7) all_57_0 = e0 & op(e3, e3) = e0 % 135.80/19.97 | | % 135.80/19.97 | | ALPHA: (7) implies: % 135.80/19.97 | | (8) op(e3, e3) = e0 % 135.80/19.97 | | % 135.80/19.97 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #495. % 135.80/19.97 | | % 135.80/19.97 | Case 2: % 135.80/19.97 | | % 135.80/19.97 | | (9) all_57_2 = e0 & op(e2, e3) = e0 % 135.80/19.97 | | % 135.80/19.97 | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #225. % 135.80/19.97 | | % 135.80/19.97 | End of split % 135.80/19.97 | % 135.80/19.97 End of proof % 135.80/19.97 % 135.80/19.97 Sub-proof #90 shows that the following formulas are inconsistent: % 135.80/19.97 ---------------------------------------------------------------- % 135.80/19.97 (1) ( ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 & $i(all_20_0)) | ( ~ % 135.80/19.97 (all_20_1 = e1) & op(e2, e2) = all_20_1 & $i(all_20_1)) % 135.80/19.97 (2) op(e2, e2) = e0 % 135.80/19.97 (3) op(e2, e0) = all_52_13 % 135.80/19.97 (4) ~ (all_52_8 = all_52_9) % 135.80/19.97 (5) ~ (e2 = e0) % 135.80/19.97 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.80/19.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.80/19.97 (7) ~ (e2 = e1) % 135.80/19.97 (8) ~ (e3 = e0) % 135.80/19.97 (9) ~ (e3 = e2) % 135.80/19.97 (10) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 135.80/19.97 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 135.80/19.97 (11) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 135.80/19.97 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) % 135.80/19.97 (12) op(e1, e1) = e2 % 135.80/19.97 (13) ~ (all_10_2 = e0) % 135.80/19.97 (14) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 135.80/19.97 (15) all_57_2 = e2 % 135.80/19.97 (16) ~ (all_52_9 = e2) % 135.80/19.97 (17) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.80/19.97 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.80/19.97 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.80/19.97 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.80/19.97 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 135.80/19.97 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.80/19.97 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) % 135.80/19.97 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.80/19.97 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.80/19.97 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 135.80/19.97 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.80/19.97 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 135.80/19.97 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 135.80/19.97 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.80/19.97 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) % 135.80/19.97 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 135.80/19.97 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 135.80/19.97 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 135.80/19.97 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.80/19.97 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.80/19.97 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.80/19.97 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 135.80/19.97 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & % 135.80/19.97 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & % 135.80/19.97 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.80/19.97 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.80/19.97 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.80/19.97 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.80/19.97 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ % 135.80/19.97 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.80/19.97 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 135.80/19.97 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 135.80/19.97 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.80/19.97 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) % 135.80/19.97 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.80/19.97 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.80/19.97 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 % 135.80/19.97 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.80/19.97 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = % 135.80/19.97 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.80/19.97 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 135.80/19.97 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.80/19.97 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.80/19.97 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 135.80/19.97 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.80/19.97 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.80/19.97 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.80/19.97 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.80/19.97 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.80/19.97 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.80/19.97 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.80/19.97 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.80/19.97 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.80/19.97 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.80/19.97 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.80/19.97 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.80/19.97 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.80/19.97 $i(all_56_29)))) % 135.80/19.97 (18) op(e3, e3) = all_10_2 % 135.80/19.97 (19) op(e2, e1) = all_52_9 % 135.80/19.97 (20) ~ (all_52_8 = e2) % 135.80/19.97 (21) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 135.80/19.97 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 135.80/19.97 (22) all_32_2 = all_10_2 % 135.80/19.97 (23) all_54_6 = all_52_9 % 135.80/19.97 (24) op(e0, e0) = e2 % 135.80/19.97 (25) ~ (all_10_2 = e2) % 135.80/19.97 (26) ~ (all_32_2 = e1) | ( ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 & % 135.80/19.97 $i(all_32_0)) | ( ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 & % 135.80/19.97 $i(all_32_1)) % 135.80/19.97 (27) ( ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 & $i(all_18_0)) | ( ~ % 135.80/19.97 (all_18_1 = e0) & op(e2, e2) = all_18_1 & $i(all_18_1)) % 135.80/19.97 (28) op(e3, e1) = all_52_8 % 135.80/19.97 (29) ~ (all_52_9 = e0) % 135.80/19.97 (30) ~ (e3 = e1) % 135.80/19.97 (31) ~ (e1 = e0) % 135.80/19.97 (32) op(e2, e3) = e2 % 135.80/19.97 (33) ~ (all_52_9 = all_52_13) % 135.80/19.97 (34) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 135.80/19.97 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 135.80/19.97 (35) op(e3, e2) = e2 % 135.80/19.97 % 135.80/19.97 Begin of proof % 135.80/19.97 | % 135.80/19.97 | BETA: splitting (27) gives: % 135.80/19.97 | % 135.80/19.97 | Case 1: % 135.80/19.97 | | % 135.80/19.97 | | (36) ~ (all_18_0 = e3) & op(e2, e1) = all_18_0 & $i(all_18_0) % 135.80/19.97 | | % 135.80/19.97 | | ALPHA: (36) implies: % 135.80/19.97 | | (37) ~ (all_18_0 = e3) % 135.80/19.97 | | (38) op(e2, e1) = all_18_0 % 135.80/19.97 | | % 135.80/19.97 | | GROUND_INST: instantiating (6) with all_52_9, all_18_0, e1, e2, simplifying % 135.80/19.97 | | with (19), (38) gives: % 135.80/19.97 | | (39) all_52_9 = all_18_0 % 135.80/19.97 | | % 135.80/19.97 | | COMBINE_EQS: (23), (39) imply: % 135.80/19.97 | | (40) all_54_6 = all_18_0 % 135.80/19.97 | | % 135.80/19.97 | | REDUCE: (4), (39) imply: % 135.80/19.97 | | (41) ~ (all_52_8 = all_18_0) % 135.80/19.97 | | % 135.80/19.97 | | REDUCE: (33), (39) imply: % 135.80/19.97 | | (42) ~ (all_52_13 = all_18_0) % 135.80/19.97 | | % 135.80/19.97 | | SIMP: (42) implies: % 135.80/19.97 | | (43) ~ (all_52_13 = all_18_0) % 135.80/19.97 | | % 135.80/19.97 | | REDUCE: (16), (39) imply: % 135.80/19.97 | | (44) ~ (all_18_0 = e2) % 135.80/19.97 | | % 135.80/19.97 | | REDUCE: (29), (39) imply: % 135.80/19.97 | | (45) ~ (all_18_0 = e0) % 135.80/19.97 | | % 135.80/19.97 | | BETA: splitting (14) gives: % 135.80/19.97 | | % 135.80/19.97 | | Case 1: % 135.80/19.97 | | | % 135.80/19.97 | | | (46) all_54_6 = e3 % 135.80/19.97 | | | % 135.80/19.97 | | | COMBINE_EQS: (40), (46) imply: % 135.80/19.97 | | | (47) all_18_0 = e3 % 135.80/19.97 | | | % 135.80/19.97 | | | SIMP: (47) implies: % 135.80/19.97 | | | (48) all_18_0 = e3 % 135.80/19.97 | | | % 135.80/19.97 | | | REDUCE: (37), (48) imply: % 135.80/19.97 | | | (49) $false % 135.80/19.97 | | | % 135.80/19.97 | | | CLOSE: (49) is inconsistent. % 135.80/19.97 | | | % 135.80/19.97 | | Case 2: % 135.80/19.97 | | | % 135.80/19.97 | | | (50) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 135.80/19.97 | | | % 135.80/19.97 | | | BETA: splitting (50) gives: % 135.80/19.97 | | | % 135.80/19.97 | | | Case 1: % 135.80/19.97 | | | | % 135.80/19.97 | | | | (51) all_54_6 = e2 % 135.80/19.97 | | | | % 135.80/19.97 | | | | COMBINE_EQS: (40), (51) imply: % 135.80/19.97 | | | | (52) all_18_0 = e2 % 135.80/19.97 | | | | % 135.80/19.97 | | | | SIMP: (52) implies: % 135.80/19.97 | | | | (53) all_18_0 = e2 % 135.80/19.97 | | | | % 135.80/19.97 | | | | REDUCE: (44), (53) imply: % 135.80/19.97 | | | | (54) $false % 135.80/19.97 | | | | % 135.80/19.97 | | | | CLOSE: (54) is inconsistent. % 135.80/19.97 | | | | % 135.80/19.97 | | | Case 2: % 135.80/19.97 | | | | % 135.80/19.97 | | | | (55) ~ (all_54_6 = e2) % 135.80/19.97 | | | | (56) all_54_6 = e1 | all_54_6 = e0 % 135.80/19.97 | | | | % 135.80/19.97 | | | | BETA: splitting (11) gives: % 135.80/19.97 | | | | % 135.80/19.97 | | | | Case 1: % 135.80/19.97 | | | | | % 135.80/19.97 | | | | | (57) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, % 135.80/19.97 | | | | | e2) = e3) % 135.80/19.97 | | | | | % 135.80/19.97 | | | | | REF_CLOSE: (2), (6), (8), (9), (15), (57) are inconsistent by % 135.80/19.97 | | | | | sub-proof #94. % 135.80/19.97 | | | | | % 135.80/19.97 | | | | Case 2: % 135.80/19.97 | | | | | % 135.80/19.97 | | | | | (58) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, % 135.80/19.97 | | | | | e0) = e3) % 135.80/19.97 | | | | | % 135.80/19.97 | | | | | BETA: splitting (58) gives: % 135.80/19.97 | | | | | % 135.80/19.97 | | | | | Case 1: % 135.80/19.97 | | | | | | % 135.80/19.97 | | | | | | (59) all_57_5 = e3 & op(e2, e1) = e3 % 135.80/19.97 | | | | | | % 135.80/19.97 | | | | | | ALPHA: (59) implies: % 135.80/19.97 | | | | | | (60) all_57_5 = e3 % 135.80/19.97 | | | | | | % 135.80/19.97 | | | | | | BETA: splitting (34) gives: % 135.80/19.97 | | | | | | % 135.80/19.97 | | | | | | Case 1: % 135.80/19.97 | | | | | | | % 135.80/19.97 | | | | | | | (61) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & % 135.80/19.97 | | | | | | | op(e2, e2) = e1) % 135.80/19.97 | | | | | | | % 135.80/19.97 | | | | | | | REF_CLOSE: (2), (6), (7), (31), (32), (61) are inconsistent by % 135.80/19.97 | | | | | | | sub-proof #93. % 135.80/19.97 | | | | | | | % 135.80/19.97 | | | | | | Case 2: % 135.80/19.97 | | | | | | | % 135.80/19.97 | | | | | | | (62) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & % 135.80/19.97 | | | | | | | op(e2, e0) = e1) % 135.80/19.97 | | | | | | | % 135.80/19.97 | | | | | | | BETA: splitting (62) gives: % 135.80/19.97 | | | | | | | % 135.80/19.97 | | | | | | | Case 1: % 135.80/19.97 | | | | | | | | % 135.80/19.97 | | | | | | | | (63) all_57_5 = e1 & op(e2, e1) = e1 % 135.80/19.97 | | | | | | | | % 135.80/19.97 | | | | | | | | REF_CLOSE: (30), (60), (63) are inconsistent by sub-proof #673. % 135.80/19.97 | | | | | | | | % 135.80/19.97 | | | | | | | Case 2: % 135.80/19.97 | | | | | | | | % 135.80/19.97 | | | | | | | | (64) all_57_10 = e1 & op(e2, e0) = e1 % 135.80/19.97 | | | | | | | | % 135.80/19.97 | | | | | | | | ALPHA: (64) implies: % 135.80/19.97 | | | | | | | | (65) op(e2, e0) = e1 % 135.80/19.97 | | | | | | | | % 135.80/19.97 | | | | | | | | BETA: splitting (56) gives: % 135.80/19.97 | | | | | | | | % 135.80/19.97 | | | | | | | | Case 1: % 135.80/19.97 | | | | | | | | | % 135.80/19.97 | | | | | | | | | (66) all_54_6 = e1 % 135.80/19.97 | | | | | | | | | % 135.80/19.97 | | | | | | | | | COMBINE_EQS: (40), (66) imply: % 135.80/19.97 | | | | | | | | | (67) all_18_0 = e1 % 135.80/19.97 | | | | | | | | | % 135.80/19.97 | | | | | | | | | SIMP: (67) implies: % 135.80/19.97 | | | | | | | | | (68) all_18_0 = e1 % 135.80/19.97 | | | | | | | | | % 135.80/19.97 | | | | | | | | | REDUCE: (43), (68) imply: % 135.80/19.97 | | | | | | | | | (69) ~ (all_52_13 = e1) % 135.80/19.97 | | | | | | | | | % 135.80/19.97 | | | | | | | | | REF_CLOSE: (3), (6), (65), (69) are inconsistent by sub-proof % 135.80/19.97 | | | | | | | | | #180. % 135.80/19.97 | | | | | | | | | % 135.80/19.97 | | | | | | | | Case 2: % 135.80/19.97 | | | | | | | | | % 135.80/19.97 | | | | | | | | | (70) all_54_6 = e0 % 135.80/19.97 | | | | | | | | | % 135.80/19.97 | | | | | | | | | REF_CLOSE: (40), (45), (70) are inconsistent by sub-proof #92. % 135.80/19.97 | | | | | | | | | % 135.80/19.97 | | | | | | | | End of split % 135.80/19.97 | | | | | | | | % 135.80/19.97 | | | | | | | End of split % 135.80/19.97 | | | | | | | % 135.80/19.97 | | | | | | End of split % 135.80/19.97 | | | | | | % 135.80/19.97 | | | | | Case 2: % 135.80/19.97 | | | | | | % 135.80/19.97 | | | | | | (71) all_57_10 = e3 & op(e2, e0) = e3 % 135.80/19.97 | | | | | | % 135.80/19.97 | | | | | | ALPHA: (71) implies: % 135.80/19.97 | | | | | | (72) op(e2, e0) = e3 % 135.80/19.97 | | | | | | % 135.80/19.97 | | | | | | BETA: splitting (56) gives: % 135.80/19.97 | | | | | | % 135.80/19.97 | | | | | | Case 1: % 135.80/19.97 | | | | | | | % 135.80/19.97 | | | | | | | (73) all_54_6 = e1 % 135.80/19.97 | | | | | | | % 135.80/19.97 | | | | | | | COMBINE_EQS: (40), (73) imply: % 135.80/19.97 | | | | | | | (74) all_18_0 = e1 % 135.80/19.97 | | | | | | | % 135.80/19.97 | | | | | | | SIMP: (74) implies: % 135.80/19.97 | | | | | | | (75) all_18_0 = e1 % 135.80/19.97 | | | | | | | % 135.80/19.97 | | | | | | | REDUCE: (41), (75) imply: % 135.80/19.97 | | | | | | | (76) ~ (all_52_8 = e1) % 135.80/19.97 | | | | | | | % 135.80/19.97 | | | | | | | REDUCE: (44), (75) imply: % 135.80/19.97 | | | | | | | (77) ~ (e2 = e1) % 135.80/19.97 | | | | | | | % 135.80/19.97 | | | | | | | REDUCE: (38), (75) imply: % 135.80/19.97 | | | | | | | (78) op(e2, e1) = e1 % 135.80/19.97 | | | | | | | % 135.80/19.97 | | | | | | | BETA: splitting (17) gives: % 135.80/19.97 | | | | | | | % 135.80/19.97 | | | | | | | Case 1: % 135.80/19.97 | | | | | | | | % 135.80/19.97 | | | | | | | | (79) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ % 135.80/19.97 | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.80/19.97 | | | | | | | | = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, % 135.80/19.97 | | | | | | | | e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) % 135.80/19.97 | | | | | | | | = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.80/19.97 | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.80/19.97 | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & % 135.80/19.97 | | | | | | | | ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.80/19.97 | | | | | | | | (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & % 135.80/19.97 | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.80/19.97 | | | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.80/19.97 | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.80/19.97 | | | | | | | | $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 135.80/19.97 | | | | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 % 135.80/19.97 | | | | | | | | = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.80/19.97 | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.80/19.97 | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.80/19.97 | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.80/19.97 | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 135.80/19.98 | | | | | | | | all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.80/19.98 | | | | | | | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 135.80/19.98 | | | | | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.80/19.98 | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e2, % 135.80/19.98 | | | | | | | | e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & % 135.80/19.98 | | | | | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 135.80/19.98 | | | | | | | | % 135.80/19.98 | | | | | | | | BETA: splitting (79) gives: % 135.80/19.98 | | | | | | | | % 135.80/19.98 | | | | | | | | Case 1: % 135.80/19.98 | | | | | | | | | % 135.80/19.98 | | | | | | | | | (80) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & % 135.80/19.98 | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.80/19.98 | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 % 135.80/19.98 | | | | | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.80/19.98 | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.80/19.98 | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.80/19.98 | | | | | | | | | $i(all_56_27)) | (all_56_1 = e1 & all_56_17 = e3 & % 135.80/19.98 | | | | | | | | | ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.80/19.98 | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) % 135.80/19.98 | | | | | | | | | = e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & % 135.80/19.98 | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.80/19.98 | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.80/19.98 | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.80/19.98 | | | | | | | | | % 135.80/19.98 | | | | | | | | | BETA: splitting (80) gives: % 135.80/19.98 | | | | | | | | | % 135.80/19.98 | | | | | | | | | Case 1: % 135.80/19.98 | | | | | | | | | | % 135.80/19.98 | | | | | | | | | | (81) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & % 135.80/19.98 | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.80/19.98 | | | | | | | | | | (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, e2) = e3 % 135.80/19.98 | | | | | | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.80/19.98 | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.80/19.98 | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.80/19.98 | | | | | | | | | | $i(all_56_27) % 135.80/19.98 | | | | | | | | | | % 135.80/19.98 | | | | | | | | | | ALPHA: (81) implies: % 135.80/19.98 | | | | | | | | | | (82) op(e3, e3) = e2 % 135.80/19.98 | | | | | | | | | | % 135.80/19.98 | | | | | | | | | | REF_CLOSE: (6), (18), (25), (82) are inconsistent by % 135.80/19.98 | | | | | | | | | | sub-proof #536. % 135.80/19.98 | | | | | | | | | | % 135.80/19.98 | | | | | | | | | Case 2: % 135.80/19.98 | | | | | | | | | | % 135.80/19.98 | | | | | | | | | | (83) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) % 135.80/19.98 | | | | | | | | | | & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.80/19.98 | | | | | | | | | | (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 % 135.80/19.98 | | | | | | | | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.80/19.98 | | | | | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.80/19.98 | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.80/19.98 | | | | | | | | | | $i(all_56_29) % 135.80/19.98 | | | | | | | | | | % 135.80/19.98 | | | | | | | | | | ALPHA: (83) implies: % 135.80/19.98 | | | | | | | | | | (84) ~ (all_56_5 = e3) % 135.84/19.98 | | | | | | | | | | (85) op(e1, e1) = all_56_21 % 135.84/19.98 | | | | | | | | | | (86) op(e1, e3) = all_56_5 % 135.84/19.98 | | | | | | | | | | (87) op(e3, e1) = e3 % 135.84/19.98 | | | | | | | | | | (88) op(e3, e3) = e1 % 135.84/19.98 | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | BETA: splitting (1) gives: % 135.84/19.98 | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | Case 1: % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | (89) ~ (all_20_0 = e3) & op(e2, e0) = all_20_0 & % 135.84/19.98 | | | | | | | | | | | $i(all_20_0) % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | ALPHA: (89) implies: % 135.84/19.98 | | | | | | | | | | | (90) ~ (all_20_0 = e3) % 135.84/19.98 | | | | | | | | | | | (91) op(e2, e0) = all_20_0 % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | GROUND_INST: instantiating (6) with e3, all_20_0, e0, e2, % 135.84/19.98 | | | | | | | | | | | simplifying with (72), (91) gives: % 135.84/19.98 | | | | | | | | | | | (92) all_20_0 = e3 % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | REDUCE: (90), (92) imply: % 135.84/19.98 | | | | | | | | | | | (93) $false % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | CLOSE: (93) is inconsistent. % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | Case 2: % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | GROUND_INST: instantiating (6) with e2, all_56_21, e1, e1, % 135.84/19.98 | | | | | | | | | | | simplifying with (12), (85) gives: % 135.84/19.98 | | | | | | | | | | | (94) all_56_21 = e2 % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | GROUND_INST: instantiating (6) with all_52_8, e3, e1, e3, % 135.84/19.98 | | | | | | | | | | | simplifying with (28), (87) gives: % 135.84/19.98 | | | | | | | | | | | (95) all_52_8 = e3 % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | GROUND_INST: instantiating (6) with all_10_2, e1, e3, e3, % 135.84/19.98 | | | | | | | | | | | simplifying with (18), (88) gives: % 135.84/19.98 | | | | | | | | | | | (96) all_10_2 = e1 % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | COMBINE_EQS: (22), (96) imply: % 135.84/19.98 | | | | | | | | | | | (97) all_32_2 = e1 % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | BETA: splitting (26) gives: % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | Case 1: % 135.84/19.98 | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | (98) ~ (all_32_2 = e1) % 135.84/19.98 | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | REDUCE: (97), (98) imply: % 135.84/19.98 | | | | | | | | | | | | (99) $false % 135.84/19.98 | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | CLOSE: (99) is inconsistent. % 135.84/19.98 | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | Case 2: % 135.84/19.98 | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | (100) ( ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 & % 135.84/19.98 | | | | | | | | | | | | $i(all_32_0)) | ( ~ (all_32_1 = e2) & op(e1, e1) % 135.84/19.98 | | | | | | | | | | | | = all_32_1 & $i(all_32_1)) % 135.84/19.98 | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | BETA: splitting (100) gives: % 135.84/19.98 | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | Case 1: % 135.84/19.98 | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | (101) ~ (all_32_0 = e0) & op(e1, e3) = all_32_0 & % 135.84/19.98 | | | | | | | | | | | | | $i(all_32_0) % 135.84/19.98 | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | ALPHA: (101) implies: % 135.84/19.98 | | | | | | | | | | | | | (102) ~ (all_32_0 = e0) % 135.84/19.98 | | | | | | | | | | | | | (103) op(e1, e3) = all_32_0 % 135.84/19.98 | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | BETA: splitting (21) gives: % 135.84/19.98 | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | Case 1: % 135.84/19.98 | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | (104) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 135.84/19.98 | | | | | | | | | | | | | | & op(e2, e3) = e0) % 135.84/19.98 | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | BETA: splitting (104) gives: % 135.84/19.98 | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | Case 1: % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | | (105) all_57_0 = e0 & op(e3, e3) = e0 % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | | ALPHA: (105) implies: % 135.84/19.98 | | | | | | | | | | | | | | | (106) op(e3, e3) = e0 % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | | REF_CLOSE: (6), (31), (88), (106) are inconsistent by % 135.84/19.98 | | | | | | | | | | | | | | | sub-proof #717. % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | Case 2: % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | | (107) all_57_2 = e0 & op(e2, e3) = e0 % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (107) are inconsistent by sub-proof % 135.84/19.98 | | | | | | | | | | | | | | | #494. % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | End of split % 135.84/19.98 | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | Case 2: % 135.84/19.98 | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | (108) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 135.84/19.98 | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 135.84/19.98 | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | BETA: splitting (108) gives: % 135.84/19.98 | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | Case 1: % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | | (109) all_57_6 = e0 & op(e1, e3) = e0 % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | | ALPHA: (109) implies: % 135.84/19.98 | | | | | | | | | | | | | | | (110) op(e1, e3) = e0 % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_32_0, all_56_5, e3, e1, % 135.84/19.98 | | | | | | | | | | | | | | | simplifying with (86), (103) gives: % 135.84/19.98 | | | | | | | | | | | | | | | (111) all_56_5 = all_32_0 % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e0, all_56_5, e3, e1, % 135.84/19.98 | | | | | | | | | | | | | | | simplifying with (86), (110) gives: % 135.84/19.98 | | | | | | | | | | | | | | | (112) all_56_5 = e0 % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | | COMBINE_EQS: (111), (112) imply: % 135.84/19.98 | | | | | | | | | | | | | | | (113) all_32_0 = e0 % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | | SIMP: (113) implies: % 135.84/19.98 | | | | | | | | | | | | | | | (114) all_32_0 = e0 % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | | REDUCE: (102), (114) imply: % 135.84/19.98 | | | | | | | | | | | | | | | (115) $false % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | | CLOSE: (115) is inconsistent. % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | Case 2: % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | | (116) all_57_12 = e0 & op(e0, e3) = e0 % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | | ALPHA: (116) implies: % 135.84/19.98 | | | | | | | | | | | | | | | (117) all_57_12 = e0 % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (15), (30), (84), (86), (88), % 135.84/19.98 | | | | | | | | | | | | | | | (117) are inconsistent by sub-proof #144. % 135.84/19.98 | | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | | End of split % 135.84/19.98 | | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | End of split % 135.84/19.98 | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | Case 2: % 135.84/19.98 | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | (118) ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 & % 135.84/19.98 | | | | | | | | | | | | | $i(all_32_1) % 135.84/19.98 | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | REF_CLOSE: (6), (12), (118) are inconsistent by sub-proof % 135.84/19.98 | | | | | | | | | | | | | #95. % 135.84/19.98 | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | End of split % 135.84/19.98 | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | End of split % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | End of split % 135.84/19.98 | | | | | | | | | | % 135.84/19.98 | | | | | | | | | End of split % 135.84/19.98 | | | | | | | | | % 135.84/19.98 | | | | | | | | Case 2: % 135.84/19.98 | | | | | | | | | % 135.84/19.98 | | | | | | | | | (119) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) % 135.84/19.98 | | | | | | | | | & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.84/19.98 | | | | | | | | | (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = % 135.84/19.98 | | | | | | | | | e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 % 135.84/19.98 | | | | | | | | | & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 135.84/19.98 | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.84/19.98 | | | | | | | | | $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & % 135.84/19.98 | | | | | | | | | ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 135.84/19.98 | | | | | | | | | (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) % 135.84/19.98 | | | | | | | | | = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 135.84/19.98 | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e2, e3) = % 135.84/19.98 | | | | | | | | | e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) % 135.84/19.98 | | | | | | | | | & $i(all_56_17) & $i(all_56_25)) % 135.84/19.98 | | | | | | | | | % 135.84/19.98 | | | | | | | | | REF_CLOSE: (2), (6), (8), (13), (18), (119) are inconsistent % 135.84/19.98 | | | | | | | | | by sub-proof #457. % 135.84/19.98 | | | | | | | | | % 135.84/19.98 | | | | | | | | End of split % 135.84/19.98 | | | | | | | | % 135.84/19.98 | | | | | | | Case 2: % 135.84/19.98 | | | | | | | | % 135.84/19.98 | | | | | | | | (120) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & % 135.84/19.98 | | | | | | | | ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.84/19.98 | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) % 135.84/19.98 | | | | | | | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = % 135.84/19.98 | | | | | | | | all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & % 135.84/19.98 | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.84/19.98 | | | | | | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & % 135.84/19.98 | | | | | | | | ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.84/19.98 | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = % 135.84/19.98 | | | | | | | | e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, % 135.84/19.98 | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 135.84/19.98 | | | | | | | | e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.84/19.98 | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & % 135.84/19.98 | | | | | | | | all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.84/19.98 | | | | | | | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.84/19.98 | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 135.84/19.98 | | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 135.84/19.98 | | | | | | | | all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.84/19.98 | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.84/19.98 | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & % 135.84/19.98 | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.84/19.98 | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 135.84/19.98 | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 135.84/19.98 | | | | | | | | all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & % 135.84/19.98 | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.84/19.98 | | | | | | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & % 135.84/19.98 | | | | | | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 135.84/19.98 | | | | | | | | (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 135.84/19.98 | | | | | | | | (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, % 135.84/19.98 | | | | | | | | e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 135.84/19.98 | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.84/19.98 | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.84/19.98 | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 % 135.84/19.98 | | | | | | | | & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.84/19.98 | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.84/19.98 | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, % 135.84/19.98 | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.84/19.98 | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.84/19.98 | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.84/19.98 | | | | | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 % 135.84/19.98 | | | | | | | | & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ % 135.84/19.98 | | | | | | | | (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, % 135.84/19.98 | | | | | | | | e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 135.84/19.98 | | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 135.84/19.98 | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.84/19.98 | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.84/19.98 | | | | | | | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.84/19.98 | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, % 135.84/19.98 | | | | | | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.84/19.98 | | | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.84/19.98 | | | | | | | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.84/19.98 | | | | | | | | $i(all_56_21) & $i(all_56_29)))) % 135.84/19.98 | | | | | | | | % 135.84/19.98 | | | | | | | | BETA: splitting (120) gives: % 135.84/19.98 | | | | | | | | % 135.84/19.98 | | | | | | | | Case 1: % 135.84/19.98 | | | | | | | | | % 135.84/19.98 | | | | | | | | | (121) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) % 135.84/19.98 | | | | | | | | | & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.84/19.98 | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 135.84/19.98 | | | | | | | | | e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.84/19.98 | | | | | | | | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = % 135.84/19.98 | | | | | | | | | e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.84/19.98 | | | | | | | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & % 135.84/19.98 | | | | | | | | | ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.84/19.98 | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) % 135.84/19.98 | | | | | | | | | = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & % 135.84/19.98 | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.84/19.98 | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.84/19.98 | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.84/19.98 | | | | | | | | | % 135.84/19.98 | | | | | | | | | REF_CLOSE: (6), (9), (12), (16), (19), (121) are inconsistent % 135.84/19.98 | | | | | | | | | by sub-proof #108. % 135.84/19.98 | | | | | | | | | % 135.84/19.98 | | | | | | | | Case 2: % 135.84/19.98 | | | | | | | | | % 135.84/19.98 | | | | | | | | | (122) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) % 135.84/19.98 | | | | | | | | | & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.84/19.98 | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = % 135.84/19.98 | | | | | | | | | e2 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 % 135.84/19.98 | | | | | | | | | & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 135.84/19.98 | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.84/19.98 | | | | | | | | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & % 135.84/19.98 | | | | | | | | | ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ % 135.84/19.98 | | | | | | | | | (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) % 135.84/19.98 | | | | | | | | | = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.84/19.98 | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = % 135.84/19.98 | | | | | | | | | e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) % 135.84/19.98 | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.84/19.98 | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.84/19.98 | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.84/19.98 | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.84/19.98 | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.84/19.98 | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 135.84/19.98 | | | | | | | | | & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.84/19.98 | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.84/19.98 | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.84/19.98 | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 135.84/19.98 | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.84/19.98 | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 % 135.84/19.98 | | | | | | | | | & op(e2, e1) = all_56_19 & op(e2, e0) = % 135.84/19.98 | | | | | | | | | all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 135.84/19.98 | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 135.84/19.98 | | | | | | | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 % 135.84/19.98 | | | | | | | | | = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.84/19.98 | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.84/19.98 | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.84/19.98 | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 % 135.84/19.98 | | | | | | | | | & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.84/19.98 | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 % 135.84/19.98 | | | | | | | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.84/19.98 | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.84/19.98 | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) % 135.84/19.98 | | | | | | | | | = all_56_21 & op(e1, e0) = all_56_29 & op(e0, % 135.84/19.98 | | | | | | | | | e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.84/19.98 | | | | | | | | | $i(all_56_21) & $i(all_56_29)))) % 135.84/19.98 | | | | | | | | | % 135.84/19.98 | | | | | | | | | BETA: splitting (122) gives: % 135.84/19.98 | | | | | | | | | % 135.84/19.98 | | | | | | | | | Case 1: % 135.84/19.98 | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | (123) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 135.84/19.98 | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.84/19.98 | | | | | | | | | | ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 135.84/19.98 | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.84/19.98 | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.84/19.98 | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 135.84/19.98 | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 135.84/19.98 | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | ALPHA: (123) implies: % 135.84/19.98 | | | | | | | | | | (124) op(e2, e0) = e2 % 135.84/19.98 | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | REF_CLOSE: (3), (6), (9), (72), (124) are inconsistent by % 135.84/19.98 | | | | | | | | | | sub-proof #546. % 135.84/19.98 | | | | | | | | | | % 135.84/19.98 | | | | | | | | | Case 2: % 135.84/19.98 | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | (125) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.84/19.98 | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 135.84/19.98 | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.84/19.98 | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.84/19.98 | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.84/19.98 | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.84/19.98 | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.84/19.98 | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.84/19.98 | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.84/19.98 | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.84/19.98 | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.84/19.98 | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 135.84/19.98 | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.84/19.98 | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.84/19.98 | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 135.84/19.98 | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.84/19.98 | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.84/19.98 | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.84/19.98 | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.84/19.98 | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.84/19.98 | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.84/19.98 | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.84/19.98 | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.84/19.98 | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.84/19.98 | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.84/19.98 | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.84/19.98 | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.84/19.98 | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.84/19.98 | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.84/19.98 | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.84/19.98 | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.84/19.98 | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = % 135.84/19.98 | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 135.84/19.98 | | | | | | | | | | e0) = all_56_29 & op(e0, e1) = e0 & % 135.84/19.98 | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.84/19.98 | | | | | | | | | | & $i(all_56_29)))) % 135.84/19.98 | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | BETA: splitting (125) gives: % 135.84/19.98 | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | Case 1: % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | (126) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.84/19.98 | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 135.84/19.98 | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.84/19.98 | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.84/19.98 | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.84/19.98 | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.84/19.98 | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | ALPHA: (126) implies: % 135.84/19.98 | | | | | | | | | | | (127) ~ (all_56_19 = e1) % 135.84/19.98 | | | | | | | | | | | (128) op(e2, e1) = all_56_19 % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | REF_CLOSE: (6), (78), (127), (128) are inconsistent by % 135.84/19.98 | | | | | | | | | | | sub-proof #106. % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | Case 2: % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | (129) op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.84/19.98 | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.84/19.98 | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.84/19.98 | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.84/19.98 | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 135.84/19.98 | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.84/19.98 | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.84/19.98 | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 135.84/19.98 | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.84/19.98 | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.84/19.98 | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.84/19.98 | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 135.84/19.98 | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.84/19.98 | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.84/19.98 | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.84/19.98 | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.84/19.98 | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.84/19.98 | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.84/19.98 | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.84/19.98 | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.84/19.98 | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.84/19.98 | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.84/19.98 | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.84/19.98 | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.84/19.98 | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 135.84/19.98 | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.84/19.98 | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 135.84/19.98 | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 135.84/19.98 | | | | | | | | | | | $i(all_56_29))) % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | ALPHA: (129) implies: % 135.84/19.98 | | | | | | | | | | | (130) op(e0, e0) = all_56_31 % 135.84/19.98 | | | | | | | | | | | (131) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.84/19.98 | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.84/19.98 | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.84/19.98 | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.84/19.98 | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.84/19.98 | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.84/19.98 | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.84/19.98 | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 135.84/19.98 | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.84/19.98 | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.84/19.98 | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 135.84/19.98 | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 135.84/19.98 | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 135.84/19.98 | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.84/19.98 | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.84/19.98 | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 135.84/19.98 | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.84/19.98 | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 135.84/19.98 | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.84/19.98 | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.84/19.98 | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.84/19.98 | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.84/19.98 | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.84/19.98 | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 135.84/19.98 | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 135.84/19.98 | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | BETA: splitting (131) gives: % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | Case 1: % 135.84/19.98 | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | (132) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 135.84/19.98 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.84/19.98 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.84/19.98 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.84/19.98 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.84/19.98 | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.84/19.98 | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.84/19.98 | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 135.84/19.98 | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.84/19.98 | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.84/19.98 | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 135.84/19.98 | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 135.84/19.98 | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) % 135.84/19.98 | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | REF_CLOSE: (6), (35), (78), (132) are inconsistent by % 135.84/19.98 | | | | | | | | | | | | sub-proof #91. % 135.84/19.98 | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | Case 2: % 135.84/19.98 | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | (133) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 135.84/19.98 | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.84/19.98 | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.84/19.98 | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.84/19.98 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.84/19.98 | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.84/19.98 | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.84/19.98 | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.84/19.98 | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.84/19.98 | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.84/19.98 | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 135.84/19.98 | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 135.84/19.98 | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 135.84/19.98 | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | BETA: splitting (133) gives: % 135.84/19.98 | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | Case 1: % 135.84/19.98 | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | (134) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 135.84/19.98 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.84/19.98 | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 135.84/19.98 | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 135.84/19.98 | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 135.84/19.98 | | | | | | | | | | | | | & $i(all_56_15) & $i(all_56_23) % 135.84/19.98 | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | ALPHA: (134) implies: % 135.84/19.98 | | | | | | | | | | | | | (135) op(e1, e1) = e0 % 135.84/19.98 | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | REF_CLOSE: (5), (6), (12), (135) are inconsistent by % 135.84/19.98 | | | | | | | | | | | | | sub-proof #98. % 135.84/19.98 | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | Case 2: % 135.84/19.98 | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | (136) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 135.84/19.98 | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) % 135.84/19.98 | | | | | | | | | | | | | & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 135.84/19.98 | | | | | | | | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 135.84/19.98 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.84/19.98 | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.84/19.98 | | | | | | | | | | | | | $i(all_56_29) % 135.84/19.98 | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | ALPHA: (136) implies: % 135.84/19.98 | | | | | | | | | | | | | (137) all_56_31 = e1 % 135.84/19.98 | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | REDUCE: (130), (137) imply: % 135.84/19.98 | | | | | | | | | | | | | (138) op(e0, e0) = e1 % 135.84/19.98 | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | | REF_CLOSE: (6), (7), (24), (138) are inconsistent by % 135.84/19.98 | | | | | | | | | | | | | sub-proof #636. % 135.84/19.98 | | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | | End of split % 135.84/19.98 | | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | | End of split % 135.84/19.98 | | | | | | | | | | | % 135.84/19.98 | | | | | | | | | | End of split % 135.84/19.98 | | | | | | | | | | % 135.84/19.98 | | | | | | | | | End of split % 135.84/19.98 | | | | | | | | | % 135.84/19.98 | | | | | | | | End of split % 135.84/19.98 | | | | | | | | % 135.84/19.98 | | | | | | | End of split % 135.84/19.98 | | | | | | | % 135.84/19.98 | | | | | | Case 2: % 135.84/19.98 | | | | | | | % 135.84/19.98 | | | | | | | (139) all_54_6 = e0 % 135.84/19.98 | | | | | | | % 135.84/19.98 | | | | | | | REF_CLOSE: (40), (45), (139) are inconsistent by sub-proof #92. % 135.84/19.98 | | | | | | | % 135.84/19.98 | | | | | | End of split % 135.84/19.98 | | | | | | % 135.84/19.98 | | | | | End of split % 135.84/19.98 | | | | | % 135.84/19.98 | | | | End of split % 135.84/19.98 | | | | % 135.84/19.98 | | | End of split % 135.84/19.98 | | | % 135.84/19.98 | | End of split % 135.84/19.98 | | % 135.84/19.98 | Case 2: % 135.84/19.98 | | % 135.84/19.98 | | (140) ~ (all_18_1 = e0) & op(e2, e2) = all_18_1 & $i(all_18_1) % 135.84/19.98 | | % 135.84/19.98 | | REF_CLOSE: (2), (6), (140) are inconsistent by sub-proof #103. % 135.84/19.98 | | % 135.84/19.98 | End of split % 135.84/19.98 | % 135.84/19.98 End of proof % 135.84/19.98 % 135.84/19.98 Sub-proof #91 shows that the following formulas are inconsistent: % 135.84/19.98 ---------------------------------------------------------------- % 135.84/19.98 (1) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 135.84/19.98 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.84/19.98 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 135.84/19.98 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.84/19.98 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) % 135.84/19.98 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.84/19.98 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 135.84/19.98 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 135.84/19.98 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 135.84/19.98 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.84/19.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.84/19.98 (3) op(e3, e2) = e2 % 135.84/19.98 (4) op(e2, e1) = e1 % 135.84/19.98 % 135.84/19.98 Begin of proof % 135.84/19.98 | % 135.84/19.98 | BETA: splitting (1) gives: % 135.84/19.98 | % 135.84/19.98 | Case 1: % 135.84/19.98 | | % 135.84/19.98 | | (5) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.84/19.98 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.84/19.98 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.84/19.98 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.84/19.98 | | $i(all_56_17) & $i(all_56_25) % 135.84/19.98 | | % 135.84/19.98 | | ALPHA: (5) implies: % 135.84/19.98 | | (6) ~ (all_56_9 = e2) % 135.84/19.98 | | (7) op(e3, e2) = all_56_9 % 135.84/19.98 | | % 135.84/19.98 | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #199. % 135.84/19.98 | | % 135.84/19.98 | Case 2: % 135.84/19.98 | | % 135.84/19.99 | | (8) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 135.84/19.99 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.84/19.99 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.84/19.99 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.84/19.99 | | $i(all_56_19) & $i(all_56_27) % 135.84/19.99 | | % 135.84/19.99 | | ALPHA: (8) implies: % 135.84/19.99 | | (9) ~ (all_56_19 = e1) % 135.84/19.99 | | (10) op(e2, e1) = all_56_19 % 135.84/19.99 | | % 135.84/19.99 | | REF_CLOSE: (2), (4), (9), (10) are inconsistent by sub-proof #106. % 135.84/19.99 | | % 135.84/19.99 | End of split % 135.84/19.99 | % 135.84/19.99 End of proof % 135.84/19.99 % 135.84/19.99 Sub-proof #92 shows that the following formulas are inconsistent: % 135.84/19.99 ---------------------------------------------------------------- % 135.84/19.99 (1) all_54_6 = all_18_0 % 135.84/19.99 (2) all_54_6 = e0 % 135.84/19.99 (3) ~ (all_18_0 = e0) % 135.84/19.99 % 135.84/19.99 Begin of proof % 135.84/19.99 | % 135.84/19.99 | COMBINE_EQS: (1), (2) imply: % 135.84/19.99 | (4) all_18_0 = e0 % 135.84/19.99 | % 135.84/19.99 | SIMP: (4) implies: % 135.84/19.99 | (5) all_18_0 = e0 % 135.84/19.99 | % 135.84/19.99 | REDUCE: (3), (5) imply: % 135.84/19.99 | (6) $false % 135.84/19.99 | % 135.84/19.99 | CLOSE: (6) is inconsistent. % 135.84/19.99 | % 135.84/19.99 End of proof % 135.84/19.99 % 135.84/19.99 Sub-proof #93 shows that the following formulas are inconsistent: % 135.84/19.99 ---------------------------------------------------------------- % 135.84/19.99 (1) op(e2, e2) = e0 % 135.84/19.99 (2) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) % 135.84/19.99 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.84/19.99 (4) ~ (e2 = e1) % 135.84/19.99 (5) ~ (e1 = e0) % 135.84/19.99 (6) op(e2, e3) = e2 % 135.84/19.99 % 135.84/19.99 Begin of proof % 135.84/19.99 | % 135.84/19.99 | BETA: splitting (2) gives: % 135.84/19.99 | % 135.84/19.99 | Case 1: % 135.84/19.99 | | % 135.84/19.99 | | (7) all_57_2 = e1 & op(e2, e3) = e1 % 135.84/19.99 | | % 135.84/19.99 | | ALPHA: (7) implies: % 135.84/19.99 | | (8) op(e2, e3) = e1 % 135.84/19.99 | | % 135.84/19.99 | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #450. % 135.84/19.99 | | % 135.84/19.99 | Case 2: % 135.84/19.99 | | % 135.84/19.99 | | (9) all_57_3 = e1 & op(e2, e2) = e1 % 135.84/19.99 | | % 135.84/19.99 | | ALPHA: (9) implies: % 135.84/19.99 | | (10) op(e2, e2) = e1 % 135.84/19.99 | | % 135.84/19.99 | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #675. % 135.84/19.99 | | % 135.84/19.99 | End of split % 135.84/19.99 | % 135.84/19.99 End of proof % 135.84/19.99 % 135.84/19.99 Sub-proof #94 shows that the following formulas are inconsistent: % 135.84/19.99 ---------------------------------------------------------------- % 135.84/19.99 (1) op(e2, e2) = e0 % 135.84/19.99 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.84/19.99 (3) ~ (e3 = e0) % 135.84/19.99 (4) ~ (e3 = e2) % 135.84/19.99 (5) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) % 135.84/19.99 (6) all_57_2 = e2 % 135.84/19.99 % 135.84/19.99 Begin of proof % 135.84/19.99 | % 135.84/19.99 | BETA: splitting (5) gives: % 135.84/19.99 | % 135.84/19.99 | Case 1: % 135.84/19.99 | | % 135.84/19.99 | | (7) all_57_2 = e3 & op(e2, e3) = e3 % 135.84/19.99 | | % 135.84/19.99 | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #590. % 135.84/19.99 | | % 135.84/19.99 | Case 2: % 135.84/19.99 | | % 135.84/19.99 | | (8) all_57_3 = e3 & op(e2, e2) = e3 % 135.84/19.99 | | % 135.84/19.99 | | ALPHA: (8) implies: % 135.84/19.99 | | (9) op(e2, e2) = e3 % 135.84/19.99 | | % 135.84/19.99 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #641. % 135.84/19.99 | | % 135.84/19.99 | End of split % 135.84/19.99 | % 135.84/19.99 End of proof % 135.84/19.99 % 135.84/19.99 Sub-proof #95 shows that the following formulas are inconsistent: % 135.84/19.99 ---------------------------------------------------------------- % 135.84/19.99 (1) ~ (all_32_1 = e2) & op(e1, e1) = all_32_1 & $i(all_32_1) % 135.84/19.99 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.84/19.99 (3) op(e1, e1) = e2 % 135.84/19.99 % 135.84/19.99 Begin of proof % 135.84/19.99 | % 135.84/19.99 | ALPHA: (1) implies: % 135.84/19.99 | (4) ~ (all_32_1 = e2) % 135.84/19.99 | (5) op(e1, e1) = all_32_1 % 135.84/19.99 | % 135.84/19.99 | GROUND_INST: instantiating (2) with e2, all_32_1, e1, e1, simplifying with % 135.84/19.99 | (3), (5) gives: % 135.84/19.99 | (6) all_32_1 = e2 % 135.84/19.99 | % 135.84/19.99 | REDUCE: (4), (6) imply: % 135.84/19.99 | (7) $false % 135.84/19.99 | % 135.84/19.99 | CLOSE: (7) is inconsistent. % 135.84/19.99 | % 135.84/19.99 End of proof % 135.84/19.99 % 135.84/19.99 Sub-proof #96 shows that the following formulas are inconsistent: % 135.84/19.99 ---------------------------------------------------------------- % 135.84/19.99 (1) all_54_8 = all_32_0 % 135.84/19.99 (2) ~ (all_32_0 = e2) % 135.84/19.99 (3) ~ (all_32_0 = e0) % 135.84/19.99 (4) ~ (all_32_0 = e1) % 135.84/19.99 (5) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 135.84/19.99 % 135.84/19.99 Begin of proof % 135.84/19.99 | % 135.84/19.99 | BETA: splitting (5) gives: % 135.84/19.99 | % 135.84/19.99 | Case 1: % 135.84/19.99 | | % 135.84/19.99 | | (6) all_54_8 = e2 % 135.84/19.99 | | % 135.84/19.99 | | COMBINE_EQS: (1), (6) imply: % 135.84/19.99 | | (7) all_32_0 = e2 % 135.84/19.99 | | % 135.84/19.99 | | REDUCE: (2), (7) imply: % 135.84/19.99 | | (8) $false % 135.84/19.99 | | % 135.84/19.99 | | CLOSE: (8) is inconsistent. % 135.84/19.99 | | % 135.84/19.99 | Case 2: % 135.84/19.99 | | % 135.84/19.99 | | (9) all_54_8 = e1 | all_54_8 = e0 % 135.84/19.99 | | % 135.84/19.99 | | BETA: splitting (9) gives: % 135.84/19.99 | | % 135.84/19.99 | | Case 1: % 135.84/19.99 | | | % 135.84/19.99 | | | (10) all_54_8 = e1 % 135.84/19.99 | | | % 135.84/19.99 | | | COMBINE_EQS: (1), (10) imply: % 135.84/19.99 | | | (11) all_32_0 = e1 % 135.84/19.99 | | | % 135.84/19.99 | | | REDUCE: (4), (11) imply: % 135.84/19.99 | | | (12) $false % 135.84/19.99 | | | % 135.84/19.99 | | | CLOSE: (12) is inconsistent. % 135.84/19.99 | | | % 135.84/19.99 | | Case 2: % 135.84/19.99 | | | % 135.84/19.99 | | | (13) all_54_8 = e0 % 135.84/19.99 | | | % 135.84/19.99 | | | COMBINE_EQS: (1), (13) imply: % 135.84/19.99 | | | (14) all_32_0 = e0 % 135.84/19.99 | | | % 135.84/19.99 | | | REDUCE: (3), (14) imply: % 135.84/19.99 | | | (15) $false % 135.84/19.99 | | | % 135.84/19.99 | | | CLOSE: (15) is inconsistent. % 135.84/19.99 | | | % 135.84/19.99 | | End of split % 135.84/19.99 | | % 135.84/19.99 | End of split % 135.84/19.99 | % 135.84/19.99 End of proof % 135.84/19.99 % 135.84/19.99 Sub-proof #97 shows that the following formulas are inconsistent: % 135.84/19.99 ---------------------------------------------------------------- % 135.84/19.99 (1) all_57_12 = e2 & op(e0, e3) = e2 % 135.84/19.99 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.84/19.99 (3) op(e0, e3) = all_52_3 % 135.84/19.99 (4) ~ (all_52_3 = e2) % 135.84/19.99 % 135.84/19.99 Begin of proof % 135.84/19.99 | % 135.84/19.99 | ALPHA: (1) implies: % 135.84/19.99 | (5) op(e0, e3) = e2 % 135.84/19.99 | % 135.84/19.99 | GROUND_INST: instantiating (2) with all_52_3, e2, e3, e0, simplifying with % 135.84/19.99 | (3), (5) gives: % 135.84/19.99 | (6) all_52_3 = e2 % 135.84/19.99 | % 135.84/19.99 | REDUCE: (4), (6) imply: % 135.84/19.99 | (7) $false % 135.84/19.99 | % 135.84/19.99 | CLOSE: (7) is inconsistent. % 135.84/19.99 | % 135.84/19.99 End of proof % 135.84/19.99 % 135.84/19.99 Sub-proof #98 shows that the following formulas are inconsistent: % 135.84/19.99 ---------------------------------------------------------------- % 135.84/19.99 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.84/19.99 (2) op(e1, e1) = e2 % 135.84/19.99 (3) op(e1, e1) = e0 % 135.84/19.99 (4) ~ (e2 = e0) % 135.84/19.99 % 135.84/19.99 Begin of proof % 135.84/19.99 | % 135.84/19.99 | GROUND_INST: instantiating (1) with e2, e0, e1, e1, simplifying with (2), (3) % 135.84/19.99 | gives: % 135.84/19.99 | (5) e2 = e0 % 135.84/19.99 | % 135.84/19.99 | REDUCE: (4), (5) imply: % 135.84/19.99 | (6) $false % 135.84/19.99 | % 135.84/19.99 | CLOSE: (6) is inconsistent. % 135.84/19.99 | % 135.84/19.99 End of proof % 135.84/19.99 % 135.84/19.99 Sub-proof #99 shows that the following formulas are inconsistent: % 135.84/19.99 ---------------------------------------------------------------- % 135.84/19.99 (1) all_54_12 = all_52_3 % 135.84/19.99 (2) all_54_12 = e1 % 135.84/19.99 (3) ~ (all_52_3 = e1) % 135.84/19.99 % 135.84/19.99 Begin of proof % 135.84/19.99 | % 135.84/19.99 | COMBINE_EQS: (1), (2) imply: % 135.84/19.99 | (4) all_52_3 = e1 % 135.84/19.99 | % 135.84/19.99 | SIMP: (4) implies: % 135.84/19.99 | (5) all_52_3 = e1 % 135.84/19.99 | % 135.84/19.99 | REDUCE: (3), (5) imply: % 135.84/19.99 | (6) $false % 135.84/19.99 | % 135.84/19.99 | CLOSE: (6) is inconsistent. % 135.84/19.99 | % 135.84/19.99 End of proof % 135.84/19.99 % 135.84/19.99 Sub-proof #100 shows that the following formulas are inconsistent: % 135.84/19.99 ---------------------------------------------------------------- % 135.84/19.99 (1) all_57_13 = e2 & op(e0, e2) = e2 % 135.84/19.99 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.84/19.99 (3) op(e0, e2) = all_52_7 % 135.84/19.99 (4) ~ (all_52_7 = e2) % 135.84/19.99 % 135.84/19.99 Begin of proof % 135.84/19.99 | % 135.84/19.99 | ALPHA: (1) implies: % 135.84/19.99 | (5) op(e0, e2) = e2 % 135.84/19.99 | % 135.84/19.99 | GROUND_INST: instantiating (2) with all_52_7, e2, e2, e0, simplifying with % 135.84/19.99 | (3), (5) gives: % 135.84/19.99 | (6) all_52_7 = e2 % 135.84/19.99 | % 135.84/19.99 | REDUCE: (4), (6) imply: % 135.84/19.99 | (7) $false % 135.84/19.99 | % 135.84/19.99 | CLOSE: (7) is inconsistent. % 135.84/19.99 | % 135.84/19.99 End of proof % 135.84/19.99 % 135.84/19.99 Sub-proof #101 shows that the following formulas are inconsistent: % 135.84/19.99 ---------------------------------------------------------------- % 135.84/19.99 (1) op(e0, e0) = all_4_2 % 135.84/19.99 (2) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 135.84/19.99 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 135.84/19.99 (3) op(e2, e0) = all_52_13 % 135.84/19.99 (4) ~ (e2 = e0) % 135.84/19.99 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.84/19.99 (6) op(e1, e1) = e2 % 135.84/19.99 (7) ~ (all_52_9 = e2) % 135.84/19.99 (8) ~ (all_4_2 = e1) % 135.84/19.99 (9) ~ (all_52_13 = e2) % 135.84/19.99 (10) op(e2, e1) = all_52_9 % 135.84/19.99 (11) ~ (all_52_1 = e2) % 135.84/19.99 (12) op(e0, e3) = all_52_3 % 135.84/19.99 (13) op(e2, e3) = all_52_1 % 135.84/19.99 (14) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.84/19.99 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.84/19.99 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 135.84/19.99 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.84/19.99 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 135.84/19.99 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.84/19.99 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.84/19.99 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.84/19.99 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.84/19.99 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.84/19.99 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.84/19.99 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.84/19.99 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.84/19.99 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.84/19.99 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.84/19.99 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 135.84/19.99 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.84/19.99 $i(all_56_21) & $i(all_56_29)) % 135.84/19.99 (15) all_57_3 = e2 % 135.84/19.99 (16) op(e2, e2) = e2 % 135.84/19.99 (17) ~ (all_52_3 = e0) % 135.84/19.99 (18) op(e0, e0) = all_56_31 % 135.84/19.99 % 135.84/19.99 Begin of proof % 135.84/19.99 | % 135.84/19.99 | BETA: splitting (14) gives: % 135.84/19.99 | % 135.84/19.99 | Case 1: % 135.84/19.99 | | % 135.84/19.99 | | (19) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.84/19.99 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.84/19.99 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.84/19.99 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 135.84/19.99 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.84/19.99 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.84/19.99 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.84/19.99 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.84/19.99 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.84/19.99 | | $i(all_56_27)) % 135.84/19.99 | | % 135.84/19.99 | | BETA: splitting (19) gives: % 135.84/19.99 | | % 135.84/19.99 | | Case 1: % 135.84/19.99 | | | % 135.84/19.99 | | | (20) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.84/19.99 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.84/19.99 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.84/19.99 | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 135.84/19.99 | | | & $i(all_56_17) & $i(all_56_25) % 135.84/19.99 | | | % 135.84/19.99 | | | ALPHA: (20) implies: % 135.84/19.99 | | | (21) op(e0, e3) = e0 % 135.84/19.99 | | | % 135.84/19.99 | | | REF_CLOSE: (5), (12), (17), (21) are inconsistent by sub-proof #219. % 135.84/19.99 | | | % 135.84/19.99 | | Case 2: % 135.84/19.99 | | | % 135.84/19.99 | | | (22) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.84/19.99 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.84/19.99 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.84/19.99 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.84/19.99 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 135.84/19.99 | | | % 135.84/19.99 | | | ALPHA: (22) implies: % 135.84/19.99 | | | (23) ~ (all_56_11 = e2) % 135.84/19.99 | | | (24) op(e2, e2) = all_56_11 % 135.84/19.99 | | | % 135.84/19.99 | | | REF_CLOSE: (5), (16), (23), (24) are inconsistent by sub-proof #531. % 135.84/19.99 | | | % 135.84/19.99 | | End of split % 135.84/19.99 | | % 135.84/19.99 | Case 2: % 135.84/19.99 | | % 135.84/19.99 | | (25) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.84/19.99 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.84/19.99 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.84/19.99 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.84/19.99 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.84/19.99 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.84/19.99 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.84/19.99 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.84/19.99 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.84/19.99 | | $i(all_56_29)) % 135.84/19.99 | | % 135.84/19.99 | | BETA: splitting (25) gives: % 135.84/19.99 | | % 135.84/19.99 | | Case 1: % 135.84/19.99 | | | % 135.84/19.99 | | | (26) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.84/19.99 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.84/19.99 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.84/19.99 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.84/19.99 | | | $i(all_56_15) & $i(all_56_23) % 135.84/19.99 | | | % 135.84/19.99 | | | ALPHA: (26) implies: % 135.84/19.99 | | | (27) op(e1, e1) = e0 % 135.84/19.99 | | | % 135.84/19.99 | | | GROUND_INST: instantiating (5) with e2, e0, e1, e1, simplifying with (6), % 135.84/19.99 | | | (27) gives: % 135.84/19.99 | | | (28) e2 = e0 % 135.84/19.99 | | | % 135.84/19.99 | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (11), (13), (15), (28) are % 135.84/19.99 | | | inconsistent by sub-proof #359. % 135.84/19.99 | | | % 135.84/19.99 | | Case 2: % 135.84/19.99 | | | % 135.84/19.99 | | | (29) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.84/19.99 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.84/19.99 | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.84/19.99 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.84/19.99 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 135.84/19.99 | | | % 135.84/19.99 | | | ALPHA: (29) implies: % 135.84/19.99 | | | (30) all_56_31 = e1 % 135.84/19.99 | | | % 135.84/19.99 | | | REDUCE: (18), (30) imply: % 135.84/19.99 | | | (31) op(e0, e0) = e1 % 135.84/19.99 | | | % 135.84/19.99 | | | REF_CLOSE: (1), (5), (8), (31) are inconsistent by sub-proof #354. % 135.84/19.99 | | | % 135.84/19.99 | | End of split % 135.84/19.99 | | % 135.84/19.99 | End of split % 135.84/19.99 | % 135.84/19.99 End of proof % 135.84/19.99 % 135.84/19.99 Sub-proof #102 shows that the following formulas are inconsistent: % 135.84/19.99 ---------------------------------------------------------------- % 135.84/19.99 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 135.84/19.99 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 135.84/19.99 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.84/19.99 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.84/19.99 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 135.84/19.99 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.84/19.99 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 135.84/19.99 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.84/19.99 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.84/19.99 $i(all_56_21) & $i(all_56_29)) % 135.84/19.99 (2) ~ (e2 = e0) % 135.84/19.99 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 135.84/19.99 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 135.84/19.99 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.84/19.99 (5) ~ (e2 = e1) % 135.84/19.99 (6) ~ (e3 = e0) % 135.84/19.99 (7) ~ (e3 = e2) % 135.84/19.99 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 135.84/19.99 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 135.84/19.99 (9) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 135.84/19.99 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 135.84/19.99 (10) ~ (e3 = e1) % 135.84/19.99 (11) ~ (e1 = e0) % 135.84/19.99 (12) all_57_12 = e2 % 135.84/19.99 (13) op(e1, e3) = e3 % 135.84/19.99 % 135.84/19.99 Begin of proof % 135.84/19.99 | % 135.84/19.99 | BETA: splitting (1) gives: % 135.84/19.99 | % 135.84/19.99 | Case 1: % 135.84/19.99 | | % 135.84/19.99 | | (14) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.84/19.99 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 % 135.84/19.99 | | & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.84/19.99 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.84/19.99 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 135.84/19.99 | | % 135.84/19.99 | | ALPHA: (14) implies: % 135.84/19.99 | | (15) op(e3, e3) = e2 % 135.84/19.99 | | % 135.84/19.99 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (15) % 135.84/19.99 | | are inconsistent by sub-proof #290. % 135.84/19.99 | | % 135.84/19.99 | Case 2: % 135.84/19.99 | | % 135.84/19.99 | | (16) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.84/19.99 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = % 135.84/19.99 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.84/19.99 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.84/19.99 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 135.84/19.99 | | % 135.84/19.99 | | ALPHA: (16) implies: % 135.84/19.99 | | (17) ~ (all_56_5 = e3) % 135.84/19.99 | | (18) op(e1, e3) = all_56_5 % 135.84/19.99 | | % 135.84/19.99 | | REF_CLOSE: (4), (13), (17), (18) are inconsistent by sub-proof #724. % 135.84/19.99 | | % 135.84/19.99 | End of split % 135.84/19.99 | % 135.84/19.99 End of proof % 135.84/19.99 % 135.84/19.99 Sub-proof #103 shows that the following formulas are inconsistent: % 135.84/19.99 ---------------------------------------------------------------- % 135.84/19.99 (1) ~ (all_18_1 = e0) & op(e2, e2) = all_18_1 & $i(all_18_1) % 135.84/19.99 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.84/19.99 (3) op(e2, e2) = e0 % 135.84/19.99 % 135.84/19.99 Begin of proof % 135.84/19.99 | % 135.84/19.99 | ALPHA: (1) implies: % 135.84/19.99 | (4) ~ (all_18_1 = e0) % 135.84/19.99 | (5) op(e2, e2) = all_18_1 % 135.84/19.99 | % 135.84/19.99 | GROUND_INST: instantiating (2) with e0, all_18_1, e2, e2, simplifying with % 135.84/19.99 | (3), (5) gives: % 135.84/19.99 | (6) all_18_1 = e0 % 135.84/19.99 | % 135.84/19.99 | REDUCE: (4), (6) imply: % 135.84/19.99 | (7) $false % 135.84/19.99 | % 135.84/19.99 | CLOSE: (7) is inconsistent. % 135.84/19.99 | % 135.84/19.99 End of proof % 135.84/19.99 % 135.84/19.99 Sub-proof #104 shows that the following formulas are inconsistent: % 135.84/19.99 ---------------------------------------------------------------- % 135.84/19.99 (1) op(e2, e1) = e1 % 135.84/19.99 (2) all_54_0 = all_10_2 % 135.84/19.99 (3) op(e0, e0) = all_4_2 % 135.84/19.99 (4) op(e1, e1) = all_6_2 % 135.84/19.99 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.84/19.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.84/19.99 (6) op(e2, e2) = e3 % 135.84/19.99 (7) all_54_2 = all_52_8 % 135.84/19.99 (8) op(e1, e1) = e2 % 135.84/19.99 (9) ~ (all_52_12 = all_10_2) % 135.84/19.99 (10) ~ (all_10_2 = e0) % 135.84/19.99 (11) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 135.84/19.99 (12) ~ (all_52_9 = e2) % 135.84/19.99 (13) ~ (all_4_2 = e1) % 135.84/20.00 (14) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.84/20.00 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 135.84/20.00 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.84/20.00 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.84/20.00 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 135.84/20.00 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.84/20.00 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) % 135.84/20.00 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.84/20.00 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.84/20.00 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 135.84/20.00 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.84/20.00 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 135.84/20.00 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 135.84/20.00 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.84/20.00 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) % 135.84/20.00 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 135.84/20.00 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 135.84/20.00 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 135.84/20.00 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.84/20.00 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.84/20.00 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.84/20.00 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 135.84/20.00 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & % 135.84/20.00 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & % 135.84/20.00 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.84/20.00 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 135.84/20.00 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.84/20.00 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.84/20.00 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ % 135.84/20.00 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 135.84/20.00 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 135.84/20.00 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 135.84/20.00 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.84/20.00 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) % 135.84/20.00 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.84/20.00 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.84/20.00 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 % 135.84/20.00 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.84/20.00 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = % 135.84/20.00 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 135.84/20.00 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 135.84/20.00 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.84/20.00 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.84/20.00 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 135.84/20.00 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.84/20.00 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.84/20.00 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.84/20.00 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.84/20.00 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.84/20.00 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.84/20.00 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.84/20.00 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.84/20.00 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.84/20.00 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.84/20.00 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.84/20.00 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.84/20.00 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.84/20.00 $i(all_56_29)))) % 135.84/20.00 (15) ~ (all_52_8 = all_6_2) % 135.84/20.00 (16) op(e3, e3) = all_10_2 % 135.84/20.00 (17) op(e2, e1) = all_52_9 % 135.84/20.00 (18) ~ (all_52_8 = e2) % 135.84/20.00 (19) op(e3, e0) = all_52_12 % 135.84/20.00 (20) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 135.84/20.00 (21) ~ (all_10_2 = e2) % 135.84/20.00 (22) op(e3, e1) = all_52_8 % 135.84/20.00 (23) ~ (all_52_8 = all_10_2) % 135.84/20.00 (24) ~ (all_10_2 = e1) % 135.84/20.00 (25) ~ (all_52_8 = e1) % 135.84/20.00 % 135.84/20.00 Begin of proof % 135.84/20.00 | % 135.84/20.00 | BETA: splitting (11) gives: % 135.84/20.00 | % 135.84/20.00 | Case 1: % 135.84/20.00 | | % 135.84/20.00 | | (26) all_54_0 = e3 % 135.84/20.00 | | % 135.84/20.00 | | COMBINE_EQS: (2), (26) imply: % 135.84/20.00 | | (27) all_10_2 = e3 % 135.84/20.00 | | % 135.84/20.00 | | REDUCE: (23), (27) imply: % 135.84/20.00 | | (28) ~ (all_52_8 = e3) % 135.84/20.00 | | % 135.84/20.00 | | REDUCE: (9), (27) imply: % 135.84/20.00 | | (29) ~ (all_52_12 = e3) % 135.84/20.00 | | % 135.84/20.00 | | REDUCE: (21), (27) imply: % 135.84/20.00 | | (30) ~ (e3 = e2) % 135.84/20.00 | | % 135.84/20.00 | | REDUCE: (24), (27) imply: % 135.84/20.00 | | (31) ~ (e3 = e1) % 135.84/20.00 | | % 135.84/20.00 | | REDUCE: (10), (27) imply: % 135.84/20.00 | | (32) ~ (e3 = e0) % 135.84/20.00 | | % 135.84/20.00 | | REDUCE: (16), (27) imply: % 135.84/20.00 | | (33) op(e3, e3) = e3 % 135.84/20.00 | | % 135.84/20.00 | | BETA: splitting (14) gives: % 135.84/20.00 | | % 135.84/20.00 | | Case 1: % 135.84/20.00 | | | % 135.84/20.00 | | | (34) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ % 135.84/20.00 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.84/20.00 | | | op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & % 135.84/20.00 | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 135.84/20.00 | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.84/20.00 | | | $i(all_56_27)) | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 % 135.84/20.00 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.84/20.00 | | | (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, % 135.84/20.00 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.84/20.00 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.84/20.00 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 % 135.84/20.00 | | | & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ % 135.84/20.00 | | | (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.84/20.00 | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 % 135.84/20.00 | | | & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) % 135.84/20.00 | | | & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = % 135.84/20.00 | | | e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & % 135.84/20.00 | | | ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 % 135.84/20.00 | | | & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = % 135.84/20.00 | | | all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & % 135.84/20.00 | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 135.84/20.00 | | | % 135.84/20.00 | | | BETA: splitting (34) gives: % 135.84/20.00 | | | % 135.84/20.00 | | | Case 1: % 135.84/20.00 | | | | % 135.84/20.00 | | | | (35) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ % 135.84/20.00 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.84/20.00 | | | | op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & % 135.84/20.00 | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 135.84/20.00 | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.84/20.00 | | | | $i(all_56_27)) | (all_56_1 = e1 & all_56_17 = e3 & ~ % 135.84/20.00 | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.84/20.00 | | | | ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & % 135.84/20.00 | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.84/20.00 | | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.84/20.00 | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.84/20.00 | | | | % 135.84/20.00 | | | | REF_CLOSE: (5), (30), (31), (33), (35) are inconsistent by sub-proof % 135.84/20.00 | | | | #623. % 135.84/20.00 | | | | % 135.84/20.00 | | | Case 2: % 135.84/20.00 | | | | % 135.84/20.00 | | | | (36) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ % 135.84/20.00 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.84/20.00 | | | | op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & % 135.84/20.00 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.84/20.00 | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.84/20.00 | | | | $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ % 135.84/20.00 | | | | (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 135.84/20.00 | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 135.84/20.00 | | | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.84/20.00 | | | | op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & % 135.84/20.00 | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 135.84/20.00 | | | | % 135.84/20.00 | | | | REF_CLOSE: (5), (19), (29), (33), (36) are inconsistent by sub-proof % 135.84/20.00 | | | | #553. % 135.84/20.00 | | | | % 135.84/20.00 | | | End of split % 135.84/20.00 | | | % 135.84/20.00 | | Case 2: % 135.84/20.00 | | | % 135.84/20.00 | | | (37) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ % 135.84/20.00 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 135.84/20.00 | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 135.84/20.00 | | | all_56_17 & op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 135.84/20.00 | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.84/20.00 | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 % 135.84/20.00 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.84/20.00 | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, % 135.84/20.00 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.84/20.00 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.84/20.00 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 135.84/20.00 | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ % 135.84/20.00 | | | (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 135.84/20.00 | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 % 135.84/20.00 | | | & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) % 135.84/20.00 | | | & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_13 = % 135.84/20.00 | | | e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 135.84/20.00 | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.84/20.00 | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 135.84/20.00 | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & % 135.84/20.00 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.84/20.00 | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.84/20.00 | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & % 135.84/20.00 | | | ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.84/20.00 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.84/20.00 | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & % 135.84/20.00 | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 135.84/20.00 | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.84/20.00 | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, % 135.84/20.00 | | | e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.84/20.00 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.84/20.00 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.84/20.00 | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 135.84/20.00 | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.84/20.00 | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & % 135.84/20.00 | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) % 135.84/20.00 | | | = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.84/20.00 | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.84/20.00 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) % 135.84/20.00 | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, % 135.84/20.00 | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 % 135.84/20.00 | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.84/20.00 | | | $i(all_56_29)))) % 135.84/20.00 | | | % 135.84/20.00 | | | BETA: splitting (37) gives: % 135.84/20.00 | | | % 135.84/20.00 | | | Case 1: % 135.84/20.00 | | | | % 135.84/20.00 | | | | (38) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ % 135.84/20.00 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 135.84/20.00 | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 135.84/20.00 | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 135.84/20.00 | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.84/20.00 | | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ % 135.84/20.00 | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.84/20.00 | | | | ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & % 135.84/20.00 | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.84/20.00 | | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.84/20.00 | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 135.84/20.00 | | | | % 135.84/20.00 | | | | REF_CLOSE: (5), (8), (12), (17), (30), (38) are inconsistent by % 135.84/20.00 | | | | sub-proof #108. % 135.84/20.00 | | | | % 135.84/20.00 | | | Case 2: % 135.84/20.00 | | | | % 135.84/20.00 | | | | (39) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.84/20.00 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.84/20.00 | | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & % 135.84/20.00 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.84/20.00 | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.84/20.00 | | | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ % 135.84/20.00 | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 135.84/20.00 | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.84/20.00 | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.84/20.00 | | | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.84/20.00 | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.84/20.00 | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & % 135.84/20.00 | | | | ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.84/20.00 | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.84/20.00 | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.84/20.00 | | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & % 135.84/20.00 | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 135.84/20.00 | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 135.84/20.00 | | | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.84/20.00 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.84/20.00 | | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = % 135.84/20.00 | | | | e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.84/20.00 | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 135.84/20.00 | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 135.84/20.00 | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 135.84/20.00 | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.84/20.00 | | | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.84/20.00 | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.84/20.00 | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.84/20.00 | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 135.84/20.00 | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 135.84/20.00 | | | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 135.84/20.00 | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)))) % 135.84/20.00 | | | | % 135.84/20.00 | | | | BETA: splitting (39) gives: % 135.84/20.00 | | | | % 135.84/20.00 | | | | Case 1: % 135.84/20.00 | | | | | % 135.84/20.00 | | | | | (40) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.84/20.00 | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.84/20.00 | | | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & % 135.84/20.00 | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.84/20.00 | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.84/20.00 | | | | | $i(all_56_31) % 135.84/20.00 | | | | | % 135.84/20.00 | | | | | ALPHA: (40) implies: % 135.84/20.00 | | | | | (41) op(e2, e2) = e0 % 135.84/20.00 | | | | | % 135.84/20.00 | | | | | REF_CLOSE: (5), (6), (32), (41) are inconsistent by sub-proof #641. % 135.84/20.00 | | | | | % 135.84/20.00 | | | | Case 2: % 135.84/20.00 | | | | | % 135.84/20.00 | | | | | (42) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.84/20.00 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) % 135.84/20.00 | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.84/20.00 | | | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 % 135.84/20.00 | | | | | & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.84/20.00 | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 & % 135.84/20.00 | | | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 135.84/20.00 | | | | | (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 135.84/20.00 | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.84/20.00 | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.84/20.00 | | | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & % 135.84/20.00 | | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.84/20.00 | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.84/20.00 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = % 135.84/20.00 | | | | | e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.84/20.00 | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 135.84/20.00 | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 135.84/20.00 | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & % 135.84/20.00 | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.84/20.00 | | | | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.84/20.00 | | | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 135.84/20.00 | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 135.84/20.00 | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.84/20.00 | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.84/20.00 | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.84/20.00 | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 135.84/20.00 | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 135.84/20.00 | | | | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 135.84/20.00 | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)))) % 135.84/20.00 | | | | | % 135.84/20.00 | | | | | BETA: splitting (42) gives: % 135.84/20.00 | | | | | % 135.84/20.00 | | | | | Case 1: % 135.84/20.00 | | | | | | % 135.84/20.00 | | | | | | (43) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.84/20.00 | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) % 135.84/20.00 | | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.84/20.00 | | | | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 % 135.84/20.00 | | | | | | & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 135.84/20.00 | | | | | | $i(all_56_19) & $i(all_56_27) % 135.84/20.00 | | | | | | % 135.84/20.00 | | | | | | ALPHA: (43) implies: % 135.84/20.00 | | | | | | (44) ~ (all_56_19 = e1) % 135.84/20.00 | | | | | | (45) op(e2, e1) = all_56_19 % 135.84/20.00 | | | | | | % 135.84/20.00 | | | | | | REF_CLOSE: (1), (5), (44), (45) are inconsistent by sub-proof #106. % 135.84/20.00 | | | | | | % 135.84/20.00 | | | | | Case 2: % 135.84/20.00 | | | | | | % 135.84/20.00 | | | | | | (46) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.84/20.00 | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 135.84/20.00 | | | | | | & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) % 135.84/20.00 | | | | | | = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 135.84/20.00 | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.84/20.00 | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.84/20.00 | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 135.84/20.00 | | | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.84/20.00 | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.84/20.00 | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.84/20.00 | | | | | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 135.84/20.00 | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.84/20.00 | | | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.84/20.00 | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = % 135.84/20.00 | | | | | | e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 135.84/20.00 | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 135.84/20.00 | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 135.84/20.00 | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~ % 135.84/20.00 | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 135.84/20.00 | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 135.84/20.00 | | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 135.84/20.00 | | | | | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 135.84/20.00 | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))) % 135.84/20.00 | | | | | | % 135.84/20.00 | | | | | | ALPHA: (46) implies: % 135.84/20.00 | | | | | | (47) op(e0, e0) = all_56_31 % 135.84/20.00 | | | | | | (48) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.84/20.00 | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = % 135.84/20.00 | | | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 135.84/20.00 | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 135.84/20.00 | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 135.84/20.00 | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 135.84/20.00 | | | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.84/20.00 | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 135.84/20.00 | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.84/20.00 | | | | | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 135.84/20.00 | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.84/20.00 | | | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.84/20.00 | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = % 135.84/20.00 | | | | | | e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 135.84/20.00 | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 % 135.84/20.00 | | | | | | & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 135.84/20.00 | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.84/20.00 | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = % 135.84/20.00 | | | | | | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.84/20.00 | | | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, % 135.84/20.00 | | | | | | e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 135.84/20.00 | | | | | | & $i(all_56_29)) % 135.84/20.00 | | | | | | % 135.84/20.00 | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (13), (15), (18), (20), (22), % 135.84/20.00 | | | | | | (25), (28), (33), (47), (48) are inconsistent by % 135.84/20.00 | | | | | | sub-proof #105. % 135.84/20.00 | | | | | | % 135.84/20.00 | | | | | End of split % 135.84/20.00 | | | | | % 135.84/20.00 | | | | End of split % 135.84/20.00 | | | | % 135.84/20.00 | | | End of split % 135.84/20.00 | | | % 135.84/20.00 | | End of split % 135.84/20.00 | | % 135.84/20.00 | Case 2: % 135.84/20.00 | | % 135.84/20.00 | | (49) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 135.84/20.00 | | % 135.84/20.00 | | REF_CLOSE: (2), (10), (21), (24), (49) are inconsistent by sub-proof #777. % 135.84/20.00 | | % 135.84/20.00 | End of split % 135.84/20.00 | % 135.84/20.00 End of proof % 135.84/20.00 % 135.84/20.00 Sub-proof #105 shows that the following formulas are inconsistent: % 135.84/20.00 ---------------------------------------------------------------- % 135.84/20.00 (1) op(e2, e1) = e1 % 135.84/20.00 (2) op(e0, e0) = all_4_2 % 135.84/20.00 (3) op(e1, e1) = all_6_2 % 135.84/20.00 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.84/20.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.84/20.00 (5) all_54_2 = all_52_8 % 135.84/20.00 (6) ~ (all_4_2 = e1) % 135.84/20.00 (7) ~ (all_52_8 = all_6_2) % 135.84/20.00 (8) ~ (all_52_8 = e2) % 135.84/20.00 (9) op(e3, e3) = e3 % 135.84/20.00 (10) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 135.84/20.00 (11) op(e3, e1) = all_52_8 % 135.84/20.00 (12) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.84/20.00 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.84/20.00 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 135.84/20.00 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 135.84/20.00 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 135.84/20.00 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 135.84/20.00 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.84/20.00 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.84/20.00 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 135.84/20.00 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.84/20.00 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 135.84/20.00 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.84/20.00 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.84/20.00 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.84/20.00 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 135.84/20.00 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 135.84/20.00 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.84/20.00 $i(all_56_21) & $i(all_56_29)) % 135.84/20.00 (13) ~ (all_52_8 = e1) % 135.84/20.00 (14) op(e0, e0) = all_56_31 % 135.84/20.00 (15) ~ (all_52_8 = e3) % 135.84/20.00 % 135.84/20.00 Begin of proof % 135.84/20.00 | % 135.84/20.00 | BETA: splitting (12) gives: % 135.84/20.00 | % 135.84/20.00 | Case 1: % 135.84/20.00 | | % 135.84/20.00 | | (16) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.84/20.00 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.84/20.00 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.84/20.00 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 135.84/20.00 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 135.84/20.00 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 135.84/20.00 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 135.84/20.00 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 135.84/20.00 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.84/20.00 | | $i(all_56_27)) % 135.84/20.00 | | % 135.84/20.00 | | BETA: splitting (16) gives: % 135.84/20.00 | | % 135.84/20.00 | | Case 1: % 135.84/20.00 | | | % 135.84/20.00 | | | (17) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.84/20.00 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.84/20.00 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.84/20.00 | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 135.84/20.00 | | | & $i(all_56_17) & $i(all_56_25) % 135.84/20.00 | | | % 135.84/20.00 | | | ALPHA: (17) implies: % 135.84/20.00 | | | (18) ~ (all_56_1 = e3) % 135.84/20.00 | | | (19) op(e3, e3) = all_56_1 % 135.84/20.00 | | | % 135.84/20.00 | | | REF_CLOSE: (4), (9), (18), (19) are inconsistent by sub-proof #766. % 135.84/20.00 | | | % 135.84/20.00 | | Case 2: % 135.84/20.00 | | | % 135.84/20.00 | | | (20) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.84/20.00 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.84/20.00 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.84/20.00 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.84/20.00 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 135.84/20.00 | | | % 135.84/20.00 | | | ALPHA: (20) implies: % 135.84/20.00 | | | (21) ~ (all_56_19 = e1) % 135.84/20.00 | | | (22) op(e2, e1) = all_56_19 % 135.84/20.00 | | | % 135.84/20.00 | | | REF_CLOSE: (1), (4), (21), (22) are inconsistent by sub-proof #106. % 135.84/20.00 | | | % 135.84/20.00 | | End of split % 135.84/20.00 | | % 135.84/20.00 | Case 2: % 135.84/20.00 | | % 135.84/20.00 | | (23) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.84/20.00 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.84/20.00 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.84/20.00 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.84/20.00 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 135.84/20.00 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 135.84/20.00 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.84/20.00 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.84/20.00 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.84/20.00 | | $i(all_56_29)) % 135.84/20.00 | | % 135.84/20.00 | | BETA: splitting (23) gives: % 135.84/20.00 | | % 135.84/20.00 | | Case 1: % 135.84/20.00 | | | % 135.84/20.00 | | | (24) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.84/20.00 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.84/20.00 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 135.84/20.00 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 135.84/20.00 | | | $i(all_56_15) & $i(all_56_23) % 135.84/20.00 | | | % 135.84/20.00 | | | ALPHA: (24) implies: % 135.84/20.00 | | | (25) op(e1, e1) = e0 % 135.84/20.00 | | | % 135.84/20.00 | | | BETA: splitting (10) gives: % 135.84/20.00 | | | % 135.84/20.00 | | | Case 1: % 135.84/20.00 | | | | % 135.84/20.00 | | | | (26) all_54_2 = e3 % 135.84/20.00 | | | | % 135.84/20.00 | | | | COMBINE_EQS: (5), (26) imply: % 135.84/20.00 | | | | (27) all_52_8 = e3 % 135.84/20.00 | | | | % 135.84/20.00 | | | | REDUCE: (15), (27) imply: % 135.84/20.00 | | | | (28) $false % 135.84/20.00 | | | | % 135.84/20.00 | | | | CLOSE: (28) is inconsistent. % 135.84/20.00 | | | | % 135.84/20.00 | | | Case 2: % 135.84/20.00 | | | | % 135.84/20.00 | | | | (29) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 135.84/20.00 | | | | % 135.84/20.00 | | | | BETA: splitting (29) gives: % 135.84/20.00 | | | | % 135.84/20.00 | | | | Case 1: % 135.84/20.00 | | | | | % 135.84/20.00 | | | | | (30) all_54_2 = e2 % 135.84/20.00 | | | | | % 135.84/20.00 | | | | | COMBINE_EQS: (5), (30) imply: % 135.84/20.00 | | | | | (31) all_52_8 = e2 % 135.84/20.00 | | | | | % 135.84/20.00 | | | | | REDUCE: (8), (31) imply: % 135.84/20.00 | | | | | (32) $false % 135.84/20.00 | | | | | % 135.84/20.00 | | | | | CLOSE: (32) is inconsistent. % 135.84/20.00 | | | | | % 135.84/20.00 | | | | Case 2: % 135.84/20.00 | | | | | % 135.84/20.00 | | | | | (33) all_54_2 = e1 | all_54_2 = e0 % 135.84/20.00 | | | | | % 135.84/20.00 | | | | | BETA: splitting (33) gives: % 135.84/20.00 | | | | | % 135.84/20.00 | | | | | Case 1: % 135.84/20.00 | | | | | | % 135.84/20.00 | | | | | | (34) all_54_2 = e1 % 135.84/20.00 | | | | | | % 135.84/20.00 | | | | | | COMBINE_EQS: (5), (34) imply: % 135.84/20.00 | | | | | | (35) all_52_8 = e1 % 135.84/20.00 | | | | | | % 135.84/20.00 | | | | | | REDUCE: (13), (35) imply: % 135.84/20.00 | | | | | | (36) $false % 135.84/20.00 | | | | | | % 135.84/20.00 | | | | | | CLOSE: (36) is inconsistent. % 135.84/20.00 | | | | | | % 135.84/20.00 | | | | | Case 2: % 135.84/20.00 | | | | | | % 135.84/20.00 | | | | | | (37) all_54_2 = e0 % 135.84/20.00 | | | | | | % 135.84/20.00 | | | | | | COMBINE_EQS: (5), (37) imply: % 135.84/20.00 | | | | | | (38) all_52_8 = e0 % 135.84/20.00 | | | | | | % 135.84/20.00 | | | | | | REDUCE: (11), (38) imply: % 135.84/20.00 | | | | | | (39) op(e3, e1) = e0 % 135.84/20.00 | | | | | | % 135.84/20.01 | | | | | | REF_CLOSE: (3), (4), (7), (11), (25), (39) are inconsistent by % 135.84/20.01 | | | | | | sub-proof #619. % 135.84/20.01 | | | | | | % 135.84/20.01 | | | | | End of split % 135.84/20.01 | | | | | % 135.84/20.01 | | | | End of split % 135.84/20.01 | | | | % 135.84/20.01 | | | End of split % 135.84/20.01 | | | % 135.84/20.01 | | Case 2: % 135.84/20.01 | | | % 135.84/20.01 | | | (40) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.84/20.01 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.84/20.01 | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.84/20.01 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.84/20.01 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 135.84/20.01 | | | % 135.84/20.01 | | | ALPHA: (40) implies: % 135.84/20.01 | | | (41) all_56_31 = e1 % 135.84/20.01 | | | % 135.84/20.01 | | | REDUCE: (14), (41) imply: % 135.84/20.01 | | | (42) op(e0, e0) = e1 % 135.84/20.01 | | | % 135.84/20.01 | | | REF_CLOSE: (2), (4), (6), (42) are inconsistent by sub-proof #354. % 135.84/20.01 | | | % 135.84/20.01 | | End of split % 135.84/20.01 | | % 135.84/20.01 | End of split % 135.84/20.01 | % 135.84/20.01 End of proof % 135.84/20.01 % 135.84/20.01 Sub-proof #106 shows that the following formulas are inconsistent: % 135.84/20.01 ---------------------------------------------------------------- % 135.84/20.01 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.84/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.84/20.01 (2) op(e2, e1) = all_56_19 % 135.84/20.01 (3) op(e2, e1) = e1 % 135.84/20.01 (4) ~ (all_56_19 = e1) % 135.84/20.01 % 135.84/20.01 Begin of proof % 135.84/20.01 | % 135.84/20.01 | GROUND_INST: instantiating (1) with e1, all_56_19, e1, e2, simplifying with % 135.84/20.01 | (2), (3) gives: % 135.84/20.01 | (5) all_56_19 = e1 % 135.84/20.01 | % 135.84/20.01 | REDUCE: (4), (5) imply: % 135.84/20.01 | (6) $false % 135.84/20.01 | % 135.84/20.01 | CLOSE: (6) is inconsistent. % 135.84/20.01 | % 135.84/20.01 End of proof % 135.84/20.01 % 135.84/20.01 Sub-proof #107 shows that the following formulas are inconsistent: % 135.84/20.01 ---------------------------------------------------------------- % 135.84/20.01 (1) all_57_15 = e2 & op(e0, e0) = e2 % 135.84/20.01 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.84/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.84/20.01 (3) op(e0, e0) = all_4_2 % 135.84/20.01 (4) ~ (all_4_2 = e2) % 135.84/20.01 % 135.84/20.01 Begin of proof % 135.84/20.01 | % 135.84/20.01 | ALPHA: (1) implies: % 135.84/20.01 | (5) op(e0, e0) = e2 % 135.84/20.01 | % 135.84/20.01 | GROUND_INST: instantiating (2) with all_4_2, e2, e0, e0, simplifying with (3), % 135.84/20.01 | (5) gives: % 135.84/20.01 | (6) all_4_2 = e2 % 135.84/20.01 | % 135.84/20.01 | REDUCE: (4), (6) imply: % 135.84/20.01 | (7) $false % 135.84/20.01 | % 135.84/20.01 | CLOSE: (7) is inconsistent. % 135.84/20.01 | % 135.84/20.01 End of proof % 135.84/20.01 % 135.84/20.01 Sub-proof #108 shows that the following formulas are inconsistent: % 135.84/20.01 ---------------------------------------------------------------- % 135.84/20.01 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 135.84/20.01 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.84/20.01 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 135.84/20.01 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.84/20.01 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ % 135.84/20.01 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.84/20.01 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = % 135.84/20.01 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.84/20.01 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.84/20.01 $i(all_56_29)) % 135.84/20.01 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.84/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.84/20.01 (3) ~ (e3 = e2) % 135.84/20.01 (4) op(e1, e1) = e2 % 135.84/20.01 (5) ~ (all_52_9 = e2) % 135.84/20.01 (6) op(e2, e1) = all_52_9 % 135.84/20.01 % 135.84/20.01 Begin of proof % 135.84/20.01 | % 135.84/20.01 | BETA: splitting (1) gives: % 135.84/20.01 | % 135.84/20.01 | Case 1: % 135.84/20.01 | | % 135.84/20.01 | | (7) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.84/20.01 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.84/20.01 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.84/20.01 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) % 135.84/20.01 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 135.84/20.01 | | % 135.84/20.01 | | ALPHA: (7) implies: % 135.84/20.01 | | (8) op(e1, e1) = e3 % 135.84/20.01 | | % 135.84/20.01 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #109. % 135.84/20.01 | | % 135.84/20.01 | Case 2: % 135.84/20.01 | | % 135.84/20.01 | | (9) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.84/20.01 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 % 135.84/20.01 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.84/20.01 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.84/20.01 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 135.84/20.01 | | % 135.84/20.01 | | ALPHA: (9) implies: % 135.84/20.01 | | (10) op(e2, e1) = e2 % 135.84/20.01 | | % 135.84/20.01 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #770. % 135.84/20.01 | | % 135.84/20.01 | End of split % 135.84/20.01 | % 135.84/20.01 End of proof % 135.84/20.01 % 135.84/20.01 Sub-proof #109 shows that the following formulas are inconsistent: % 135.84/20.01 ---------------------------------------------------------------- % 135.84/20.01 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.84/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.84/20.01 (2) op(e1, e1) = e3 % 135.84/20.01 (3) op(e1, e1) = e2 % 135.84/20.01 (4) ~ (e3 = e2) % 135.84/20.01 % 135.84/20.01 Begin of proof % 135.84/20.01 | % 135.98/20.01 | GROUND_INST: instantiating (1) with e2, e3, e1, e1, simplifying with (2), (3) % 135.98/20.01 | gives: % 135.98/20.01 | (5) e3 = e2 % 135.98/20.01 | % 135.98/20.01 | REDUCE: (4), (5) imply: % 135.98/20.01 | (6) $false % 135.98/20.01 | % 135.98/20.01 | CLOSE: (6) is inconsistent. % 135.98/20.01 | % 135.98/20.01 End of proof % 135.98/20.01 % 135.98/20.01 Sub-proof #110 shows that the following formulas are inconsistent: % 135.98/20.01 ---------------------------------------------------------------- % 135.98/20.01 (1) op(e2, e2) = all_8_2 % 135.98/20.01 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.01 (3) ~ (e3 = e2) % 135.98/20.01 (4) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.98/20.01 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.98/20.01 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.98/20.01 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.98/20.01 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 135.98/20.01 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 135.98/20.01 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 135.98/20.01 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.98/20.01 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.98/20.01 $i(all_56_17) & $i(all_56_25)) % 135.98/20.01 (5) op(e3, e0) = all_52_12 % 135.98/20.01 (6) ~ (all_8_2 = e3) % 135.98/20.01 (7) op(e3, e0) = e2 % 135.98/20.01 % 135.98/20.01 Begin of proof % 135.98/20.01 | % 135.98/20.01 | BETA: splitting (4) gives: % 135.98/20.01 | % 135.98/20.01 | Case 1: % 135.98/20.01 | | % 135.98/20.01 | | (8) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.98/20.01 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.98/20.01 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.98/20.01 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.98/20.01 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 135.98/20.01 | | % 135.98/20.01 | | ALPHA: (8) implies: % 135.98/20.01 | | (9) op(e3, e0) = e3 % 135.98/20.01 | | % 135.98/20.01 | | REF_CLOSE: (2), (3), (5), (7), (9) are inconsistent by sub-proof #111. % 135.98/20.01 | | % 135.98/20.01 | Case 2: % 135.98/20.01 | | % 135.98/20.01 | | (10) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.98/20.01 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.98/20.01 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.98/20.01 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) % 135.98/20.01 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 135.98/20.01 | | % 135.98/20.01 | | ALPHA: (10) implies: % 135.98/20.01 | | (11) op(e2, e2) = e3 % 135.98/20.01 | | % 135.98/20.01 | | REF_CLOSE: (1), (2), (6), (11) are inconsistent by sub-proof #228. % 135.98/20.01 | | % 135.98/20.01 | End of split % 135.98/20.01 | % 135.98/20.01 End of proof % 135.98/20.01 % 135.98/20.01 Sub-proof #111 shows that the following formulas are inconsistent: % 135.98/20.01 ---------------------------------------------------------------- % 135.98/20.01 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.01 (2) ~ (e3 = e2) % 135.98/20.01 (3) op(e3, e0) = e3 % 135.98/20.01 (4) op(e3, e0) = all_52_12 % 135.98/20.01 (5) op(e3, e0) = e2 % 135.98/20.01 % 135.98/20.01 Begin of proof % 135.98/20.01 | % 135.98/20.01 | GROUND_INST: instantiating (1) with all_52_12, e2, e0, e3, simplifying with % 135.98/20.01 | (4), (5) gives: % 135.98/20.01 | (6) all_52_12 = e2 % 135.98/20.01 | % 135.98/20.01 | GROUND_INST: instantiating (1) with all_52_12, e3, e0, e3, simplifying with % 135.98/20.01 | (3), (4) gives: % 135.98/20.01 | (7) all_52_12 = e3 % 135.98/20.01 | % 135.98/20.01 | COMBINE_EQS: (6), (7) imply: % 135.98/20.01 | (8) e3 = e2 % 135.98/20.01 | % 135.98/20.01 | SIMP: (8) implies: % 135.98/20.01 | (9) e3 = e2 % 135.98/20.01 | % 135.98/20.01 | REDUCE: (2), (9) imply: % 135.98/20.01 | (10) $false % 135.98/20.01 | % 135.98/20.01 | CLOSE: (10) is inconsistent. % 135.98/20.01 | % 135.98/20.01 End of proof % 135.98/20.01 % 135.98/20.01 Sub-proof #112 shows that the following formulas are inconsistent: % 135.98/20.01 ---------------------------------------------------------------- % 135.98/20.01 (1) op(e2, e0) = all_52_13 % 135.98/20.01 (2) ~ (all_52_13 = e1) % 135.98/20.01 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.01 (4) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 135.98/20.01 (5) op(e2, e1) = all_52_9 % 135.98/20.01 (6) ~ (all_52_9 = e1) % 135.98/20.01 % 135.98/20.01 Begin of proof % 135.98/20.01 | % 135.98/20.01 | BETA: splitting (4) gives: % 135.98/20.01 | % 135.98/20.01 | Case 1: % 135.98/20.01 | | % 135.98/20.01 | | (7) all_57_5 = e1 & op(e2, e1) = e1 % 135.98/20.01 | | % 135.98/20.01 | | REF_CLOSE: (3), (5), (6), (7) are inconsistent by sub-proof #161. % 135.98/20.01 | | % 135.98/20.01 | Case 2: % 135.98/20.01 | | % 135.98/20.01 | | (8) all_57_10 = e1 & op(e2, e0) = e1 % 135.98/20.01 | | % 135.98/20.01 | | ALPHA: (8) implies: % 135.98/20.01 | | (9) op(e2, e0) = e1 % 135.98/20.01 | | % 135.98/20.01 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #180. % 135.98/20.01 | | % 135.98/20.01 | End of split % 135.98/20.01 | % 135.98/20.01 End of proof % 135.98/20.01 % 135.98/20.01 Sub-proof #113 shows that the following formulas are inconsistent: % 135.98/20.01 ---------------------------------------------------------------- % 135.98/20.01 (1) ~ (all_20_1 = e1) & op(e2, e2) = all_20_1 & $i(all_20_1) % 135.98/20.01 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.01 (3) op(e2, e2) = e1 % 135.98/20.01 % 135.98/20.01 Begin of proof % 135.98/20.01 | % 135.98/20.01 | ALPHA: (1) implies: % 135.98/20.01 | (4) ~ (all_20_1 = e1) % 135.98/20.01 | (5) op(e2, e2) = all_20_1 % 135.98/20.01 | % 135.98/20.01 | GROUND_INST: instantiating (2) with e1, all_20_1, e2, e2, simplifying with % 135.98/20.01 | (3), (5) gives: % 135.98/20.01 | (6) all_20_1 = e1 % 135.98/20.01 | % 135.98/20.01 | REDUCE: (4), (6) imply: % 135.98/20.01 | (7) $false % 135.98/20.01 | % 135.98/20.01 | CLOSE: (7) is inconsistent. % 135.98/20.01 | % 135.98/20.01 End of proof % 135.98/20.01 % 135.98/20.01 Sub-proof #114 shows that the following formulas are inconsistent: % 135.98/20.01 ---------------------------------------------------------------- % 135.98/20.01 (1) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.98/20.01 e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & % 135.98/20.01 op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, % 135.98/20.01 e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) % 135.98/20.01 & $i(all_56_21) & $i(all_56_29) % 135.98/20.01 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.01 (3) op(e2, e1) = e3 % 135.98/20.01 (4) ~ (e3 = e2) % 135.98/20.01 % 135.98/20.01 Begin of proof % 135.98/20.01 | % 135.98/20.01 | ALPHA: (1) implies: % 135.98/20.01 | (5) op(e2, e1) = e2 % 135.98/20.01 | % 135.98/20.01 | GROUND_INST: instantiating (2) with e3, e2, e1, e2, simplifying with (3), (5) % 135.98/20.01 | gives: % 135.98/20.01 | (6) e3 = e2 % 135.98/20.01 | % 135.98/20.01 | REDUCE: (4), (6) imply: % 135.98/20.01 | (7) $false % 135.98/20.01 | % 135.98/20.01 | CLOSE: (7) is inconsistent. % 135.98/20.01 | % 135.98/20.01 End of proof % 135.98/20.01 % 135.98/20.01 Sub-proof #115 shows that the following formulas are inconsistent: % 135.98/20.01 ---------------------------------------------------------------- % 135.98/20.01 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.01 (2) op(e2, e2) = e1 % 135.98/20.01 (3) op(e0, e3) = e3 % 135.98/20.01 (4) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.98/20.01 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.98/20.01 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.98/20.01 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.98/20.01 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 135.98/20.01 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 135.98/20.01 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 135.98/20.01 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 135.98/20.01 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.98/20.01 $i(all_56_17) & $i(all_56_25)) % 135.98/20.01 (5) ~ (e3 = e1) % 135.98/20.01 % 135.98/20.01 Begin of proof % 135.98/20.01 | % 135.98/20.01 | BETA: splitting (4) gives: % 135.98/20.01 | % 135.98/20.01 | Case 1: % 135.98/20.01 | | % 135.98/20.01 | | (6) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 135.98/20.01 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 135.98/20.01 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 135.98/20.01 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 135.98/20.01 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 135.98/20.01 | | % 135.98/20.01 | | ALPHA: (6) implies: % 135.98/20.01 | | (7) ~ (all_56_7 = e3) % 135.98/20.01 | | (8) op(e0, e3) = all_56_7 % 135.98/20.01 | | % 135.98/20.01 | | REF_CLOSE: (1), (3), (7), (8) are inconsistent by sub-proof #209. % 135.98/20.01 | | % 135.98/20.01 | Case 2: % 135.98/20.01 | | % 135.98/20.01 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.98/20.01 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.98/20.01 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.98/20.01 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) % 135.98/20.01 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 135.98/20.01 | | % 135.98/20.01 | | ALPHA: (9) implies: % 135.98/20.01 | | (10) op(e2, e2) = e3 % 135.98/20.01 | | % 135.98/20.01 | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #325. % 135.98/20.01 | | % 135.98/20.01 | End of split % 135.98/20.01 | % 135.98/20.01 End of proof % 135.98/20.01 % 135.98/20.01 Sub-proof #116 shows that the following formulas are inconsistent: % 135.98/20.01 ---------------------------------------------------------------- % 135.98/20.01 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 135.98/20.01 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 135.98/20.01 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.98/20.01 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.98/20.01 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 135.98/20.01 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.98/20.01 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 135.98/20.01 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.98/20.01 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 135.98/20.01 $i(all_56_21) & $i(all_56_29)) % 135.98/20.01 (2) ~ (all_52_4 = e0) % 135.98/20.01 (3) ~ (e2 = e0) % 135.98/20.01 (4) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 135.98/20.01 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 135.98/20.01 (5) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 135.98/20.01 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 135.98/20.01 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.01 (7) ~ (e2 = e1) % 135.98/20.01 (8) ~ (e3 = e0) % 135.98/20.01 (9) ~ (e3 = e2) % 135.98/20.01 (10) all_57_2 = e2 % 135.98/20.01 (11) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 135.98/20.01 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 135.98/20.01 (12) all_57_12 = e3 % 135.98/20.01 (13) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 135.98/20.01 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 135.98/20.01 (14) op(e3, e2) = all_52_4 % 135.98/20.01 (15) all_57_9 = e1 % 135.98/20.01 (16) ~ (e3 = e1) % 135.98/20.01 (17) ~ (e1 = e0) % 135.98/20.01 (18) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 135.98/20.01 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 135.98/20.01 % 135.98/20.01 Begin of proof % 135.98/20.01 | % 135.98/20.01 | BETA: splitting (1) gives: % 135.98/20.01 | % 135.98/20.01 | Case 1: % 135.98/20.01 | | % 135.98/20.01 | | (19) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.98/20.01 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 % 135.98/20.01 | | & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 135.98/20.01 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 135.98/20.01 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 135.98/20.01 | | % 135.98/20.01 | | ALPHA: (19) implies: % 135.98/20.01 | | (20) op(e3, e3) = e2 % 135.98/20.01 | | % 135.98/20.01 | | REF_CLOSE: (3), (5), (6), (7), (8), (10), (12), (13), (16), (17), (20) are % 135.98/20.01 | | inconsistent by sub-proof #489. % 135.98/20.01 | | % 135.98/20.01 | Case 2: % 135.98/20.01 | | % 135.98/20.01 | | (21) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.98/20.01 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = % 135.98/20.01 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 135.98/20.01 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 135.98/20.01 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 135.98/20.01 | | % 135.98/20.01 | | ALPHA: (21) implies: % 135.98/20.01 | | (22) op(e3, e3) = e1 % 135.98/20.01 | | % 135.98/20.01 | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (11), (14), (15), (16), (17), % 135.98/20.01 | | (18), (22) are inconsistent by sub-proof #686. % 135.98/20.01 | | % 135.98/20.01 | End of split % 135.98/20.01 | % 135.98/20.01 End of proof % 135.98/20.01 % 135.98/20.01 Sub-proof #117 shows that the following formulas are inconsistent: % 135.98/20.01 ---------------------------------------------------------------- % 135.98/20.01 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.01 (2) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) % 135.98/20.01 (3) op(e3, e2) = all_52_4 % 135.98/20.01 (4) op(e3, e3) = e0 % 135.98/20.01 (5) ~ (e1 = e0) % 135.98/20.01 (6) ~ (all_52_4 = e1) % 135.98/20.01 % 135.98/20.01 Begin of proof % 135.98/20.01 | % 135.98/20.01 | BETA: splitting (2) gives: % 135.98/20.01 | % 135.98/20.01 | Case 1: % 135.98/20.01 | | % 135.98/20.01 | | (7) all_57_0 = e1 & op(e3, e3) = e1 % 135.98/20.01 | | % 135.98/20.01 | | ALPHA: (7) implies: % 135.98/20.01 | | (8) op(e3, e3) = e1 % 135.98/20.01 | | % 135.98/20.01 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #717. % 135.98/20.01 | | % 135.98/20.01 | Case 2: % 135.98/20.01 | | % 135.98/20.01 | | (9) all_57_1 = e1 & op(e3, e2) = e1 % 135.98/20.01 | | % 135.98/20.01 | | REF_CLOSE: (1), (3), (6), (9) are inconsistent by sub-proof #684. % 135.98/20.01 | | % 135.98/20.01 | End of split % 135.98/20.01 | % 135.98/20.01 End of proof % 135.98/20.01 % 135.98/20.01 Sub-proof #118 shows that the following formulas are inconsistent: % 135.98/20.01 ---------------------------------------------------------------- % 135.98/20.01 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.01 (2) ~ (all_52_1 = e1) % 135.98/20.01 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) % 135.98/20.01 (4) op(e2, e3) = all_52_1 % 135.98/20.01 (5) op(e3, e3) = e0 % 135.98/20.01 (6) ~ (e1 = e0) % 135.98/20.01 % 135.98/20.01 Begin of proof % 135.98/20.01 | % 135.98/20.01 | BETA: splitting (3) gives: % 135.98/20.01 | % 135.98/20.01 | Case 1: % 135.98/20.01 | | % 135.98/20.01 | | (7) all_57_0 = e1 & op(e3, e3) = e1 % 135.98/20.01 | | % 135.98/20.01 | | ALPHA: (7) implies: % 135.98/20.01 | | (8) op(e3, e3) = e1 % 135.98/20.01 | | % 135.98/20.01 | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #717. % 135.98/20.01 | | % 135.98/20.01 | Case 2: % 135.98/20.01 | | % 135.98/20.01 | | (9) all_57_2 = e1 & op(e2, e3) = e1 % 135.98/20.01 | | % 135.98/20.01 | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #676. % 135.98/20.01 | | % 135.98/20.01 | End of split % 135.98/20.01 | % 135.98/20.01 End of proof % 135.98/20.01 % 135.98/20.01 Sub-proof #119 shows that the following formulas are inconsistent: % 135.98/20.01 ---------------------------------------------------------------- % 135.98/20.02 (1) all_54_7 = all_20_0 % 135.98/20.02 (2) all_54_7 = e3 % 135.98/20.02 (3) ~ (all_20_0 = e3) % 135.98/20.02 % 135.98/20.02 Begin of proof % 135.98/20.02 | % 135.98/20.02 | COMBINE_EQS: (1), (2) imply: % 135.98/20.02 | (4) all_20_0 = e3 % 135.98/20.02 | % 135.98/20.02 | SIMP: (4) implies: % 135.98/20.02 | (5) all_20_0 = e3 % 135.98/20.02 | % 135.98/20.02 | REDUCE: (3), (5) imply: % 135.98/20.02 | (6) $false % 135.98/20.02 | % 135.98/20.02 | CLOSE: (6) is inconsistent. % 135.98/20.02 | % 135.98/20.02 End of proof % 135.98/20.02 % 135.98/20.02 Sub-proof #120 shows that the following formulas are inconsistent: % 135.98/20.02 ---------------------------------------------------------------- % 135.98/20.02 (1) ~ (all_24_0 = e1) % 135.98/20.02 (2) ~ (all_24_0 = e2) % 135.98/20.02 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 135.98/20.02 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 135.98/20.02 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.02 (5) all_54_12 = all_24_0 % 135.98/20.02 (6) op(e0, e1) = all_52_11 % 135.98/20.02 (7) op(e0, e2) = all_52_7 % 135.98/20.02 (8) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 135.98/20.02 (9) ~ (all_52_11 = all_24_0) % 135.98/20.02 (10) ~ (all_24_0 = e0) % 135.98/20.02 (11) ~ (all_52_7 = all_24_0) % 135.98/20.02 (12) op(e0, e0) = e2 % 135.98/20.02 (13) all_57_12 = e1 % 135.98/20.02 % 135.98/20.02 Begin of proof % 135.98/20.02 | % 135.98/20.02 | BETA: splitting (8) gives: % 135.98/20.02 | % 135.98/20.02 | Case 1: % 135.98/20.02 | | % 135.98/20.02 | | (14) all_54_12 = e3 % 135.98/20.02 | | % 135.98/20.02 | | COMBINE_EQS: (5), (14) imply: % 135.98/20.02 | | (15) all_24_0 = e3 % 135.98/20.02 | | % 135.98/20.02 | | SIMP: (15) implies: % 135.98/20.02 | | (16) all_24_0 = e3 % 135.98/20.02 | | % 135.98/20.02 | | REDUCE: (11), (16) imply: % 135.98/20.02 | | (17) ~ (all_52_7 = e3) % 135.98/20.02 | | % 135.98/20.02 | | REDUCE: (9), (16) imply: % 135.98/20.02 | | (18) ~ (all_52_11 = e3) % 135.98/20.02 | | % 135.98/20.02 | | REDUCE: (2), (16) imply: % 135.98/20.02 | | (19) ~ (e3 = e2) % 135.98/20.02 | | % 135.98/20.02 | | REDUCE: (1), (16) imply: % 135.98/20.02 | | (20) ~ (e3 = e1) % 135.98/20.02 | | % 135.98/20.02 | | REF_CLOSE: (3), (4), (6), (7), (12), (13), (17), (18), (19), (20) are % 135.98/20.02 | | inconsistent by sub-proof #123. % 135.98/20.02 | | % 135.98/20.02 | Case 2: % 135.98/20.02 | | % 135.98/20.02 | | (21) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 135.98/20.02 | | % 135.98/20.02 | | REF_CLOSE: (1), (2), (5), (10), (21) are inconsistent by sub-proof #205. % 135.98/20.02 | | % 135.98/20.02 | End of split % 135.98/20.02 | % 135.98/20.02 End of proof % 135.98/20.02 % 135.98/20.02 Sub-proof #121 shows that the following formulas are inconsistent: % 135.98/20.02 ---------------------------------------------------------------- % 135.98/20.02 (1) all_54_8 = all_52_2 % 135.98/20.02 (2) all_54_8 = e3 % 135.98/20.02 (3) ~ (all_52_2 = e3) % 135.98/20.02 % 135.98/20.02 Begin of proof % 135.98/20.02 | % 135.98/20.02 | COMBINE_EQS: (1), (2) imply: % 135.98/20.02 | (4) all_52_2 = e3 % 135.98/20.02 | % 135.98/20.02 | SIMP: (4) implies: % 135.98/20.02 | (5) all_52_2 = e3 % 135.98/20.02 | % 135.98/20.02 | REDUCE: (3), (5) imply: % 135.98/20.02 | (6) $false % 135.98/20.02 | % 135.98/20.02 | CLOSE: (6) is inconsistent. % 135.98/20.02 | % 135.98/20.02 End of proof % 135.98/20.02 % 135.98/20.02 Sub-proof #122 shows that the following formulas are inconsistent: % 135.98/20.02 ---------------------------------------------------------------- % 135.98/20.02 (1) all_57_13 = e2 & op(e0, e2) = e2 % 135.98/20.02 (2) all_57_13 = e0 % 135.98/20.02 (3) ~ (e2 = e0) % 135.98/20.02 % 135.98/20.02 Begin of proof % 135.98/20.02 | % 135.98/20.02 | ALPHA: (1) implies: % 135.98/20.02 | (4) all_57_13 = e2 % 135.98/20.02 | % 135.98/20.02 | COMBINE_EQS: (2), (4) imply: % 135.98/20.02 | (5) e2 = e0 % 135.98/20.02 | % 135.98/20.02 | REDUCE: (3), (5) imply: % 135.98/20.02 | (6) $false % 135.98/20.02 | % 135.98/20.02 | CLOSE: (6) is inconsistent. % 135.98/20.02 | % 135.98/20.02 End of proof % 135.98/20.02 % 135.98/20.02 Sub-proof #123 shows that the following formulas are inconsistent: % 135.98/20.02 ---------------------------------------------------------------- % 135.98/20.02 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 135.98/20.02 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 135.98/20.02 (2) ~ (all_52_7 = e3) % 135.98/20.02 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.02 (4) ~ (e3 = e2) % 135.98/20.02 (5) op(e0, e1) = all_52_11 % 135.98/20.02 (6) op(e0, e2) = all_52_7 % 135.98/20.02 (7) ~ (all_52_11 = e3) % 135.98/20.02 (8) op(e0, e0) = e2 % 135.98/20.02 (9) ~ (e3 = e1) % 135.98/20.02 (10) all_57_12 = e1 % 135.98/20.02 % 135.98/20.02 Begin of proof % 135.98/20.02 | % 135.98/20.02 | BETA: splitting (1) gives: % 135.98/20.02 | % 135.98/20.02 | Case 1: % 135.98/20.02 | | % 135.98/20.02 | | (11) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = % 135.98/20.02 | | e3) % 135.98/20.02 | | % 135.98/20.02 | | BETA: splitting (11) gives: % 135.98/20.02 | | % 135.98/20.02 | | Case 1: % 135.98/20.02 | | | % 135.98/20.02 | | | (12) all_57_12 = e3 & op(e0, e3) = e3 % 135.98/20.02 | | | % 135.98/20.02 | | | REF_CLOSE: (9), (10), (12) are inconsistent by sub-proof #394. % 135.98/20.02 | | | % 135.98/20.02 | | Case 2: % 135.98/20.02 | | | % 135.98/20.02 | | | (13) all_57_13 = e3 & op(e0, e2) = e3 % 135.98/20.02 | | | % 135.98/20.02 | | | REF_CLOSE: (2), (3), (6), (13) are inconsistent by sub-proof #556. % 135.98/20.02 | | | % 135.98/20.02 | | End of split % 135.98/20.02 | | % 135.98/20.02 | Case 2: % 135.98/20.02 | | % 135.98/20.02 | | (14) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = % 135.98/20.02 | | e3) % 135.98/20.02 | | % 135.98/20.02 | | REF_CLOSE: (3), (4), (5), (7), (8), (14) are inconsistent by sub-proof #459. % 135.98/20.02 | | % 135.98/20.02 | End of split % 135.98/20.02 | % 135.98/20.02 End of proof % 135.98/20.02 % 135.98/20.02 Sub-proof #124 shows that the following formulas are inconsistent: % 135.98/20.02 ---------------------------------------------------------------- % 135.98/20.02 (1) op(e1, e1) = all_6_2 % 135.98/20.02 (2) ~ (all_6_2 = e3) % 135.98/20.02 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.02 (4) all_54_10 = all_6_2 % 135.98/20.02 (5) ~ (all_6_2 = e2) % 135.98/20.02 (6) ~ (all_6_2 = e0) % 135.98/20.02 (7) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 135.98/20.02 (8) ~ (all_56_21 = e1) % 135.98/20.02 (9) op(e1, e1) = all_56_21 % 135.98/20.02 % 135.98/20.02 Begin of proof % 135.98/20.02 | % 135.98/20.02 | BETA: splitting (7) gives: % 135.98/20.02 | % 135.98/20.02 | Case 1: % 135.98/20.02 | | % 135.98/20.02 | | (10) all_54_10 = e3 % 135.98/20.02 | | % 135.98/20.02 | | REF_CLOSE: (2), (4), (10) are inconsistent by sub-proof #742. % 135.98/20.02 | | % 135.98/20.02 | Case 2: % 135.98/20.02 | | % 135.98/20.02 | | (11) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 135.98/20.02 | | % 135.98/20.02 | | BETA: splitting (11) gives: % 135.98/20.02 | | % 135.98/20.02 | | Case 1: % 135.98/20.02 | | | % 135.98/20.02 | | | (12) all_54_10 = e2 % 135.98/20.02 | | | % 135.98/20.02 | | | REF_CLOSE: (4), (5), (12) are inconsistent by sub-proof #741. % 135.98/20.02 | | | % 135.98/20.02 | | Case 2: % 135.98/20.02 | | | % 135.98/20.02 | | | (13) all_54_10 = e1 | all_54_10 = e0 % 135.98/20.02 | | | % 135.98/20.02 | | | BETA: splitting (13) gives: % 135.98/20.02 | | | % 135.98/20.02 | | | Case 1: % 135.98/20.02 | | | | % 135.98/20.02 | | | | (14) all_54_10 = e1 % 135.98/20.02 | | | | % 135.98/20.02 | | | | COMBINE_EQS: (4), (14) imply: % 135.98/20.02 | | | | (15) all_6_2 = e1 % 135.98/20.02 | | | | % 135.98/20.02 | | | | SIMP: (15) implies: % 135.98/20.02 | | | | (16) all_6_2 = e1 % 135.98/20.02 | | | | % 135.98/20.02 | | | | REDUCE: (1), (16) imply: % 135.98/20.02 | | | | (17) op(e1, e1) = e1 % 135.98/20.02 | | | | % 135.98/20.02 | | | | REF_CLOSE: (3), (8), (9), (17) are inconsistent by sub-proof #510. % 135.98/20.02 | | | | % 135.98/20.02 | | | Case 2: % 135.98/20.02 | | | | % 135.98/20.02 | | | | (18) all_54_10 = e0 % 135.98/20.02 | | | | % 135.98/20.02 | | | | REF_CLOSE: (4), (6), (18) are inconsistent by sub-proof #506. % 135.98/20.02 | | | | % 135.98/20.02 | | | End of split % 135.98/20.02 | | | % 135.98/20.02 | | End of split % 135.98/20.02 | | % 135.98/20.02 | End of split % 135.98/20.02 | % 135.98/20.02 End of proof % 135.98/20.02 % 135.98/20.02 Sub-proof #125 shows that the following formulas are inconsistent: % 135.98/20.02 ---------------------------------------------------------------- % 135.98/20.02 (1) ~ (all_38_1 = e1) & op(e2, e2) = all_38_1 & $i(all_38_1) % 135.98/20.02 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.02 (3) op(e2, e2) = e1 % 135.98/20.02 % 135.98/20.02 Begin of proof % 135.98/20.02 | % 135.98/20.02 | ALPHA: (1) implies: % 135.98/20.02 | (4) ~ (all_38_1 = e1) % 135.98/20.02 | (5) op(e2, e2) = all_38_1 % 135.98/20.02 | % 135.98/20.02 | GROUND_INST: instantiating (2) with e1, all_38_1, e2, e2, simplifying with % 135.98/20.02 | (3), (5) gives: % 135.98/20.02 | (6) all_38_1 = e1 % 135.98/20.02 | % 135.98/20.02 | REDUCE: (4), (6) imply: % 135.98/20.02 | (7) $false % 135.98/20.02 | % 135.98/20.02 | CLOSE: (7) is inconsistent. % 135.98/20.02 | % 135.98/20.02 End of proof % 135.98/20.02 % 135.98/20.02 Sub-proof #126 shows that the following formulas are inconsistent: % 135.98/20.02 ---------------------------------------------------------------- % 135.98/20.02 (1) ~ (all_38_0 = e1) % 135.98/20.02 (2) ~ (all_38_0 = e2) % 135.98/20.02 (3) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 135.98/20.02 (4) ~ (all_38_0 = e0) % 135.98/20.02 (5) all_54_4 = all_38_0 % 135.98/20.02 % 135.98/20.02 Begin of proof % 135.98/20.02 | % 135.98/20.02 | BETA: splitting (3) gives: % 135.98/20.02 | % 135.98/20.02 | Case 1: % 135.98/20.02 | | % 135.98/20.02 | | (6) all_54_4 = e2 % 135.98/20.02 | | % 135.98/20.02 | | COMBINE_EQS: (5), (6) imply: % 135.98/20.02 | | (7) all_38_0 = e2 % 135.98/20.02 | | % 135.98/20.02 | | SIMP: (7) implies: % 135.98/20.02 | | (8) all_38_0 = e2 % 135.98/20.02 | | % 135.98/20.02 | | REDUCE: (2), (8) imply: % 135.98/20.02 | | (9) $false % 135.98/20.02 | | % 135.98/20.02 | | CLOSE: (9) is inconsistent. % 135.98/20.02 | | % 135.98/20.02 | Case 2: % 135.98/20.02 | | % 135.98/20.02 | | (10) all_54_4 = e1 | all_54_4 = e0 % 135.98/20.02 | | % 135.98/20.02 | | BETA: splitting (10) gives: % 135.98/20.02 | | % 135.98/20.02 | | Case 1: % 135.98/20.02 | | | % 135.98/20.02 | | | (11) all_54_4 = e1 % 135.98/20.02 | | | % 135.98/20.02 | | | COMBINE_EQS: (5), (11) imply: % 135.98/20.02 | | | (12) all_38_0 = e1 % 135.98/20.02 | | | % 135.98/20.02 | | | SIMP: (12) implies: % 135.98/20.02 | | | (13) all_38_0 = e1 % 135.98/20.02 | | | % 135.98/20.02 | | | REDUCE: (1), (13) imply: % 135.98/20.02 | | | (14) $false % 135.98/20.02 | | | % 135.98/20.02 | | | CLOSE: (14) is inconsistent. % 135.98/20.02 | | | % 135.98/20.02 | | Case 2: % 135.98/20.02 | | | % 135.98/20.02 | | | (15) all_54_4 = e0 % 135.98/20.02 | | | % 135.98/20.02 | | | COMBINE_EQS: (5), (15) imply: % 135.98/20.02 | | | (16) all_38_0 = e0 % 135.98/20.02 | | | % 135.98/20.02 | | | SIMP: (16) implies: % 135.98/20.02 | | | (17) all_38_0 = e0 % 135.98/20.02 | | | % 135.98/20.02 | | | REDUCE: (4), (17) imply: % 135.98/20.02 | | | (18) $false % 135.98/20.02 | | | % 135.98/20.02 | | | CLOSE: (18) is inconsistent. % 135.98/20.02 | | | % 135.98/20.02 | | End of split % 135.98/20.02 | | % 135.98/20.02 | End of split % 135.98/20.02 | % 135.98/20.02 End of proof % 135.98/20.02 % 135.98/20.02 Sub-proof #127 shows that the following formulas are inconsistent: % 135.98/20.02 ---------------------------------------------------------------- % 135.98/20.02 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.02 (2) ~ (e2 = e1) % 135.98/20.02 (3) all_57_3 = e1 % 135.98/20.02 (4) ~ (all_52_1 = e2) % 135.98/20.02 (5) op(e2, e3) = all_52_1 % 135.98/20.02 (6) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) % 135.98/20.02 % 135.98/20.02 Begin of proof % 135.98/20.02 | % 135.98/20.02 | BETA: splitting (6) gives: % 135.98/20.02 | % 135.98/20.02 | Case 1: % 135.98/20.02 | | % 135.98/20.02 | | (7) all_57_2 = e2 & op(e2, e3) = e2 % 135.98/20.02 | | % 135.98/20.02 | | ALPHA: (7) implies: % 135.98/20.02 | | (8) op(e2, e3) = e2 % 135.98/20.02 | | % 135.98/20.02 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #779. % 135.98/20.02 | | % 135.98/20.02 | Case 2: % 135.98/20.02 | | % 135.98/20.02 | | (9) all_57_3 = e2 & op(e2, e2) = e2 % 135.98/20.02 | | % 135.98/20.02 | | ALPHA: (9) implies: % 135.98/20.02 | | (10) all_57_3 = e2 % 135.98/20.02 | | % 135.98/20.02 | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #728. % 135.98/20.02 | | % 135.98/20.02 | End of split % 135.98/20.02 | % 135.98/20.02 End of proof % 135.98/20.02 % 135.98/20.02 Sub-proof #128 shows that the following formulas are inconsistent: % 135.98/20.02 ---------------------------------------------------------------- % 135.98/20.02 (1) ~ (all_8_1 = e3) & op(e1, e1) = all_8_1 & $i(all_8_1) % 135.98/20.02 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.02 (3) op(e1, e1) = e3 % 135.98/20.02 % 135.98/20.02 Begin of proof % 135.98/20.02 | % 135.98/20.02 | ALPHA: (1) implies: % 135.98/20.02 | (4) ~ (all_8_1 = e3) % 135.98/20.02 | (5) op(e1, e1) = all_8_1 % 135.98/20.02 | % 135.98/20.02 | GROUND_INST: instantiating (2) with e3, all_8_1, e1, e1, simplifying with (3), % 135.98/20.02 | (5) gives: % 135.98/20.02 | (6) all_8_1 = e3 % 135.98/20.02 | % 135.98/20.02 | REDUCE: (4), (6) imply: % 135.98/20.02 | (7) $false % 135.98/20.02 | % 135.98/20.02 | CLOSE: (7) is inconsistent. % 135.98/20.02 | % 135.98/20.02 End of proof % 135.98/20.02 % 135.98/20.02 Sub-proof #129 shows that the following formulas are inconsistent: % 135.98/20.02 ---------------------------------------------------------------- % 135.98/20.02 (1) all_57_11 = e0 & op(e1, e0) = e0 % 135.98/20.02 (2) all_57_11 = e3 % 135.98/20.02 (3) ~ (e3 = e0) % 135.98/20.02 % 135.98/20.02 Begin of proof % 135.98/20.02 | % 135.98/20.02 | ALPHA: (1) implies: % 135.98/20.02 | (4) all_57_11 = e0 % 135.98/20.02 | % 135.98/20.02 | COMBINE_EQS: (2), (4) imply: % 135.98/20.02 | (5) e3 = e0 % 135.98/20.02 | % 135.98/20.02 | REDUCE: (3), (5) imply: % 135.98/20.02 | (6) $false % 135.98/20.02 | % 135.98/20.02 | CLOSE: (6) is inconsistent. % 135.98/20.02 | % 135.98/20.02 End of proof % 135.98/20.02 % 135.98/20.02 Sub-proof #130 shows that the following formulas are inconsistent: % 135.98/20.02 ---------------------------------------------------------------- % 135.98/20.02 (1) all_57_6 = e1 & op(e1, e3) = e1 % 135.98/20.02 (2) all_57_6 = e0 % 135.98/20.02 (3) ~ (e1 = e0) % 135.98/20.02 % 135.98/20.02 Begin of proof % 135.98/20.02 | % 135.98/20.02 | ALPHA: (1) implies: % 135.98/20.02 | (4) all_57_6 = e1 % 135.98/20.02 | % 135.98/20.02 | COMBINE_EQS: (2), (4) imply: % 135.98/20.02 | (5) e1 = e0 % 135.98/20.02 | % 135.98/20.02 | REDUCE: (3), (5) imply: % 135.98/20.02 | (6) $false % 135.98/20.02 | % 135.98/20.02 | CLOSE: (6) is inconsistent. % 135.98/20.02 | % 135.98/20.02 End of proof % 135.98/20.02 % 135.98/20.02 Sub-proof #131 shows that the following formulas are inconsistent: % 135.98/20.02 ---------------------------------------------------------------- % 135.98/20.02 (1) op(e1, e1) = all_6_2 % 135.98/20.02 (2) op(e1, e2) = e2 % 135.98/20.02 (3) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 135.98/20.02 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.98/20.02 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 135.98/20.02 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.98/20.02 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ % 135.98/20.02 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.98/20.02 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = % 135.98/20.02 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.98/20.02 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.98/20.02 $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) % 135.98/20.02 & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.98/20.02 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) % 135.98/20.02 = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 135.98/20.02 $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 135.98/20.02 (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.98/20.02 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.98/20.02 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) % 135.98/20.02 = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 135.98/20.02 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 135.98/20.02 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 135.98/20.02 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 135.98/20.02 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 135.98/20.02 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.98/20.02 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.98/20.02 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 135.98/20.02 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 135.98/20.02 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 135.98/20.02 e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 135.98/20.02 & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 % 135.98/20.02 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 135.98/20.02 ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) % 135.98/20.02 = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.98/20.02 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & % 135.98/20.02 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.98/20.02 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 135.98/20.02 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.98/20.02 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.98/20.02 $i(all_56_21) & $i(all_56_29)))) % 135.98/20.02 (4) op(e3, e1) = e1 % 135.98/20.02 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.02 (6) ~ (e3 = e0) % 135.98/20.02 (7) op(e2, e2) = e1 % 135.98/20.02 (8) op(e1, e1) = e3 % 135.98/20.02 (9) ~ (all_6_2 = e2) % 135.98/20.02 (10) op(e2, e3) = e3 % 135.98/20.02 (11) ~ (e1 = e0) % 135.98/20.02 % 135.98/20.02 Begin of proof % 135.98/20.02 | % 135.98/20.02 | BETA: splitting (3) gives: % 135.98/20.02 | % 135.98/20.02 | Case 1: % 135.98/20.02 | | % 135.98/20.02 | | (12) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 135.98/20.02 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.98/20.02 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.98/20.02 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & % 135.98/20.02 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.98/20.02 | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 135.98/20.02 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 135.98/20.02 | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, % 135.98/20.02 | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 135.98/20.02 | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.98/20.02 | | $i(all_56_29)) % 135.98/20.02 | | % 135.98/20.02 | | REF_CLOSE: (2), (4), (5), (12) are inconsistent by sub-proof #132. % 135.98/20.02 | | % 135.98/20.02 | Case 2: % 135.98/20.02 | | % 135.98/20.02 | | (13) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.98/20.02 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.98/20.02 | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 135.98/20.02 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.98/20.02 | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.98/20.02 | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 135.98/20.02 | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 135.98/20.02 | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.98/20.02 | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 135.98/20.02 | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.98/20.02 | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.98/20.02 | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.98/20.02 | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 135.98/20.02 | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 135.98/20.02 | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.98/20.02 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.98/20.02 | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.98/20.02 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.98/20.02 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.98/20.02 | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.98/20.02 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 135.98/20.02 | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.98/20.02 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.98/20.02 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.98/20.02 | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 135.98/20.02 | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.98/20.02 | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.98/20.02 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 % 135.98/20.02 | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.98/20.02 | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.98/20.02 | | $i(all_56_21) & $i(all_56_29)))) % 135.98/20.02 | | % 135.98/20.02 | | BETA: splitting (13) gives: % 135.98/20.02 | | % 135.98/20.02 | | Case 1: % 135.98/20.02 | | | % 135.98/20.02 | | | (14) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 135.98/20.02 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.98/20.02 | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 135.98/20.02 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 135.98/20.02 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 135.98/20.02 | | | $i(all_56_31) % 135.98/20.02 | | | % 135.98/20.02 | | | ALPHA: (14) implies: % 135.98/20.02 | | | (15) op(e2, e2) = e0 % 135.98/20.02 | | | % 135.98/20.02 | | | REF_CLOSE: (5), (7), (11), (15) are inconsistent by sub-proof #675. % 135.98/20.02 | | | % 135.98/20.02 | | Case 2: % 135.98/20.02 | | | % 135.98/20.02 | | | (16) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.98/20.02 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.98/20.02 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.98/20.02 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.98/20.02 | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.98/20.02 | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 135.98/20.02 | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.98/20.02 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) % 135.98/20.02 | | | & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 135.98/20.02 | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.98/20.02 | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 135.98/20.02 | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.98/20.02 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) % 135.98/20.02 | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.98/20.02 | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 % 135.98/20.02 | | | & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.98/20.02 | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 135.98/20.02 | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.98/20.02 | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & % 135.98/20.02 | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) % 135.98/20.02 | | | = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.98/20.02 | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.98/20.02 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) % 135.98/20.02 | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, % 135.98/20.02 | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 % 135.98/20.02 | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.98/20.02 | | | $i(all_56_29)))) % 135.98/20.02 | | | % 135.98/20.02 | | | BETA: splitting (16) gives: % 135.98/20.02 | | | % 135.98/20.02 | | | Case 1: % 135.98/20.02 | | | | % 135.98/20.02 | | | | (17) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 135.98/20.02 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.98/20.02 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.98/20.02 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 135.98/20.02 | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.98/20.02 | | | | $i(all_56_27) % 135.98/20.02 | | | | % 135.98/20.02 | | | | ALPHA: (17) implies: % 135.98/20.02 | | | | (18) op(e1, e1) = e2 % 135.98/20.02 | | | | % 135.98/20.02 | | | | REF_CLOSE: (1), (5), (9), (18) are inconsistent by sub-proof #767. % 135.98/20.02 | | | | % 135.98/20.02 | | | Case 2: % 135.98/20.02 | | | | % 135.98/20.02 | | | | (19) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 135.98/20.02 | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & % 135.98/20.02 | | | | ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.98/20.02 | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 135.98/20.02 | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & % 135.98/20.02 | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 135.98/20.02 | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 135.98/20.02 | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, % 135.98/20.02 | | | | e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.98/20.02 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.98/20.02 | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.98/20.02 | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 135.98/20.02 | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 135.98/20.02 | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & % 135.98/20.02 | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) % 135.98/20.02 | | | | = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 135.98/20.02 | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.98/20.02 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) % 135.98/20.02 | | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, % 135.98/20.02 | | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 % 135.98/20.02 | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.98/20.02 | | | | $i(all_56_29))) % 135.98/20.02 | | | | % 135.98/20.02 | | | | ALPHA: (19) implies: % 135.98/20.02 | | | | (20) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.98/20.02 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 135.98/20.02 | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 135.98/20.02 | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.98/20.02 | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 135.98/20.02 | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.98/20.02 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 135.98/20.02 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 135.98/20.02 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 135.98/20.02 | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 135.98/20.02 | | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.98/20.02 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 135.98/20.02 | | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 135.98/20.02 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 135.98/20.02 | | | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 135.98/20.02 | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 135.98/20.02 | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 % 135.98/20.02 | | | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.98/20.02 | | | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 135.98/20.02 | | | | $i(all_56_21) & $i(all_56_29)) % 135.98/20.02 | | | | % 135.98/20.02 | | | | BETA: splitting (20) gives: % 135.98/20.02 | | | | % 135.98/20.02 | | | | Case 1: % 135.98/20.02 | | | | | % 135.98/20.02 | | | | | (21) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 135.98/20.02 | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) % 135.98/20.02 | | | | | & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 135.98/20.02 | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 135.98/20.02 | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 135.98/20.02 | | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 135.98/20.02 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) % 135.98/20.02 | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 135.98/20.02 | | | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 % 135.98/20.02 | | | | | & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 135.98/20.02 | | | | | $i(all_56_27)) % 135.98/20.02 | | | | | % 135.98/20.02 | | | | | REF_CLOSE: (4), (5), (10), (21) are inconsistent by sub-proof #346. % 135.98/20.02 | | | | | % 135.98/20.02 | | | | Case 2: % 135.98/20.02 | | | | | % 135.98/20.02 | | | | | (22) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.98/20.02 | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) % 135.98/20.02 | | | | | & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 % 135.98/20.02 | | | | | & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.98/20.02 | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = % 135.98/20.02 | | | | | e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 135.98/20.02 | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, % 135.98/20.02 | | | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 135.98/20.02 | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 135.98/20.02 | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.98/20.02 | | | | | $i(all_56_29)) % 135.98/20.02 | | | | | % 135.98/20.02 | | | | | BETA: splitting (22) gives: % 135.98/20.02 | | | | | % 135.98/20.02 | | | | | Case 1: % 135.98/20.02 | | | | | | % 135.98/20.03 | | | | | | (23) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 135.98/20.03 | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) % 135.98/20.03 | | | | | | & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 % 135.98/20.03 | | | | | | & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 135.98/20.03 | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) % 135.98/20.03 | | | | | | % 135.98/20.03 | | | | | | ALPHA: (23) implies: % 135.98/20.03 | | | | | | (24) op(e1, e1) = e0 % 135.98/20.03 | | | | | | % 135.98/20.03 | | | | | | REF_CLOSE: (5), (6), (8), (24) are inconsistent by sub-proof #753. % 135.98/20.03 | | | | | | % 135.98/20.03 | | | | | Case 2: % 135.98/20.03 | | | | | | % 135.98/20.03 | | | | | | (25) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 135.98/20.03 | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) % 135.98/20.03 | | | | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, % 135.98/20.03 | | | | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 % 135.98/20.03 | | | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.98/20.03 | | | | | | $i(all_56_29) % 135.98/20.03 | | | | | | % 135.98/20.03 | | | | | | ALPHA: (25) implies: % 135.98/20.03 | | | | | | (26) ~ (all_56_13 = e2) % 135.98/20.03 | | | | | | (27) op(e1, e2) = all_56_13 % 135.98/20.03 | | | | | | % 135.98/20.03 | | | | | | REF_CLOSE: (2), (5), (26), (27) are inconsistent by sub-proof #165. % 135.98/20.03 | | | | | | % 135.98/20.03 | | | | | End of split % 135.98/20.03 | | | | | % 135.98/20.03 | | | | End of split % 135.98/20.03 | | | | % 135.98/20.03 | | | End of split % 135.98/20.03 | | | % 135.98/20.03 | | End of split % 135.98/20.03 | | % 135.98/20.03 | End of split % 135.98/20.03 | % 135.98/20.03 End of proof % 135.98/20.03 % 135.98/20.03 Sub-proof #132 shows that the following formulas are inconsistent: % 135.98/20.03 ---------------------------------------------------------------- % 135.98/20.03 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 135.98/20.03 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 135.98/20.03 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 135.98/20.03 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 135.98/20.03 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ % 135.98/20.03 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 135.98/20.03 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = % 135.98/20.03 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 135.98/20.03 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 135.98/20.03 $i(all_56_29)) % 135.98/20.03 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.03 (3) op(e3, e1) = e1 % 135.98/20.03 (4) op(e1, e2) = e2 % 135.98/20.03 % 135.98/20.03 Begin of proof % 135.98/20.03 | % 135.98/20.03 | BETA: splitting (1) gives: % 135.98/20.03 | % 135.98/20.03 | Case 1: % 135.98/20.03 | | % 135.98/20.03 | | (5) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 135.98/20.03 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 135.98/20.03 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 135.98/20.03 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) % 135.98/20.03 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 135.98/20.03 | | % 135.98/20.03 | | ALPHA: (5) implies: % 135.98/20.03 | | (6) ~ (all_56_17 = e1) % 135.98/20.03 | | (7) op(e3, e1) = all_56_17 % 135.98/20.03 | | % 135.98/20.03 | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #349. % 135.98/20.03 | | % 135.98/20.03 | Case 2: % 135.98/20.03 | | % 135.98/20.03 | | (8) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 % 135.98/20.03 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 % 135.98/20.03 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 135.98/20.03 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 135.98/20.03 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 135.98/20.03 | | % 135.98/20.03 | | ALPHA: (8) implies: % 135.98/20.03 | | (9) ~ (all_56_13 = e2) % 135.98/20.03 | | (10) op(e1, e2) = all_56_13 % 135.98/20.03 | | % 135.98/20.03 | | REF_CLOSE: (2), (4), (9), (10) are inconsistent by sub-proof #165. % 135.98/20.03 | | % 135.98/20.03 | End of split % 135.98/20.03 | % 135.98/20.03 End of proof % 135.98/20.03 % 135.98/20.03 Sub-proof #133 shows that the following formulas are inconsistent: % 135.98/20.03 ---------------------------------------------------------------- % 135.98/20.03 (1) ~ (e2 = e0) % 135.98/20.03 (2) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 135.98/20.03 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 135.98/20.03 (3) ~ (e2 = e1) % 135.98/20.03 (4) ~ (e3 = e0) % 135.98/20.03 (5) all_57_0 = e2 % 135.98/20.03 (6) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 135.98/20.03 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 135.98/20.03 (7) all_57_2 = e3 % 135.98/20.03 (8) ~ (e3 = e1) % 135.98/20.03 (9) ~ (e1 = e0) % 135.98/20.03 (10) all_57_12 = e2 % 135.98/20.03 % 135.98/20.03 Begin of proof % 135.98/20.03 | % 135.98/20.03 | BETA: splitting (6) gives: % 135.98/20.03 | % 135.98/20.03 | Case 1: % 135.98/20.03 | | % 135.98/20.03 | | (11) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = % 135.98/20.03 | | e0) % 135.98/20.03 | | % 135.98/20.03 | | BETA: splitting (11) gives: % 135.98/20.03 | | % 135.98/20.03 | | Case 1: % 135.98/20.03 | | | % 135.98/20.03 | | | (12) all_57_0 = e0 & op(e3, e3) = e0 % 135.98/20.03 | | | % 135.98/20.03 | | | ALPHA: (12) implies: % 135.98/20.03 | | | (13) all_57_0 = e0 % 135.98/20.03 | | | % 135.98/20.03 | | | COMBINE_EQS: (5), (13) imply: % 135.98/20.03 | | | (14) e2 = e0 % 135.98/20.03 | | | % 135.98/20.03 | | | REDUCE: (1), (14) imply: % 135.98/20.03 | | | (15) $false % 135.98/20.03 | | | % 135.98/20.03 | | | CLOSE: (15) is inconsistent. % 135.98/20.03 | | | % 135.98/20.03 | | Case 2: % 135.98/20.03 | | | % 135.98/20.03 | | | (16) all_57_2 = e0 & op(e2, e3) = e0 % 135.98/20.03 | | | % 135.98/20.03 | | | REF_CLOSE: (4), (7), (16) are inconsistent by sub-proof #521. % 135.98/20.03 | | | % 135.98/20.03 | | End of split % 135.98/20.03 | | % 135.98/20.03 | Case 2: % 135.98/20.03 | | % 135.98/20.03 | | (17) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = % 135.98/20.03 | | e0) % 135.98/20.03 | | % 135.98/20.03 | | BETA: splitting (17) gives: % 135.98/20.03 | | % 135.98/20.03 | | Case 1: % 135.98/20.03 | | | % 135.98/20.03 | | | (18) all_57_6 = e0 & op(e1, e3) = e0 % 135.98/20.03 | | | % 135.98/20.03 | | | ALPHA: (18) implies: % 135.98/20.03 | | | (19) all_57_6 = e0 % 135.98/20.03 | | | % 135.98/20.03 | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (19) are inconsistent by % 135.98/20.03 | | | sub-proof #416. % 135.98/20.03 | | | % 135.98/20.03 | | Case 2: % 135.98/20.03 | | | % 135.98/20.03 | | | (20) all_57_12 = e0 & op(e0, e3) = e0 % 135.98/20.03 | | | % 135.98/20.03 | | | REF_CLOSE: (1), (10), (20) are inconsistent by sub-proof #578. % 135.98/20.03 | | | % 135.98/20.03 | | End of split % 135.98/20.03 | | % 135.98/20.03 | End of split % 135.98/20.03 | % 135.98/20.03 End of proof % 135.98/20.03 % 135.98/20.03 Sub-proof #134 shows that the following formulas are inconsistent: % 135.98/20.03 ---------------------------------------------------------------- % 135.98/20.03 (1) op(e3, e3) = e2 % 135.98/20.03 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 135.98/20.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 135.98/20.03 (3) ~ (e2 = e1) % 135.98/20.03 (4) ( ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 & $i(all_44_0)) | ( ~ % 135.98/20.03 (all_44_1 = e2) & op(e3, e3) = all_44_1 & $i(all_44_1)) % 135.98/20.03 (5) op(e3, e2) = all_52_4 % 135.98/20.03 (6) all_57_4 = e3 % 135.98/20.03 (7) ~ (e3 = e1) % 135.98/20.03 (8) ~ (all_52_4 = e1) % 135.98/20.03 (9) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 135.98/20.03 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 135.98/20.03 % 135.98/20.03 Begin of proof % 135.98/20.03 | % 135.98/20.03 | BETA: splitting (9) gives: % 135.98/20.03 | % 135.98/20.03 | Case 1: % 135.98/20.03 | | % 135.98/20.03 | | (10) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = % 135.98/20.03 | | e1) % 135.98/20.03 | | % 135.98/20.03 | | REF_CLOSE: (1), (2), (3), (5), (8), (10) are inconsistent by sub-proof #378. % 135.98/20.03 | | % 135.98/20.03 | Case 2: % 135.98/20.03 | | % 135.98/20.03 | | (11) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = % 135.98/20.03 | | e1) % 135.98/20.03 | | % 135.98/20.03 | | BETA: splitting (11) gives: % 135.98/20.03 | | % 135.98/20.03 | | Case 1: % 135.98/20.03 | | | % 135.98/20.03 | | | (12) all_57_4 = e1 & op(e3, e1) = e1 % 135.98/20.03 | | | % 135.98/20.03 | | | REF_CLOSE: (6), (7), (12) are inconsistent by sub-proof #382. % 135.98/20.03 | | | % 135.98/20.03 | | Case 2: % 135.98/20.03 | | | % 135.98/20.03 | | | (13) all_57_9 = e1 & op(e3, e0) = e1 % 135.98/20.03 | | | % 135.98/20.03 | | | ALPHA: (13) implies: % 135.98/20.03 | | | (14) op(e3, e0) = e1 % 135.98/20.03 | | | % 135.98/20.03 | | | BETA: splitting (4) gives: % 135.98/20.03 | | | % 135.98/20.03 | | | Case 1: % 135.98/20.03 | | | | % 135.98/20.03 | | | | (15) ~ (all_44_0 = e1) & op(e3, e0) = all_44_0 & $i(all_44_0) % 135.98/20.03 | | | | % 135.98/20.03 | | | | ALPHA: (15) implies: % 135.98/20.03 | | | | (16) ~ (all_44_0 = e1) % 135.98/20.03 | | | | (17) op(e3, e0) = all_44_0 % 135.98/20.03 | | | | % 135.98/20.03 | | | | REF_CLOSE: (2), (14), (16), (17) are inconsistent by sub-proof #432. % 135.98/20.03 | | | | % 135.98/20.03 | | | Case 2: % 135.98/20.03 | | | | % 135.98/20.03 | | | | (18) ~ (all_44_1 = e2) & op(e3, e3) = all_44_1 & $i(all_44_1) % 135.98/20.03 | | | | % 135.98/20.03 | | | | REF_CLOSE: (1), (2), (18) are inconsistent by sub-proof #431. % 135.98/20.03 | | | | % 135.98/20.03 | | | End of split % 135.98/20.03 | | | % 135.98/20.03 | | End of split % 135.98/20.03 | | % 135.98/20.03 | End of split % 135.98/20.03 | % 135.98/20.03 End of proof % 135.98/20.03 % 135.98/20.03 Sub-proof #135 shows that the following formulas are inconsistent: % 135.98/20.03 ---------------------------------------------------------------- % 135.98/20.03 (1) op(e0, e0) = e0 % 135.98/20.03 (2) op(e1, e1) = all_6_2 % 135.98/20.03 (3) ~ (all_52_9 = all_6_2) % 135.98/20.03 (4) ~ (all_52_13 = e0) % 135.98/20.03 (5) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 135.98/20.03 (6) ~ (e2 = e0) % 136.03/20.03 (7) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.03/20.03 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.03/20.03 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.03/20.03 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.03/20.03 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ % 136.03/20.03 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 136.03/20.03 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = % 136.03/20.03 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.03/20.03 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.03/20.03 $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) % 136.03/20.03 & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.03 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) % 136.03/20.03 = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 136.03/20.03 $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 136.03/20.03 (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.03/20.03 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.03/20.03 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) % 136.03/20.03 = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 136.03/20.03 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 136.03/20.03 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 136.03/20.03 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 136.03/20.03 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 136.03/20.03 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.03/20.03 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.03/20.03 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.03/20.03 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.03/20.03 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.03/20.03 e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 136.03/20.03 & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 % 136.03/20.03 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 136.03/20.03 ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) % 136.03/20.03 = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.03/20.03 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & % 136.03/20.03 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.03/20.03 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 136.03/20.03 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.03/20.03 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.03 $i(all_56_21) & $i(all_56_29)))) % 136.03/20.03 (8) ~ (all_52_13 = e1) % 136.03/20.03 (9) ~ (all_6_2 = e3) % 136.03/20.03 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.03 (11) ~ (e3 = e0) % 136.03/20.03 (12) ~ (all_52_13 = all_52_14) % 136.03/20.03 (13) op(e2, e2) = e1 % 136.03/20.03 (14) all_48_2 = e1 % 136.03/20.03 (15) all_54_10 = all_6_2 % 136.03/20.03 (16) ~ (all_6_2 = e2) % 136.03/20.03 (17) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & % 136.03/20.03 $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 & % 136.03/20.03 $i(all_48_1)) % 136.03/20.03 (18) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 136.03/20.03 (19) op(e2, e1) = all_52_9 % 136.03/20.03 (20) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 136.03/20.03 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 136.03/20.03 (21) all_54_7 = all_52_13 % 136.03/20.03 (22) ~ (e1 = e0) % 136.03/20.03 (23) ~ (all_52_9 = all_52_13) % 136.03/20.03 (24) op(e1, e0) = all_52_14 % 136.03/20.03 % 136.03/20.03 Begin of proof % 136.03/20.03 | % 136.03/20.03 | BETA: splitting (7) gives: % 136.03/20.03 | % 136.03/20.03 | Case 1: % 136.03/20.03 | | % 136.03/20.03 | | (25) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.03/20.03 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.03 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.03 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & % 136.03/20.03 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.03/20.03 | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 136.03/20.03 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.03/20.03 | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, % 136.03/20.03 | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.03/20.03 | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.03/20.03 | | $i(all_56_29)) % 136.03/20.03 | | % 136.03/20.03 | | BETA: splitting (25) gives: % 136.03/20.03 | | % 136.03/20.03 | | Case 1: % 136.03/20.03 | | | % 136.03/20.03 | | | (26) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.03/20.03 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.03 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.03 | | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & % 136.03/20.03 | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.03/20.03 | | | % 136.03/20.03 | | | ALPHA: (26) implies: % 136.03/20.03 | | | (27) op(e1, e1) = e3 % 136.03/20.03 | | | % 136.03/20.03 | | | REF_CLOSE: (2), (9), (10), (27) are inconsistent by sub-proof #771. % 136.03/20.03 | | | % 136.03/20.03 | | Case 2: % 136.03/20.03 | | | % 136.03/20.03 | | | (28) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 136.03/20.03 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.03/20.03 | | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, % 136.03/20.03 | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.03/20.03 | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.03/20.03 | | | $i(all_56_29) % 136.03/20.03 | | | % 136.03/20.03 | | | ALPHA: (28) implies: % 136.03/20.03 | | | (29) ~ (all_56_21 = e1) % 136.03/20.03 | | | (30) ~ (all_56_5 = e3) % 136.03/20.03 | | | (31) op(e1, e0) = all_56_29 % 136.03/20.03 | | | (32) op(e1, e1) = all_56_21 % 136.03/20.03 | | | (33) op(e1, e3) = all_56_5 % 136.03/20.03 | | | (34) op(e2, e1) = e2 % 136.03/20.03 | | | % 136.03/20.03 | | | REF_CLOSE: (2), (3), (4), (5), (8), (9), (10), (12), (14), (15), (17), % 136.03/20.03 | | | (18), (19), (20), (21), (23), (24), (29), (30), (31), (32), % 136.03/20.03 | | | (33), (34) are inconsistent by sub-proof #185. % 136.03/20.03 | | | % 136.03/20.03 | | End of split % 136.03/20.03 | | % 136.03/20.03 | Case 2: % 136.03/20.03 | | % 136.03/20.03 | | (35) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 136.03/20.03 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.03 | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 136.03/20.03 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 136.03/20.03 | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.03/20.03 | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 136.03/20.03 | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 136.03/20.03 | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.03/20.03 | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 136.03/20.03 | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.03/20.03 | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 136.03/20.03 | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.03/20.03 | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.03/20.03 | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.03/20.03 | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.03/20.03 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.03/20.03 | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.03 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.03 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.03 | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.03/20.03 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 136.03/20.03 | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.03/20.03 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.03 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 136.03/20.03 | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 136.03/20.03 | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 136.03/20.03 | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.03/20.03 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 % 136.03/20.03 | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.03/20.03 | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.03 | | $i(all_56_21) & $i(all_56_29)))) % 136.03/20.03 | | % 136.03/20.03 | | REF_CLOSE: (1), (2), (6), (10), (11), (13), (16), (22), (35) are % 136.03/20.03 | | inconsistent by sub-proof #184. % 136.03/20.03 | | % 136.03/20.03 | End of split % 136.03/20.03 | % 136.03/20.03 End of proof % 136.03/20.03 % 136.03/20.03 Sub-proof #136 shows that the following formulas are inconsistent: % 136.03/20.03 ---------------------------------------------------------------- % 136.03/20.03 (1) op(e3, e3) = e2 % 136.03/20.03 (2) ~ (e2 = e0) % 136.03/20.03 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.03 (4) op(e2, e2) = e1 % 136.03/20.03 (5) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.03 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.03/20.03 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.03 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.03 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 136.03/20.03 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 136.03/20.03 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 136.03/20.03 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.03/20.03 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.03/20.03 $i(all_56_17) & $i(all_56_25)) % 136.03/20.03 (6) ~ (e3 = e1) % 136.03/20.03 % 136.03/20.03 Begin of proof % 136.03/20.03 | % 136.03/20.03 | BETA: splitting (5) gives: % 136.03/20.03 | % 136.03/20.03 | Case 1: % 136.03/20.03 | | % 136.03/20.03 | | (7) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.03 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.03/20.03 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.03 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.03 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.03/20.03 | | % 136.03/20.03 | | ALPHA: (7) implies: % 136.03/20.03 | | (8) op(e3, e3) = e0 % 136.03/20.03 | | % 136.03/20.03 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #495. % 136.03/20.03 | | % 136.03/20.03 | Case 2: % 136.03/20.03 | | % 136.03/20.03 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.03/20.03 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.03 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.03 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) % 136.03/20.03 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.03/20.03 | | % 136.03/20.03 | | ALPHA: (9) implies: % 136.03/20.03 | | (10) op(e2, e2) = e3 % 136.03/20.03 | | % 136.03/20.03 | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #325. % 136.03/20.03 | | % 136.03/20.03 | End of split % 136.03/20.03 | % 136.03/20.03 End of proof % 136.03/20.03 % 136.03/20.03 Sub-proof #137 shows that the following formulas are inconsistent: % 136.03/20.03 ---------------------------------------------------------------- % 136.03/20.03 (1) all_57_12 = e0 % 136.03/20.03 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.03 (3) ~ (all_52_2 = e1) % 136.03/20.03 (4) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 136.03/20.03 (5) op(e1, e3) = all_52_2 % 136.03/20.03 (6) ~ (e1 = e0) % 136.03/20.03 % 136.03/20.03 Begin of proof % 136.03/20.03 | % 136.03/20.03 | BETA: splitting (4) gives: % 136.03/20.03 | % 136.03/20.03 | Case 1: % 136.03/20.03 | | % 136.03/20.03 | | (7) all_57_6 = e1 & op(e1, e3) = e1 % 136.03/20.03 | | % 136.03/20.03 | | ALPHA: (7) implies: % 136.03/20.03 | | (8) op(e1, e3) = e1 % 136.03/20.03 | | % 136.03/20.03 | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #725. % 136.03/20.03 | | % 136.03/20.03 | Case 2: % 136.03/20.03 | | % 136.03/20.03 | | (9) all_57_12 = e1 & op(e0, e3) = e1 % 136.03/20.03 | | % 136.03/20.03 | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #405. % 136.03/20.03 | | % 136.03/20.03 | End of split % 136.03/20.03 | % 136.03/20.03 End of proof % 136.03/20.03 % 136.03/20.03 Sub-proof #138 shows that the following formulas are inconsistent: % 136.03/20.03 ---------------------------------------------------------------- % 136.03/20.03 (1) op(e1, e1) = all_6_2 % 136.03/20.03 (2) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & % 136.03/20.03 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & % 136.03/20.03 $i(all_40_1)) % 136.03/20.03 (3) ~ (all_52_11 = e2) % 136.03/20.03 (4) all_57_5 = e2 % 136.03/20.03 (5) all_40_2 = all_6_2 % 136.03/20.03 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.03 (7) ~ (e2 = e1) % 136.03/20.03 (8) ~ (e3 = e2) % 136.03/20.03 (9) ~ (all_52_11 = all_6_2) % 136.03/20.03 (10) op(e0, e1) = all_52_11 % 136.03/20.03 (11) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 136.03/20.03 (12) ~ (all_6_2 = e2) % 136.03/20.03 (13) op(e2, e0) = e0 % 136.03/20.03 (14) op(e0, e0) = e2 % 136.03/20.03 (15) all_57_2 = e3 % 136.03/20.03 (16) all_54_14 = all_52_11 % 136.03/20.03 (17) ~ (e3 = e1) % 136.03/20.03 (18) ~ (e1 = e0) % 136.03/20.03 (19) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.03/20.03 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.03/20.03 (20) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.03 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 136.03/20.03 op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.03 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.03 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 & % 136.03/20.03 all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ % 136.03/20.03 (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 136.03/20.03 op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 136.03/20.03 all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 136.03/20.03 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 136.03/20.03 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 136.03/20.03 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 136.03/20.03 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 136.03/20.03 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 % 136.03/20.03 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.03/20.03 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.03 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.03 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.03 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.03/20.03 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.03/20.03 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.03/20.03 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.03 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.03/20.03 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.03/20.03 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.03/20.03 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.03/20.03 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.03/20.03 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.03/20.03 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.03/20.03 $i(all_56_29)))) % 136.03/20.03 % 136.03/20.03 Begin of proof % 136.03/20.03 | % 136.03/20.03 | BETA: splitting (20) gives: % 136.03/20.03 | % 136.03/20.03 | Case 1: % 136.03/20.03 | | % 136.03/20.03 | | (21) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 % 136.03/20.03 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = % 136.03/20.03 | | e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 136.03/20.03 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 136.03/20.03 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.03/20.03 | | % 136.03/20.03 | | ALPHA: (21) implies: % 136.03/20.03 | | (22) op(e2, e2) = e0 % 136.03/20.03 | | % 136.03/20.03 | | REF_CLOSE: (4), (6), (7), (13), (15), (17), (18), (19), (22) are % 136.03/20.03 | | inconsistent by sub-proof #452. % 136.03/20.03 | | % 136.03/20.03 | Case 2: % 136.03/20.03 | | % 136.03/20.03 | | (23) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.03 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.03 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.03 | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) % 136.03/20.03 | | = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.03/20.03 | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 136.03/20.03 | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.03/20.03 | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.03/20.03 | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.03/20.03 | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.03/20.03 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.03/20.03 | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.03 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.03 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.03 | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.03/20.03 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 136.03/20.03 | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.03/20.03 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.03 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 136.03/20.03 | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 136.03/20.03 | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 136.03/20.03 | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.03/20.03 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 % 136.03/20.03 | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.03/20.03 | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.03 | | $i(all_56_21) & $i(all_56_29)))) % 136.03/20.03 | | % 136.03/20.03 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 136.03/20.03 | | (14), (16), (23) are inconsistent by sub-proof #266. % 136.03/20.03 | | % 136.03/20.03 | End of split % 136.03/20.03 | % 136.03/20.03 End of proof % 136.03/20.03 % 136.03/20.03 Sub-proof #139 shows that the following formulas are inconsistent: % 136.03/20.03 ---------------------------------------------------------------- % 136.03/20.03 (1) all_57_6 = e0 % 136.03/20.03 (2) ~ (e2 = e0) % 136.03/20.03 (3) all_57_12 = e0 % 136.03/20.03 (4) op(e3, e3) = e1 % 136.03/20.03 (5) ~ (all_56_5 = e3) % 136.03/20.03 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.03 (7) ~ (e2 = e1) % 136.03/20.03 (8) ~ (e3 = e0) % 136.03/20.03 (9) ~ (e3 = e2) % 136.03/20.03 (10) op(e1, e3) = all_56_5 % 136.03/20.03 (11) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.03/20.03 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.03/20.03 (12) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) | % 136.03/20.03 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2) % 136.03/20.03 (13) ~ (e3 = e1) % 136.03/20.03 % 136.03/20.03 Begin of proof % 136.03/20.03 | % 136.03/20.03 | BETA: splitting (12) gives: % 136.03/20.03 | % 136.03/20.03 | Case 1: % 136.03/20.03 | | % 136.03/20.03 | | (14) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = % 136.03/20.03 | | e2) % 136.03/20.03 | | % 136.03/20.03 | | BETA: splitting (14) gives: % 136.03/20.03 | | % 136.03/20.03 | | Case 1: % 136.03/20.03 | | | % 136.03/20.03 | | | (15) all_57_0 = e2 & op(e3, e3) = e2 % 136.03/20.03 | | | % 136.03/20.03 | | | ALPHA: (15) implies: % 136.03/20.03 | | | (16) op(e3, e3) = e2 % 136.03/20.03 | | | % 136.03/20.03 | | | REF_CLOSE: (4), (6), (7), (16) are inconsistent by sub-proof #743. % 136.03/20.04 | | | % 136.03/20.04 | | Case 2: % 136.03/20.04 | | | % 136.03/20.04 | | | (17) all_57_2 = e2 & op(e2, e3) = e2 % 136.03/20.04 | | | % 136.03/20.04 | | | ALPHA: (17) implies: % 136.03/20.04 | | | (18) all_57_2 = e2 % 136.03/20.04 | | | % 136.03/20.04 | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (10), (11), (13), (18) are % 136.03/20.04 | | | inconsistent by sub-proof #144. % 136.03/20.04 | | | % 136.03/20.04 | | End of split % 136.03/20.04 | | % 136.03/20.04 | Case 2: % 136.03/20.04 | | % 136.03/20.04 | | (19) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = % 136.03/20.04 | | e2) % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (1), (2), (3), (19) are inconsistent by sub-proof #140. % 136.03/20.04 | | % 136.03/20.04 | End of split % 136.03/20.04 | % 136.03/20.04 End of proof % 136.03/20.04 % 136.03/20.04 Sub-proof #140 shows that the following formulas are inconsistent: % 136.03/20.04 ---------------------------------------------------------------- % 136.03/20.04 (1) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2) % 136.03/20.04 (2) all_57_6 = e0 % 136.03/20.04 (3) ~ (e2 = e0) % 136.03/20.04 (4) all_57_12 = e0 % 136.03/20.04 % 136.03/20.04 Begin of proof % 136.03/20.04 | % 136.03/20.04 | BETA: splitting (1) gives: % 136.03/20.04 | % 136.03/20.04 | Case 1: % 136.03/20.04 | | % 136.03/20.04 | | (5) all_57_6 = e2 & op(e1, e3) = e2 % 136.03/20.04 | | % 136.03/20.04 | | ALPHA: (5) implies: % 136.03/20.04 | | (6) all_57_6 = e2 % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #586. % 136.03/20.04 | | % 136.03/20.04 | Case 2: % 136.03/20.04 | | % 136.03/20.04 | | (7) all_57_12 = e2 & op(e0, e3) = e2 % 136.03/20.04 | | % 136.03/20.04 | | ALPHA: (7) implies: % 136.03/20.04 | | (8) all_57_12 = e2 % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #682. % 136.03/20.04 | | % 136.03/20.04 | End of split % 136.03/20.04 | % 136.03/20.04 End of proof % 136.03/20.04 % 136.03/20.04 Sub-proof #141 shows that the following formulas are inconsistent: % 136.03/20.04 ---------------------------------------------------------------- % 136.03/20.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.04 (2) ~ (e2 = e1) % 136.03/20.04 (3) all_57_3 = e1 % 136.03/20.04 (4) ~ (all_52_1 = e2) % 136.03/20.04 (5) op(e2, e3) = all_52_1 % 136.03/20.04 (6) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) % 136.03/20.04 % 136.03/20.04 Begin of proof % 136.03/20.04 | % 136.03/20.04 | BETA: splitting (6) gives: % 136.03/20.04 | % 136.03/20.04 | Case 1: % 136.03/20.04 | | % 136.03/20.04 | | (7) all_57_2 = e2 & op(e2, e3) = e2 % 136.03/20.04 | | % 136.03/20.04 | | ALPHA: (7) implies: % 136.03/20.04 | | (8) op(e2, e3) = e2 % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #779. % 136.03/20.04 | | % 136.03/20.04 | Case 2: % 136.03/20.04 | | % 136.03/20.04 | | (9) all_57_3 = e2 & op(e2, e2) = e2 % 136.03/20.04 | | % 136.03/20.04 | | ALPHA: (9) implies: % 136.03/20.04 | | (10) all_57_3 = e2 % 136.03/20.04 | | % 136.03/20.04 | | COMBINE_EQS: (3), (10) imply: % 136.03/20.04 | | (11) e2 = e1 % 136.03/20.04 | | % 136.03/20.04 | | REDUCE: (2), (11) imply: % 136.03/20.04 | | (12) $false % 136.03/20.04 | | % 136.03/20.04 | | CLOSE: (12) is inconsistent. % 136.03/20.04 | | % 136.03/20.04 | End of split % 136.03/20.04 | % 136.03/20.04 End of proof % 136.03/20.04 % 136.03/20.04 Sub-proof #142 shows that the following formulas are inconsistent: % 136.03/20.04 ---------------------------------------------------------------- % 136.03/20.04 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.04 (2) ~ (all_52_1 = e0) % 136.03/20.04 (3) ~ (all_10_2 = e0) % 136.03/20.04 (4) op(e3, e3) = all_10_2 % 136.03/20.04 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) % 136.03/20.04 (6) op(e2, e3) = all_52_1 % 136.03/20.04 % 136.03/20.04 Begin of proof % 136.03/20.04 | % 136.03/20.04 | BETA: splitting (5) gives: % 136.03/20.04 | % 136.03/20.04 | Case 1: % 136.03/20.04 | | % 136.03/20.04 | | (7) all_57_0 = e0 & op(e3, e3) = e0 % 136.03/20.04 | | % 136.03/20.04 | | ALPHA: (7) implies: % 136.03/20.04 | | (8) op(e3, e3) = e0 % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #534. % 136.03/20.04 | | % 136.03/20.04 | Case 2: % 136.03/20.04 | | % 136.03/20.04 | | (9) all_57_2 = e0 & op(e2, e3) = e0 % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #225. % 136.03/20.04 | | % 136.03/20.04 | End of split % 136.03/20.04 | % 136.03/20.04 End of proof % 136.03/20.04 % 136.03/20.04 Sub-proof #143 shows that the following formulas are inconsistent: % 136.03/20.04 ---------------------------------------------------------------- % 136.03/20.04 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.03/20.04 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.03/20.04 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.03/20.04 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.03/20.04 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ % 136.03/20.04 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 136.03/20.04 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = % 136.03/20.04 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.03/20.04 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.03/20.04 $i(all_56_29)) % 136.03/20.04 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.04 (3) ~ (e3 = e0) % 136.03/20.04 (4) ~ (all_52_9 = e2) % 136.03/20.04 (5) op(e1, e1) = e0 % 136.03/20.04 (6) op(e2, e1) = all_52_9 % 136.03/20.04 % 136.03/20.04 Begin of proof % 136.03/20.04 | % 136.03/20.04 | BETA: splitting (1) gives: % 136.03/20.04 | % 136.03/20.04 | Case 1: % 136.03/20.04 | | % 136.03/20.04 | | (7) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.03/20.04 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.04 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.04 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) % 136.03/20.04 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.03/20.04 | | % 136.03/20.04 | | ALPHA: (7) implies: % 136.03/20.04 | | (8) op(e1, e1) = e3 % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #753. % 136.03/20.04 | | % 136.03/20.04 | Case 2: % 136.03/20.04 | | % 136.03/20.04 | | (9) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.03/20.04 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 % 136.03/20.04 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.03/20.04 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.03/20.04 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.03/20.04 | | % 136.03/20.04 | | ALPHA: (9) implies: % 136.03/20.04 | | (10) op(e2, e1) = e2 % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #770. % 136.03/20.04 | | % 136.03/20.04 | End of split % 136.03/20.04 | % 136.03/20.04 End of proof % 136.03/20.04 % 136.03/20.04 Sub-proof #144 shows that the following formulas are inconsistent: % 136.03/20.04 ---------------------------------------------------------------- % 136.03/20.04 (1) all_57_12 = e0 % 136.03/20.04 (2) op(e3, e3) = e1 % 136.03/20.04 (3) ~ (all_56_5 = e3) % 136.03/20.04 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.04 (5) ~ (e3 = e0) % 136.03/20.04 (6) ~ (e3 = e2) % 136.03/20.04 (7) op(e1, e3) = all_56_5 % 136.03/20.04 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.03/20.04 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.03/20.04 (9) all_57_2 = e2 % 136.03/20.04 (10) ~ (e3 = e1) % 136.03/20.04 % 136.03/20.04 Begin of proof % 136.03/20.04 | % 136.03/20.04 | BETA: splitting (8) gives: % 136.03/20.04 | % 136.03/20.04 | Case 1: % 136.03/20.04 | | % 136.03/20.04 | | (11) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = % 136.03/20.04 | | e3) % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (2), (4), (6), (9), (10), (11) are inconsistent by sub-proof % 136.03/20.04 | | #589. % 136.03/20.04 | | % 136.03/20.04 | Case 2: % 136.03/20.04 | | % 136.03/20.04 | | (12) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = % 136.03/20.04 | | e3) % 136.03/20.04 | | % 136.03/20.04 | | BETA: splitting (12) gives: % 136.03/20.04 | | % 136.03/20.04 | | Case 1: % 136.03/20.04 | | | % 136.03/20.04 | | | (13) all_57_6 = e3 & op(e1, e3) = e3 % 136.03/20.04 | | | % 136.03/20.04 | | | ALPHA: (13) implies: % 136.03/20.04 | | | (14) op(e1, e3) = e3 % 136.03/20.04 | | | % 136.03/20.04 | | | REF_CLOSE: (3), (4), (7), (14) are inconsistent by sub-proof #724. % 136.03/20.04 | | | % 136.03/20.04 | | Case 2: % 136.03/20.04 | | | % 136.03/20.04 | | | (15) all_57_12 = e3 & op(e0, e3) = e3 % 136.03/20.04 | | | % 136.03/20.04 | | | ALPHA: (15) implies: % 136.03/20.04 | | | (16) all_57_12 = e3 % 136.03/20.04 | | | % 136.03/20.04 | | | REF_CLOSE: (1), (5), (16) are inconsistent by sub-proof #492. % 136.03/20.04 | | | % 136.03/20.04 | | End of split % 136.03/20.04 | | % 136.03/20.04 | End of split % 136.03/20.04 | % 136.03/20.04 End of proof % 136.03/20.04 % 136.03/20.04 Sub-proof #145 shows that the following formulas are inconsistent: % 136.03/20.04 ---------------------------------------------------------------- % 136.03/20.04 (1) ~ (all_52_14 = e3) % 136.03/20.04 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.04 (3) ~ (e3 = e0) % 136.03/20.04 (4) ~ (all_52_1 = e0) % 136.03/20.04 (5) all_57_9 = e3 % 136.03/20.04 (6) ~ (e3 = e2) % 136.03/20.04 (7) op(e2, e2) = e1 % 136.03/20.04 (8) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) | % 136.03/20.04 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.03/20.04 (9) op(e2, e1) = all_52_9 % 136.03/20.04 (10) op(e0, e0) = e2 % 136.03/20.04 (11) op(e2, e3) = all_52_1 % 136.03/20.04 (12) e3 = e1 % 136.03/20.04 (13) ~ (all_52_9 = e0) % 136.03/20.04 (14) ~ (e3 = e1) % 136.03/20.04 (15) ~ (e1 = e0) % 136.03/20.04 (16) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.03/20.04 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 136.03/20.04 (17) op(e1, e0) = all_52_14 % 136.03/20.04 % 136.03/20.04 Begin of proof % 136.03/20.04 | % 136.03/20.04 | SIMP: (12) implies: % 136.03/20.04 | (18) e3 = e1 % 136.03/20.04 | % 136.03/20.04 | COMBINE_EQS: (5), (18) imply: % 136.03/20.04 | (19) all_57_9 = e1 % 136.03/20.04 | % 136.03/20.04 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14), % 136.03/20.04 | (15), (16), (17), (19) are inconsistent by sub-proof #150. % 136.03/20.04 | % 136.03/20.04 End of proof % 136.03/20.04 % 136.03/20.04 Sub-proof #146 shows that the following formulas are inconsistent: % 136.03/20.04 ---------------------------------------------------------------- % 136.03/20.04 (1) op(e1, e1) = all_6_2 % 136.03/20.04 (2) ~ (e2 = e0) % 136.03/20.04 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.04 (4) ~ (e2 = e1) % 136.03/20.04 (5) ~ (e3 = e0) % 136.03/20.04 (6) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 136.03/20.04 (7) all_57_9 = e3 % 136.03/20.04 (8) ~ (all_6_2 = e2) % 136.03/20.04 (9) op(e0, e0) = e2 % 136.03/20.04 (10) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.03/20.04 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.03/20.04 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.03/20.04 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.03/20.04 (11) ~ (e3 = e1) % 136.03/20.04 (12) ~ (e1 = e0) % 136.03/20.04 (13) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) | % 136.03/20.04 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.03/20.04 % 136.03/20.04 Begin of proof % 136.03/20.04 | % 136.03/20.04 | BETA: splitting (6) gives: % 136.03/20.04 | % 136.03/20.04 | Case 1: % 136.03/20.04 | | % 136.03/20.04 | | (14) all_57_8 = e2 & op(e1, e1) = e2 % 136.03/20.04 | | % 136.03/20.04 | | ALPHA: (14) implies: % 136.03/20.04 | | (15) op(e1, e1) = e2 % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (1), (3), (8), (15) are inconsistent by sub-proof #767. % 136.03/20.04 | | % 136.03/20.04 | Case 2: % 136.03/20.04 | | % 136.03/20.04 | | (16) all_57_11 = e2 & op(e1, e0) = e2 % 136.03/20.04 | | % 136.03/20.04 | | ALPHA: (16) implies: % 136.03/20.04 | | (17) all_57_11 = e2 % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (11), (12), (13), (17) are % 136.03/20.04 | | inconsistent by sub-proof #635. % 136.03/20.04 | | % 136.03/20.04 | End of split % 136.03/20.04 | % 136.03/20.04 End of proof % 136.03/20.04 % 136.03/20.04 Sub-proof #147 shows that the following formulas are inconsistent: % 136.03/20.04 ---------------------------------------------------------------- % 136.03/20.04 (1) all_57_7 = e0 & op(e1, e2) = e0 % 136.03/20.04 (2) all_57_7 = e3 % 136.03/20.04 (3) ~ (e3 = e0) % 136.03/20.04 % 136.03/20.04 Begin of proof % 136.03/20.04 | % 136.03/20.04 | ALPHA: (1) implies: % 136.03/20.04 | (4) all_57_7 = e0 % 136.03/20.04 | % 136.03/20.04 | COMBINE_EQS: (2), (4) imply: % 136.03/20.04 | (5) e3 = e0 % 136.03/20.04 | % 136.03/20.04 | REDUCE: (3), (5) imply: % 136.03/20.04 | (6) $false % 136.03/20.04 | % 136.03/20.04 | CLOSE: (6) is inconsistent. % 136.03/20.04 | % 136.03/20.04 End of proof % 136.03/20.04 % 136.03/20.04 Sub-proof #148 shows that the following formulas are inconsistent: % 136.03/20.04 ---------------------------------------------------------------- % 136.03/20.04 (1) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) % 136.03/20.04 (2) ~ (e2 = e0) % 136.03/20.04 (3) op(e3, e3) = e1 % 136.03/20.04 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.04 (5) ~ (e2 = e1) % 136.03/20.04 (6) all_57_1 = e0 % 136.03/20.04 % 136.03/20.04 Begin of proof % 136.03/20.04 | % 136.03/20.04 | BETA: splitting (1) gives: % 136.03/20.04 | % 136.03/20.04 | Case 1: % 136.03/20.04 | | % 136.03/20.04 | | (7) all_57_0 = e2 & op(e3, e3) = e2 % 136.03/20.04 | | % 136.03/20.04 | | ALPHA: (7) implies: % 136.03/20.04 | | (8) op(e3, e3) = e2 % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #743. % 136.03/20.04 | | % 136.03/20.04 | Case 2: % 136.03/20.04 | | % 136.03/20.04 | | (9) all_57_1 = e2 & op(e3, e2) = e2 % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #149. % 136.03/20.04 | | % 136.03/20.04 | End of split % 136.03/20.04 | % 136.03/20.04 End of proof % 136.03/20.04 % 136.03/20.04 Sub-proof #149 shows that the following formulas are inconsistent: % 136.03/20.04 ---------------------------------------------------------------- % 136.03/20.04 (1) all_57_1 = e2 & op(e3, e2) = e2 % 136.03/20.04 (2) all_57_1 = e0 % 136.03/20.04 (3) ~ (e2 = e0) % 136.03/20.04 % 136.03/20.04 Begin of proof % 136.03/20.04 | % 136.03/20.04 | ALPHA: (1) implies: % 136.03/20.04 | (4) all_57_1 = e2 % 136.03/20.04 | % 136.03/20.04 | COMBINE_EQS: (2), (4) imply: % 136.03/20.04 | (5) e2 = e0 % 136.03/20.04 | % 136.03/20.04 | SIMP: (5) implies: % 136.03/20.04 | (6) e2 = e0 % 136.03/20.04 | % 136.03/20.04 | REDUCE: (3), (6) imply: % 136.03/20.04 | (7) $false % 136.03/20.04 | % 136.03/20.04 | CLOSE: (7) is inconsistent. % 136.03/20.04 | % 136.03/20.04 End of proof % 136.03/20.04 % 136.03/20.04 Sub-proof #150 shows that the following formulas are inconsistent: % 136.03/20.04 ---------------------------------------------------------------- % 136.03/20.04 (1) ~ (all_52_14 = e3) % 136.03/20.04 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.04 (3) ~ (e3 = e0) % 136.03/20.04 (4) ~ (all_52_1 = e0) % 136.03/20.04 (5) ~ (e3 = e2) % 136.03/20.04 (6) op(e2, e2) = e1 % 136.03/20.04 (7) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) | % 136.03/20.04 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.03/20.04 (8) op(e2, e1) = all_52_9 % 136.03/20.04 (9) op(e0, e0) = e2 % 136.03/20.04 (10) op(e2, e3) = all_52_1 % 136.03/20.04 (11) all_57_9 = e1 % 136.03/20.04 (12) ~ (all_52_9 = e0) % 136.03/20.04 (13) ~ (e3 = e1) % 136.03/20.04 (14) ~ (e1 = e0) % 136.03/20.04 (15) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.03/20.04 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 136.03/20.04 (16) op(e1, e0) = all_52_14 % 136.03/20.04 % 136.03/20.04 Begin of proof % 136.03/20.04 | % 136.03/20.04 | BETA: splitting (7) gives: % 136.03/20.04 | % 136.03/20.04 | Case 1: % 136.03/20.04 | | % 136.03/20.04 | | (17) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = % 136.03/20.04 | | e3) % 136.03/20.04 | | % 136.03/20.04 | | BETA: splitting (17) gives: % 136.03/20.04 | | % 136.03/20.04 | | Case 1: % 136.03/20.04 | | | % 136.03/20.04 | | | (18) all_57_9 = e3 & op(e3, e0) = e3 % 136.03/20.04 | | | % 136.03/20.04 | | | ALPHA: (18) implies: % 136.03/20.04 | | | (19) all_57_9 = e3 % 136.03/20.04 | | | % 136.03/20.04 | | | REF_CLOSE: (11), (13), (19) are inconsistent by sub-proof #690. % 136.03/20.04 | | | % 136.03/20.04 | | Case 2: % 136.03/20.04 | | | % 136.03/20.04 | | | (20) all_57_10 = e3 & op(e2, e0) = e3 % 136.03/20.04 | | | % 136.03/20.04 | | | ALPHA: (20) implies: % 136.03/20.04 | | | (21) all_57_10 = e3 % 136.03/20.04 | | | % 136.03/20.04 | | | REF_CLOSE: (2), (3), (4), (6), (8), (10), (12), (14), (15), (21) are % 136.03/20.04 | | | inconsistent by sub-proof #151. % 136.03/20.04 | | | % 136.03/20.04 | | End of split % 136.03/20.04 | | % 136.03/20.04 | Case 2: % 136.03/20.04 | | % 136.03/20.04 | | (22) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = % 136.03/20.04 | | e3) % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (1), (2), (5), (9), (16), (22) are inconsistent by sub-proof % 136.03/20.04 | | #330. % 136.03/20.04 | | % 136.03/20.04 | End of split % 136.03/20.04 | % 136.03/20.04 End of proof % 136.03/20.04 % 136.03/20.04 Sub-proof #151 shows that the following formulas are inconsistent: % 136.03/20.04 ---------------------------------------------------------------- % 136.03/20.04 (1) all_57_10 = e3 % 136.03/20.04 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.04 (3) ~ (e3 = e0) % 136.03/20.04 (4) ~ (all_52_1 = e0) % 136.03/20.04 (5) op(e2, e2) = e1 % 136.03/20.04 (6) op(e2, e1) = all_52_9 % 136.03/20.04 (7) op(e2, e3) = all_52_1 % 136.03/20.04 (8) ~ (all_52_9 = e0) % 136.03/20.04 (9) ~ (e1 = e0) % 136.03/20.04 (10) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.03/20.04 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 136.03/20.04 % 136.03/20.04 Begin of proof % 136.03/20.04 | % 136.03/20.04 | BETA: splitting (10) gives: % 136.03/20.04 | % 136.03/20.04 | Case 1: % 136.03/20.04 | | % 136.03/20.04 | | (11) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = % 136.03/20.04 | | e0) % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (2), (4), (5), (7), (9), (11) are inconsistent by sub-proof #152. % 136.03/20.04 | | % 136.03/20.04 | Case 2: % 136.03/20.04 | | % 136.03/20.04 | | (12) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = % 136.03/20.04 | | e0) % 136.03/20.04 | | % 136.03/20.04 | | BETA: splitting (12) gives: % 136.03/20.04 | | % 136.03/20.04 | | Case 1: % 136.03/20.04 | | | % 136.03/20.04 | | | (13) all_57_5 = e0 & op(e2, e1) = e0 % 136.03/20.04 | | | % 136.03/20.04 | | | REF_CLOSE: (2), (6), (8), (13) are inconsistent by sub-proof #455. % 136.03/20.04 | | | % 136.03/20.04 | | Case 2: % 136.03/20.04 | | | % 136.03/20.04 | | | (14) all_57_10 = e0 & op(e2, e0) = e0 % 136.03/20.04 | | | % 136.03/20.04 | | | ALPHA: (14) implies: % 136.03/20.04 | | | (15) all_57_10 = e0 % 136.03/20.04 | | | % 136.03/20.04 | | | REF_CLOSE: (1), (3), (15) are inconsistent by sub-proof #448. % 136.03/20.04 | | | % 136.03/20.04 | | End of split % 136.03/20.04 | | % 136.03/20.04 | End of split % 136.03/20.04 | % 136.03/20.04 End of proof % 136.03/20.04 % 136.03/20.04 Sub-proof #152 shows that the following formulas are inconsistent: % 136.03/20.04 ---------------------------------------------------------------- % 136.03/20.04 (1) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) % 136.03/20.04 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.04 (3) ~ (all_52_1 = e0) % 136.03/20.04 (4) op(e2, e2) = e1 % 136.03/20.04 (5) op(e2, e3) = all_52_1 % 136.03/20.04 (6) ~ (e1 = e0) % 136.03/20.04 % 136.03/20.04 Begin of proof % 136.03/20.04 | % 136.03/20.04 | BETA: splitting (1) gives: % 136.03/20.04 | % 136.03/20.04 | Case 1: % 136.03/20.04 | | % 136.03/20.04 | | (7) all_57_2 = e0 & op(e2, e3) = e0 % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #225. % 136.03/20.04 | | % 136.03/20.04 | Case 2: % 136.03/20.04 | | % 136.03/20.04 | | (8) all_57_3 = e0 & op(e2, e2) = e0 % 136.03/20.04 | | % 136.03/20.04 | | ALPHA: (8) implies: % 136.03/20.04 | | (9) op(e2, e2) = e0 % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #675. % 136.03/20.04 | | % 136.03/20.04 | End of split % 136.03/20.04 | % 136.03/20.04 End of proof % 136.03/20.04 % 136.03/20.04 Sub-proof #153 shows that the following formulas are inconsistent: % 136.03/20.04 ---------------------------------------------------------------- % 136.03/20.04 (1) all_54_4 = e1 | all_54_4 = e0 % 136.03/20.04 (2) all_54_4 = all_52_1 % 136.03/20.04 (3) ~ (all_52_1 = e1) % 136.03/20.04 (4) ~ (all_52_1 = e0) % 136.03/20.04 % 136.03/20.04 Begin of proof % 136.03/20.04 | % 136.03/20.04 | BETA: splitting (1) gives: % 136.03/20.04 | % 136.03/20.04 | Case 1: % 136.03/20.04 | | % 136.03/20.04 | | (5) all_54_4 = e1 % 136.03/20.04 | | % 136.03/20.04 | | COMBINE_EQS: (2), (5) imply: % 136.03/20.04 | | (6) all_52_1 = e1 % 136.03/20.04 | | % 136.03/20.04 | | REDUCE: (3), (6) imply: % 136.03/20.04 | | (7) $false % 136.03/20.04 | | % 136.03/20.04 | | CLOSE: (7) is inconsistent. % 136.03/20.04 | | % 136.03/20.04 | Case 2: % 136.03/20.04 | | % 136.03/20.04 | | (8) all_54_4 = e0 % 136.03/20.04 | | % 136.03/20.04 | | COMBINE_EQS: (2), (8) imply: % 136.03/20.04 | | (9) all_52_1 = e0 % 136.03/20.04 | | % 136.03/20.04 | | REDUCE: (4), (9) imply: % 136.03/20.04 | | (10) $false % 136.03/20.04 | | % 136.03/20.04 | | CLOSE: (10) is inconsistent. % 136.03/20.04 | | % 136.03/20.04 | End of split % 136.03/20.04 | % 136.03/20.04 End of proof % 136.03/20.04 % 136.03/20.04 Sub-proof #154 shows that the following formulas are inconsistent: % 136.03/20.04 ---------------------------------------------------------------- % 136.03/20.04 (1) op(e1, e1) = all_6_2 % 136.03/20.04 (2) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & % 136.03/20.04 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & % 136.03/20.04 $i(all_40_1)) % 136.03/20.04 (3) ~ (all_52_11 = e2) % 136.03/20.04 (4) all_40_2 = all_6_2 % 136.03/20.04 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.04 (6) ~ (e2 = e1) % 136.03/20.04 (7) ~ (e3 = e2) % 136.03/20.04 (8) op(e2, e2) = e1 % 136.03/20.04 (9) ~ (all_52_11 = all_6_2) % 136.03/20.04 (10) op(e0, e1) = all_52_11 % 136.03/20.04 (11) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 136.03/20.04 (12) ~ (all_6_2 = e2) % 136.03/20.04 (13) op(e2, e0) = e0 % 136.03/20.04 (14) op(e0, e0) = e2 % 136.03/20.04 (15) all_54_14 = all_52_11 % 136.03/20.04 (16) ~ (e1 = e0) % 136.03/20.04 (17) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.04 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 136.03/20.04 op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.04 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.04 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 & % 136.03/20.04 all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ % 136.03/20.04 (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 136.03/20.04 op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 136.03/20.04 all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 136.03/20.04 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 136.03/20.04 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 136.03/20.04 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 136.03/20.04 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 136.03/20.04 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 % 136.03/20.04 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.03/20.04 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.04 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.04 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.04 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.03/20.04 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.03/20.04 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.03/20.04 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.04 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.03/20.04 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.03/20.04 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.03/20.04 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.03/20.04 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.03/20.04 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.03/20.04 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.03/20.04 $i(all_56_29)))) % 136.03/20.04 % 136.03/20.04 Begin of proof % 136.03/20.04 | % 136.03/20.04 | BETA: splitting (17) gives: % 136.03/20.04 | % 136.03/20.04 | Case 1: % 136.03/20.04 | | % 136.03/20.04 | | (18) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 % 136.03/20.04 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = % 136.03/20.04 | | e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 136.03/20.04 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 136.03/20.04 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.03/20.04 | | % 136.03/20.04 | | ALPHA: (18) implies: % 136.03/20.04 | | (19) op(e2, e2) = e0 % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (5), (8), (16), (19) are inconsistent by sub-proof #675. % 136.03/20.04 | | % 136.03/20.04 | Case 2: % 136.03/20.04 | | % 136.03/20.04 | | (20) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.04 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.04 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.04 | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) % 136.03/20.04 | | = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.03/20.04 | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 136.03/20.04 | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.03/20.04 | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.03/20.04 | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.03/20.04 | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.03/20.04 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.03/20.04 | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.04 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.04 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.04 | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.03/20.04 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 136.03/20.04 | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.03/20.04 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.04 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 136.03/20.04 | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 136.03/20.04 | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 136.03/20.04 | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.03/20.04 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 % 136.03/20.04 | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.03/20.04 | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.04 | | $i(all_56_21) & $i(all_56_29)))) % 136.03/20.04 | | % 136.03/20.04 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), % 136.03/20.04 | | (14), (15), (20) are inconsistent by sub-proof #266. % 136.03/20.04 | | % 136.03/20.04 | End of split % 136.03/20.04 | % 136.03/20.04 End of proof % 136.03/20.04 % 136.03/20.04 Sub-proof #155 shows that the following formulas are inconsistent: % 136.03/20.04 ---------------------------------------------------------------- % 136.03/20.04 (1) all_54_9 = e1 | all_54_9 = e0 % 136.03/20.04 (2) all_54_9 = all_8_0 % 136.03/20.04 (3) ~ (all_8_0 = e1) % 136.03/20.04 (4) ~ (all_8_0 = e0) % 136.03/20.04 % 136.03/20.04 Begin of proof % 136.03/20.04 | % 136.03/20.04 | BETA: splitting (1) gives: % 136.03/20.04 | % 136.03/20.04 | Case 1: % 136.03/20.04 | | % 136.03/20.04 | | (5) all_54_9 = e1 % 136.03/20.04 | | % 136.03/20.04 | | COMBINE_EQS: (2), (5) imply: % 136.03/20.04 | | (6) all_8_0 = e1 % 136.03/20.04 | | % 136.03/20.04 | | REDUCE: (3), (6) imply: % 136.03/20.04 | | (7) $false % 136.03/20.04 | | % 136.03/20.04 | | CLOSE: (7) is inconsistent. % 136.03/20.04 | | % 136.03/20.04 | Case 2: % 136.03/20.04 | | % 136.03/20.04 | | (8) all_54_9 = e0 % 136.03/20.04 | | % 136.03/20.04 | | COMBINE_EQS: (2), (8) imply: % 136.03/20.04 | | (9) all_8_0 = e0 % 136.03/20.04 | | % 136.03/20.04 | | REDUCE: (4), (9) imply: % 136.03/20.04 | | (10) $false % 136.03/20.04 | | % 136.03/20.04 | | CLOSE: (10) is inconsistent. % 136.03/20.04 | | % 136.03/20.04 | End of split % 136.03/20.04 | % 136.03/20.04 End of proof % 136.03/20.04 % 136.03/20.04 Sub-proof #156 shows that the following formulas are inconsistent: % 136.03/20.04 ---------------------------------------------------------------- % 136.03/20.04 (1) op(e0, e0) = all_4_2 % 136.03/20.04 (2) op(e1, e1) = all_6_2 % 136.03/20.04 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.04 (4) ~ (all_4_2 = e2) % 136.03/20.04 (5) op(e2, e2) = e1 % 136.03/20.04 (6) ~ (all_6_2 = e2) % 136.03/20.04 (7) op(e0, e0) = e2 % 136.03/20.04 (8) ~ (e1 = e0) % 136.03/20.05 (9) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.05 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 136.03/20.05 op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.05 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.05 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 & % 136.03/20.05 all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ % 136.03/20.05 (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, % 136.03/20.05 e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.03/20.05 op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 136.03/20.05 $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 & % 136.03/20.05 $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & % 136.03/20.05 ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.03/20.05 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.03/20.05 all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) % 136.03/20.05 & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & % 136.03/20.05 all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ % 136.03/20.05 (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 136.03/20.05 op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 136.03/20.05 all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 136.03/20.05 $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & % 136.03/20.05 ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.03/20.05 (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 136.03/20.05 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.03/20.05 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & % 136.03/20.05 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.03/20.05 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 136.03/20.05 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.03/20.05 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.05 $i(all_56_21) & $i(all_56_29)))) % 136.03/20.05 % 136.03/20.05 Begin of proof % 136.03/20.05 | % 136.03/20.05 | BETA: splitting (9) gives: % 136.03/20.05 | % 136.03/20.05 | Case 1: % 136.03/20.05 | | % 136.03/20.05 | | (10) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 % 136.03/20.05 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = % 136.03/20.05 | | e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 136.03/20.05 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 136.03/20.05 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.03/20.05 | | % 136.03/20.05 | | ALPHA: (10) implies: % 136.03/20.05 | | (11) op(e2, e2) = e0 % 136.03/20.05 | | % 136.03/20.05 | | REF_CLOSE: (3), (5), (8), (11) are inconsistent by sub-proof #675. % 136.03/20.05 | | % 136.03/20.05 | Case 2: % 136.03/20.05 | | % 136.03/20.05 | | (12) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.05 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.05 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.05 | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) % 136.03/20.05 | | = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.03/20.05 | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 136.03/20.05 | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.03/20.05 | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.03/20.05 | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.03/20.05 | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.03/20.05 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.03/20.05 | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.05 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.05 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.05 | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.03/20.05 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 136.03/20.05 | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.03/20.05 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.05 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 136.03/20.05 | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 136.03/20.05 | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 136.03/20.05 | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.03/20.05 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 % 136.03/20.05 | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.03/20.05 | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.05 | | $i(all_56_21) & $i(all_56_29)))) % 136.03/20.05 | | % 136.03/20.05 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (12) are inconsistent by sub-proof % 136.03/20.05 | | #352. % 136.03/20.05 | | % 136.03/20.05 | End of split % 136.03/20.05 | % 136.03/20.05 End of proof % 136.03/20.05 % 136.03/20.05 Sub-proof #157 shows that the following formulas are inconsistent: % 136.03/20.05 ---------------------------------------------------------------- % 136.03/20.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.05 (2) op(e2, e2) = e1 % 136.03/20.05 (3) op(e0, e2) = e2 % 136.03/20.05 (4) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.05 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.03/20.05 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.05 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.05 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 136.03/20.05 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 136.03/20.05 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 136.03/20.05 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.03/20.05 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.03/20.05 $i(all_56_17) & $i(all_56_25)) % 136.03/20.05 (5) ~ (e3 = e1) % 136.03/20.05 % 136.03/20.05 Begin of proof % 136.03/20.05 | % 136.03/20.05 | BETA: splitting (4) gives: % 136.03/20.05 | % 136.03/20.05 | Case 1: % 136.03/20.05 | | % 136.03/20.05 | | (6) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.05 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.03/20.05 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.05 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.05 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.03/20.05 | | % 136.03/20.05 | | ALPHA: (6) implies: % 136.03/20.05 | | (7) ~ (all_56_15 = e2) % 136.03/20.05 | | (8) op(e0, e2) = all_56_15 % 136.03/20.05 | | % 136.03/20.05 | | REF_CLOSE: (1), (3), (7), (8) are inconsistent by sub-proof #609. % 136.03/20.05 | | % 136.03/20.05 | Case 2: % 136.03/20.05 | | % 136.03/20.05 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.03/20.05 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.05 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.05 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) % 136.03/20.05 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.03/20.05 | | % 136.03/20.05 | | ALPHA: (9) implies: % 136.03/20.05 | | (10) op(e2, e2) = e3 % 136.03/20.05 | | % 136.03/20.05 | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #325. % 136.03/20.05 | | % 136.03/20.05 | End of split % 136.03/20.05 | % 136.03/20.05 End of proof % 136.03/20.05 % 136.03/20.05 Sub-proof #158 shows that the following formulas are inconsistent: % 136.03/20.05 ---------------------------------------------------------------- % 136.03/20.05 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 136.03/20.05 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 136.03/20.05 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.03/20.05 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.03/20.05 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.03/20.05 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.03/20.05 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 136.03/20.05 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.03/20.05 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.05 $i(all_56_21) & $i(all_56_29)) % 136.03/20.05 (2) op(e1, e2) = e2 % 136.03/20.05 (3) op(e3, e3) = e1 % 136.03/20.05 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.05 (5) ~ (e2 = e1) % 136.03/20.05 % 136.03/20.05 Begin of proof % 136.03/20.05 | % 136.03/20.05 | BETA: splitting (1) gives: % 136.03/20.05 | % 136.03/20.05 | Case 1: % 136.03/20.05 | | % 136.03/20.05 | | (6) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.03/20.05 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.03/20.05 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.03/20.05 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.03/20.05 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.03/20.05 | | % 136.03/20.05 | | ALPHA: (6) implies: % 136.03/20.05 | | (7) op(e3, e3) = e2 % 136.03/20.05 | | % 136.03/20.05 | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #743. % 136.03/20.05 | | % 136.03/20.05 | Case 2: % 136.03/20.05 | | % 136.03/20.05 | | (8) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.03/20.05 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 136.03/20.05 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.03/20.05 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.03/20.05 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.03/20.05 | | % 136.03/20.05 | | ALPHA: (8) implies: % 136.03/20.05 | | (9) ~ (all_56_13 = e2) % 136.03/20.05 | | (10) op(e1, e2) = all_56_13 % 136.03/20.05 | | % 136.03/20.05 | | REF_CLOSE: (2), (4), (9), (10) are inconsistent by sub-proof #165. % 136.03/20.05 | | % 136.03/20.05 | End of split % 136.03/20.05 | % 136.03/20.05 End of proof % 136.03/20.05 % 136.03/20.05 Sub-proof #159 shows that the following formulas are inconsistent: % 136.03/20.05 ---------------------------------------------------------------- % 136.03/20.05 (1) op(e0, e0) = all_4_2 % 136.03/20.05 (2) op(e1, e1) = all_6_2 % 136.03/20.05 (3) op(e1, e2) = e2 % 136.03/20.05 (4) ~ (e2 = e0) % 136.03/20.05 (5) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.03/20.05 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.03/20.05 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.03/20.05 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.03/20.05 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ % 136.03/20.05 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 136.03/20.05 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = % 136.03/20.05 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.03/20.05 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.03/20.05 $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) % 136.03/20.05 & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.05 op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) % 136.03/20.05 = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 136.03/20.05 $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 136.03/20.05 (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.03/20.05 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.03/20.05 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) % 136.03/20.05 = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 136.03/20.05 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 136.03/20.05 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 136.03/20.05 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 136.03/20.05 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 136.03/20.05 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.03/20.05 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.03/20.05 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.03/20.05 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.03/20.05 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.03/20.05 e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 136.03/20.05 & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 % 136.03/20.05 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 136.03/20.05 ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) % 136.03/20.05 = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.03/20.05 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & % 136.03/20.05 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.03/20.05 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 136.03/20.05 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.03/20.05 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.05 $i(all_56_21) & $i(all_56_29)))) % 136.03/20.05 (6) op(e3, e3) = e1 % 136.03/20.05 (7) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.03/20.05 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.03/20.05 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.05 (9) ~ (e2 = e1) % 136.03/20.05 (10) ~ (all_4_2 = e2) % 136.03/20.05 (11) ~ (e3 = e0) % 136.03/20.05 (12) ~ (all_52_2 = e1) % 136.03/20.05 (13) op(e2, e2) = e1 % 136.03/20.05 (14) op(e1, e1) = e3 % 136.03/20.05 (15) ~ (all_4_2 = e1) % 136.03/20.05 (16) ~ (all_6_2 = e2) % 136.03/20.05 (17) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 136.03/20.05 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 136.03/20.05 (18) ~ (all_52_4 = e2) % 136.03/20.05 (19) ~ (all_52_3 = e1) % 136.03/20.05 (20) op(e1, e3) = all_52_2 % 136.03/20.05 (21) op(e3, e2) = all_52_4 % 136.03/20.05 (22) op(e0, e3) = all_52_3 % 136.03/20.05 (23) op(e3, e0) = all_52_12 % 136.03/20.05 (24) op(e3, e1) = all_52_8 % 136.03/20.05 (25) ~ (all_52_3 = all_4_2) % 136.03/20.05 (26) ~ (e1 = e0) % 136.03/20.05 (27) ~ (all_34_2 = e3) | ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & % 136.03/20.05 $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 & % 136.03/20.05 $i(all_34_1)) % 136.03/20.05 (28) ~ (all_52_12 = all_4_2) % 136.03/20.05 (29) all_34_2 = all_4_2 % 136.03/20.05 (30) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.03/20.05 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.03/20.05 (31) ~ (all_52_8 = e3) % 136.03/20.05 % 136.03/20.05 Begin of proof % 136.03/20.05 | % 136.03/20.05 | BETA: splitting (5) gives: % 136.03/20.05 | % 136.03/20.05 | Case 1: % 136.03/20.05 | | % 136.03/20.05 | | (32) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.03/20.05 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.05 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.05 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & % 136.03/20.05 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.03/20.05 | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 136.03/20.05 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.03/20.05 | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, % 136.03/20.05 | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.03/20.05 | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.03/20.05 | | $i(all_56_29)) % 136.03/20.05 | | % 136.03/20.05 | | REF_CLOSE: (3), (8), (12), (20), (32) are inconsistent by sub-proof #160. % 136.03/20.05 | | % 136.03/20.05 | Case 2: % 136.03/20.05 | | % 136.03/20.05 | | (33) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 136.03/20.05 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.05 | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 136.03/20.05 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 136.03/20.05 | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.03/20.05 | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 136.03/20.05 | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 136.03/20.05 | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.03/20.05 | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 136.03/20.05 | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.03/20.05 | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 136.03/20.05 | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.03/20.05 | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.03/20.05 | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.03/20.05 | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.03/20.05 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.03/20.05 | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.05 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.05 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.05 | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.03/20.05 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 136.03/20.05 | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.03/20.05 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.05 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 136.03/20.05 | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 136.03/20.05 | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 136.03/20.05 | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.03/20.05 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 % 136.03/20.05 | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.03/20.05 | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.05 | | $i(all_56_21) & $i(all_56_29)))) % 136.03/20.05 | | % 136.03/20.05 | | BETA: splitting (33) gives: % 136.03/20.05 | | % 136.03/20.05 | | Case 1: % 136.03/20.05 | | | % 136.03/20.05 | | | (34) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 136.03/20.05 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.05 | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 136.03/20.05 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 136.03/20.05 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.03/20.05 | | | $i(all_56_31) % 136.03/20.05 | | | % 136.03/20.05 | | | ALPHA: (34) implies: % 136.03/20.05 | | | (35) op(e2, e2) = e0 % 136.03/20.05 | | | % 136.03/20.05 | | | REF_CLOSE: (8), (13), (26), (35) are inconsistent by sub-proof #675. % 136.03/20.05 | | | % 136.03/20.05 | | Case 2: % 136.03/20.05 | | | % 136.03/20.05 | | | (36) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.05 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.05 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.05 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 136.03/20.05 | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.03/20.05 | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 136.03/20.05 | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.03/20.05 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) % 136.03/20.05 | | | & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 136.03/20.05 | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.03/20.05 | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 136.03/20.05 | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.05 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) % 136.03/20.05 | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.03/20.05 | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 % 136.03/20.05 | | | & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.03/20.05 | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 136.03/20.05 | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 136.03/20.05 | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & % 136.03/20.05 | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) % 136.03/20.05 | | | = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 136.03/20.05 | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.03/20.05 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) % 136.03/20.05 | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, % 136.03/20.05 | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 % 136.03/20.05 | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.03/20.05 | | | $i(all_56_29)))) % 136.03/20.05 | | | % 136.03/20.05 | | | BETA: splitting (36) gives: % 136.03/20.05 | | | % 136.03/20.05 | | | Case 1: % 136.03/20.05 | | | | % 136.03/20.05 | | | | (37) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.05 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.05 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.05 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 136.03/20.05 | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.03/20.05 | | | | $i(all_56_27) % 136.03/20.05 | | | | % 136.03/20.05 | | | | ALPHA: (37) implies: % 136.03/20.05 | | | | (38) op(e1, e1) = e2 % 136.03/20.05 | | | | % 136.03/20.05 | | | | REF_CLOSE: (2), (8), (16), (38) are inconsistent by sub-proof #767. % 136.03/20.05 | | | | % 136.03/20.05 | | | Case 2: % 136.03/20.05 | | | | % 136.03/20.05 | | | | (39) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 136.03/20.05 | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & % 136.03/20.05 | | | | ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.05 | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 136.03/20.05 | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & % 136.03/20.05 | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 136.03/20.05 | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.03/20.05 | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, % 136.03/20.05 | | | | e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.05 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.03/20.05 | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.03/20.05 | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 136.03/20.05 | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 136.03/20.05 | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & % 136.03/20.05 | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) % 136.03/20.05 | | | | = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 136.03/20.05 | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.03/20.05 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) % 136.03/20.05 | | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, % 136.03/20.05 | | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 % 136.03/20.05 | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.03/20.05 | | | | $i(all_56_29))) % 136.03/20.05 | | | | % 136.03/20.05 | | | | ALPHA: (39) implies: % 136.03/20.05 | | | | (40) op(e0, e0) = all_56_31 % 136.03/20.05 | | | | (41) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.03/20.05 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.03/20.05 | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.03/20.05 | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.03/20.05 | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.03/20.05 | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.05 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.05 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.05 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.03/20.05 | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 136.03/20.05 | | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.03/20.05 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.05 | | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 136.03/20.05 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 136.03/20.05 | | | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 136.03/20.05 | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.03/20.05 | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 % 136.03/20.05 | | | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.03/20.05 | | | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.05 | | | | $i(all_56_21) & $i(all_56_29)) % 136.03/20.05 | | | | % 136.03/20.05 | | | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (11), (14), (15), (17), % 136.03/20.05 | | | | (18), (19), (21), (22), (23), (24), (25), (27), (28), (29), % 136.03/20.05 | | | | (30), (31), (40), (41) are inconsistent by sub-proof #548. % 136.03/20.05 | | | | % 136.03/20.05 | | | End of split % 136.03/20.05 | | | % 136.03/20.05 | | End of split % 136.03/20.05 | | % 136.03/20.05 | End of split % 136.03/20.05 | % 136.03/20.05 End of proof % 136.03/20.05 % 136.03/20.05 Sub-proof #160 shows that the following formulas are inconsistent: % 136.03/20.05 ---------------------------------------------------------------- % 136.03/20.05 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.03/20.05 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.03/20.05 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.03/20.05 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.03/20.05 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ % 136.03/20.05 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 136.03/20.05 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = % 136.03/20.05 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.03/20.05 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.03/20.05 $i(all_56_29)) % 136.03/20.05 (2) op(e1, e2) = e2 % 136.03/20.05 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.05 (4) ~ (all_52_2 = e1) % 136.03/20.05 (5) op(e1, e3) = all_52_2 % 136.03/20.05 % 136.03/20.05 Begin of proof % 136.03/20.05 | % 136.03/20.05 | BETA: splitting (1) gives: % 136.03/20.05 | % 136.03/20.05 | Case 1: % 136.03/20.05 | | % 136.03/20.05 | | (6) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.03/20.05 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.05 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.05 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) % 136.03/20.05 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.03/20.05 | | % 136.03/20.05 | | ALPHA: (6) implies: % 136.03/20.05 | | (7) op(e1, e3) = e1 % 136.03/20.05 | | % 136.03/20.05 | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #725. % 136.03/20.05 | | % 136.03/20.05 | Case 2: % 136.03/20.05 | | % 136.03/20.05 | | (8) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.03/20.05 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 % 136.03/20.05 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.03/20.05 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.03/20.05 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.03/20.05 | | % 136.03/20.05 | | ALPHA: (8) implies: % 136.03/20.05 | | (9) ~ (all_56_13 = e2) % 136.03/20.05 | | (10) op(e1, e2) = all_56_13 % 136.03/20.05 | | % 136.03/20.05 | | REF_CLOSE: (2), (3), (9), (10) are inconsistent by sub-proof #165. % 136.03/20.05 | | % 136.03/20.05 | End of split % 136.03/20.05 | % 136.03/20.05 End of proof % 136.03/20.05 % 136.03/20.05 Sub-proof #161 shows that the following formulas are inconsistent: % 136.03/20.05 ---------------------------------------------------------------- % 136.03/20.05 (1) all_57_5 = e1 & op(e2, e1) = e1 % 136.03/20.05 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.05 (3) op(e2, e1) = all_52_9 % 136.03/20.05 (4) ~ (all_52_9 = e1) % 136.03/20.05 % 136.03/20.05 Begin of proof % 136.03/20.05 | % 136.03/20.05 | ALPHA: (1) implies: % 136.03/20.05 | (5) op(e2, e1) = e1 % 136.03/20.05 | % 136.03/20.05 | GROUND_INST: instantiating (2) with all_52_9, e1, e1, e2, simplifying with % 136.03/20.05 | (3), (5) gives: % 136.03/20.05 | (6) all_52_9 = e1 % 136.03/20.05 | % 136.03/20.05 | REDUCE: (4), (6) imply: % 136.03/20.05 | (7) $false % 136.03/20.05 | % 136.03/20.05 | CLOSE: (7) is inconsistent. % 136.03/20.05 | % 136.03/20.05 End of proof % 136.03/20.05 % 136.03/20.05 Sub-proof #162 shows that the following formulas are inconsistent: % 136.03/20.05 ---------------------------------------------------------------- % 136.03/20.05 (1) ~ (e2 = e0) % 136.03/20.05 (2) op(e3, e3) = e1 % 136.03/20.05 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.03/20.05 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.03/20.05 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.05 (5) ~ (e2 = e1) % 136.03/20.05 (6) ~ (e3 = e0) % 136.03/20.05 (7) ~ (e3 = e2) % 136.03/20.05 (8) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 136.03/20.05 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 136.03/20.05 (9) ~ (all_52_4 = e2) % 136.03/20.05 (10) op(e3, e2) = all_52_4 % 136.03/20.05 (11) all_57_4 = e1 % 136.03/20.05 (12) op(e3, e1) = all_52_8 % 136.03/20.05 (13) ~ (e3 = e1) % 136.03/20.05 (14) ~ (e1 = e0) % 136.03/20.05 (15) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.03/20.05 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.03/20.05 (16) ~ (all_52_8 = e3) % 136.03/20.05 % 136.03/20.05 Begin of proof % 136.03/20.05 | % 136.03/20.05 | BETA: splitting (8) gives: % 136.03/20.05 | % 136.03/20.05 | Case 1: % 136.03/20.05 | | % 136.03/20.05 | | (17) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = % 136.03/20.05 | | e2) % 136.03/20.05 | | % 136.03/20.05 | | BETA: splitting (17) gives: % 136.03/20.05 | | % 136.03/20.05 | | Case 1: % 136.03/20.05 | | | % 136.03/20.05 | | | (18) all_57_0 = e2 & op(e3, e3) = e2 % 136.03/20.05 | | | % 136.03/20.05 | | | ALPHA: (18) implies: % 136.03/20.05 | | | (19) op(e3, e3) = e2 % 136.03/20.05 | | | % 136.03/20.05 | | | REF_CLOSE: (2), (4), (5), (19) are inconsistent by sub-proof #743. % 136.03/20.05 | | | % 136.03/20.05 | | Case 2: % 136.03/20.05 | | | % 136.03/20.05 | | | (20) all_57_1 = e2 & op(e3, e2) = e2 % 136.03/20.05 | | | % 136.03/20.05 | | | REF_CLOSE: (4), (9), (10), (20) are inconsistent by sub-proof #396. % 136.03/20.05 | | | % 136.03/20.05 | | End of split % 136.03/20.05 | | % 136.03/20.05 | Case 2: % 136.03/20.05 | | % 136.03/20.05 | | (21) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = % 136.03/20.05 | | e2) % 136.03/20.05 | | % 136.03/20.05 | | BETA: splitting (21) gives: % 136.03/20.05 | | % 136.03/20.05 | | Case 1: % 136.03/20.05 | | | % 136.03/20.05 | | | (22) all_57_4 = e2 & op(e3, e1) = e2 % 136.03/20.05 | | | % 136.03/20.05 | | | ALPHA: (22) implies: % 136.03/20.05 | | | (23) all_57_4 = e2 % 136.03/20.05 | | | % 136.03/20.05 | | | REF_CLOSE: (5), (11), (23) are inconsistent by sub-proof #669. % 136.03/20.05 | | | % 136.03/20.05 | | Case 2: % 136.03/20.05 | | | % 136.03/20.05 | | | (24) all_57_9 = e2 & op(e3, e0) = e2 % 136.03/20.05 | | | % 136.03/20.05 | | | ALPHA: (24) implies: % 136.03/20.05 | | | (25) all_57_9 = e2 % 136.03/20.05 | | | % 136.03/20.05 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (12), (13), (14), % 136.03/20.05 | | | (15), (16), (25) are inconsistent by sub-proof #163. % 136.03/20.05 | | | % 136.03/20.05 | | End of split % 136.03/20.05 | | % 136.03/20.05 | End of split % 136.03/20.05 | % 136.03/20.05 End of proof % 136.03/20.05 % 136.03/20.05 Sub-proof #163 shows that the following formulas are inconsistent: % 136.03/20.05 ---------------------------------------------------------------- % 136.03/20.05 (1) ~ (e2 = e0) % 136.03/20.05 (2) op(e3, e3) = e1 % 136.03/20.05 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.03/20.05 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.03/20.05 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.05 (5) ~ (e2 = e1) % 136.03/20.05 (6) ~ (e3 = e0) % 136.03/20.05 (7) ~ (e3 = e2) % 136.03/20.05 (8) all_57_9 = e2 % 136.03/20.06 (9) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 136.03/20.06 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 136.03/20.06 (10) all_57_4 = e1 % 136.03/20.06 (11) op(e3, e1) = all_52_8 % 136.03/20.06 (12) ~ (e3 = e1) % 136.03/20.06 (13) ~ (e1 = e0) % 136.03/20.06 (14) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.03/20.06 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.03/20.06 (15) ~ (all_52_8 = e3) % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | BETA: splitting (14) gives: % 136.03/20.06 | % 136.03/20.06 | Case 1: % 136.03/20.06 | | % 136.03/20.06 | | (16) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = % 136.03/20.06 | | e3) % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (12), (13), (14), % 136.03/20.06 | | (16) are inconsistent by sub-proof #164. % 136.03/20.06 | | % 136.03/20.06 | Case 2: % 136.03/20.06 | | % 136.03/20.06 | | (17) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = % 136.03/20.06 | | e3) % 136.03/20.06 | | % 136.03/20.06 | | BETA: splitting (17) gives: % 136.03/20.06 | | % 136.03/20.06 | | Case 1: % 136.03/20.06 | | | % 136.03/20.06 | | | (18) all_57_4 = e3 & op(e3, e1) = e3 % 136.03/20.06 | | | % 136.03/20.06 | | | ALPHA: (18) implies: % 136.03/20.06 | | | (19) op(e3, e1) = e3 % 136.03/20.06 | | | % 136.03/20.06 | | | REF_CLOSE: (4), (11), (15), (19) are inconsistent by sub-proof #705. % 136.03/20.06 | | | % 136.03/20.06 | | Case 2: % 136.03/20.06 | | | % 136.03/20.06 | | | (20) all_57_9 = e3 & op(e3, e0) = e3 % 136.03/20.06 | | | % 136.03/20.06 | | | ALPHA: (20) implies: % 136.03/20.06 | | | (21) all_57_9 = e3 % 136.03/20.06 | | | % 136.03/20.06 | | | COMBINE_EQS: (8), (21) imply: % 136.03/20.06 | | | (22) e3 = e2 % 136.03/20.06 | | | % 136.03/20.06 | | | SIMP: (22) implies: % 136.03/20.06 | | | (23) e3 = e2 % 136.03/20.06 | | | % 136.03/20.06 | | | REDUCE: (7), (23) imply: % 136.03/20.06 | | | (24) $false % 136.03/20.06 | | | % 136.03/20.06 | | | CLOSE: (24) is inconsistent. % 136.03/20.06 | | | % 136.03/20.06 | | End of split % 136.03/20.06 | | % 136.03/20.06 | End of split % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #164 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) ~ (e2 = e0) % 136.03/20.06 (2) op(e3, e3) = e1 % 136.03/20.06 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.03/20.06 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.03/20.06 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.06 (5) ~ (e2 = e1) % 136.03/20.06 (6) ~ (e3 = e0) % 136.03/20.06 (7) ~ (e3 = e2) % 136.03/20.06 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) % 136.03/20.06 (9) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 136.03/20.06 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 136.03/20.06 (10) all_57_4 = e1 % 136.03/20.06 (11) ~ (e3 = e1) % 136.03/20.06 (12) ~ (e1 = e0) % 136.03/20.06 (13) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.03/20.06 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | BETA: splitting (8) gives: % 136.03/20.06 | % 136.03/20.06 | Case 1: % 136.03/20.06 | | % 136.03/20.06 | | (14) all_57_0 = e3 & op(e3, e3) = e3 % 136.03/20.06 | | % 136.03/20.06 | | ALPHA: (14) implies: % 136.03/20.06 | | (15) op(e3, e3) = e3 % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (2), (4), (11), (15) are inconsistent by sub-proof #775. % 136.03/20.06 | | % 136.03/20.06 | Case 2: % 136.03/20.06 | | % 136.03/20.06 | | (16) all_57_1 = e3 & op(e3, e2) = e3 % 136.03/20.06 | | % 136.03/20.06 | | ALPHA: (16) implies: % 136.03/20.06 | | (17) all_57_1 = e3 % 136.03/20.06 | | % 136.03/20.06 | | BETA: splitting (3) gives: % 136.03/20.06 | | % 136.03/20.06 | | Case 1: % 136.03/20.06 | | | % 136.03/20.06 | | | (18) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = % 136.03/20.06 | | | e0) % 136.03/20.06 | | | % 136.03/20.06 | | | REF_CLOSE: (2), (4), (6), (12), (17), (18) are inconsistent by sub-proof % 136.03/20.06 | | | #648. % 136.03/20.06 | | | % 136.03/20.06 | | Case 2: % 136.03/20.06 | | | % 136.03/20.06 | | | (19) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = % 136.03/20.06 | | | e0) % 136.03/20.06 | | | % 136.03/20.06 | | | BETA: splitting (19) gives: % 136.03/20.06 | | | % 136.03/20.06 | | | Case 1: % 136.03/20.06 | | | | % 136.03/20.06 | | | | (20) all_57_4 = e0 & op(e3, e1) = e0 % 136.03/20.06 | | | | % 136.03/20.06 | | | | REF_CLOSE: (10), (12), (20) are inconsistent by sub-proof #672. % 136.03/20.06 | | | | % 136.03/20.06 | | | Case 2: % 136.03/20.06 | | | | % 136.03/20.06 | | | | (21) all_57_9 = e0 & op(e3, e0) = e0 % 136.03/20.06 | | | | % 136.03/20.06 | | | | ALPHA: (21) implies: % 136.03/20.06 | | | | (22) all_57_9 = e0 % 136.03/20.06 | | | | % 136.03/20.06 | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (13), (22) are % 136.03/20.06 | | | | inconsistent by sub-proof #668. % 136.03/20.06 | | | | % 136.03/20.06 | | | End of split % 136.03/20.06 | | | % 136.03/20.06 | | End of split % 136.03/20.06 | | % 136.03/20.06 | End of split % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #165 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.06 (2) op(e1, e2) = all_56_13 % 136.03/20.06 (3) op(e1, e2) = e2 % 136.03/20.06 (4) ~ (all_56_13 = e2) % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | GROUND_INST: instantiating (1) with e2, all_56_13, e2, e1, simplifying with % 136.03/20.06 | (2), (3) gives: % 136.03/20.06 | (5) all_56_13 = e2 % 136.03/20.06 | % 136.03/20.06 | REDUCE: (4), (5) imply: % 136.03/20.06 | (6) $false % 136.03/20.06 | % 136.03/20.06 | CLOSE: (6) is inconsistent. % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #166 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.06 (2) op(e2, e2) = e1 % 136.03/20.06 (3) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) % 136.03/20.06 (4) ~ (all_52_1 = e3) % 136.03/20.06 (5) op(e2, e3) = all_52_1 % 136.03/20.06 (6) ~ (e3 = e1) % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | BETA: splitting (3) gives: % 136.03/20.06 | % 136.03/20.06 | Case 1: % 136.03/20.06 | | % 136.03/20.06 | | (7) all_57_2 = e3 & op(e2, e3) = e3 % 136.03/20.06 | | % 136.03/20.06 | | ALPHA: (7) implies: % 136.03/20.06 | | (8) op(e2, e3) = e3 % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #763. % 136.03/20.06 | | % 136.03/20.06 | Case 2: % 136.03/20.06 | | % 136.03/20.06 | | (9) all_57_3 = e3 & op(e2, e2) = e3 % 136.03/20.06 | | % 136.03/20.06 | | ALPHA: (9) implies: % 136.03/20.06 | | (10) op(e2, e2) = e3 % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #325. % 136.03/20.06 | | % 136.03/20.06 | End of split % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #167 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) all_57_11 = e3 % 136.03/20.06 (2) all_57_11 = e1 % 136.03/20.06 (3) ~ (e3 = e1) % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | COMBINE_EQS: (1), (2) imply: % 136.03/20.06 | (4) e3 = e1 % 136.03/20.06 | % 136.03/20.06 | SIMP: (4) implies: % 136.03/20.06 | (5) e3 = e1 % 136.03/20.06 | % 136.03/20.06 | REDUCE: (3), (5) imply: % 136.03/20.06 | (6) $false % 136.03/20.06 | % 136.03/20.06 | CLOSE: (6) is inconsistent. % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #168 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) all_54_9 = e1 | all_54_9 = e0 % 136.03/20.06 (2) all_54_9 = all_52_6 % 136.03/20.06 (3) ~ (all_52_6 = e1) % 136.03/20.06 (4) ~ (all_52_6 = e0) % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | BETA: splitting (1) gives: % 136.03/20.06 | % 136.03/20.06 | Case 1: % 136.03/20.06 | | % 136.03/20.06 | | (5) all_54_9 = e1 % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #169. % 136.03/20.06 | | % 136.03/20.06 | Case 2: % 136.03/20.06 | | % 136.03/20.06 | | (6) all_54_9 = e0 % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #568. % 136.03/20.06 | | % 136.03/20.06 | End of split % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #169 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) all_54_9 = all_52_6 % 136.03/20.06 (2) all_54_9 = e1 % 136.03/20.06 (3) ~ (all_52_6 = e1) % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | COMBINE_EQS: (1), (2) imply: % 136.03/20.06 | (4) all_52_6 = e1 % 136.03/20.06 | % 136.03/20.06 | SIMP: (4) implies: % 136.03/20.06 | (5) all_52_6 = e1 % 136.03/20.06 | % 136.03/20.06 | REDUCE: (3), (5) imply: % 136.03/20.06 | (6) $false % 136.03/20.06 | % 136.03/20.06 | CLOSE: (6) is inconsistent. % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #170 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) ~ (e2 = e0) % 136.03/20.06 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.06 (3) ~ (all_52_6 = e0) % 136.03/20.06 (4) op(e1, e2) = all_52_6 % 136.03/20.06 (5) all_57_13 = e2 % 136.03/20.06 (6) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | BETA: splitting (6) gives: % 136.03/20.06 | % 136.03/20.06 | Case 1: % 136.03/20.06 | | % 136.03/20.06 | | (7) all_57_7 = e0 & op(e1, e2) = e0 % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #505. % 136.03/20.06 | | % 136.03/20.06 | Case 2: % 136.03/20.06 | | % 136.03/20.06 | | (8) all_57_13 = e0 & op(e0, e2) = e0 % 136.03/20.06 | | % 136.03/20.06 | | ALPHA: (8) implies: % 136.03/20.06 | | (9) all_57_13 = e0 % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #404. % 136.03/20.06 | | % 136.03/20.06 | End of split % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #171 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) op(e1, e1) = all_6_2 % 136.03/20.06 (2) all_57_7 = e3 & op(e1, e2) = e3 % 136.03/20.06 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.06 (4) ~ (e2 = e1) % 136.03/20.06 (5) ~ (e3 = e2) % 136.03/20.06 (6) op(e1, e0) = e1 % 136.03/20.06 (7) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 136.03/20.06 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 136.03/20.06 (8) ~ (all_6_2 = e2) % 136.03/20.06 (9) op(e1, e3) = all_50_0 % 136.03/20.06 (10) ~ (all_50_0 = e2) % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | ALPHA: (2) implies: % 136.03/20.06 | (11) all_57_7 = e3 % 136.03/20.06 | % 136.03/20.06 | BETA: splitting (7) gives: % 136.03/20.06 | % 136.03/20.06 | Case 1: % 136.03/20.06 | | % 136.03/20.06 | | (12) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = % 136.03/20.06 | | e2) % 136.03/20.06 | | % 136.03/20.06 | | BETA: splitting (12) gives: % 136.03/20.06 | | % 136.03/20.06 | | Case 1: % 136.03/20.06 | | | % 136.03/20.06 | | | (13) all_57_6 = e2 & op(e1, e3) = e2 % 136.03/20.06 | | | % 136.03/20.06 | | | ALPHA: (13) implies: % 136.03/20.06 | | | (14) op(e1, e3) = e2 % 136.03/20.06 | | | % 136.03/20.06 | | | REF_CLOSE: (3), (9), (10), (14) are inconsistent by sub-proof #735. % 136.03/20.06 | | | % 136.03/20.06 | | Case 2: % 136.03/20.06 | | | % 136.03/20.06 | | | (15) all_57_7 = e2 & op(e1, e2) = e2 % 136.03/20.06 | | | % 136.03/20.06 | | | REF_CLOSE: (5), (11), (15) are inconsistent by sub-proof #385. % 136.03/20.06 | | | % 136.03/20.06 | | End of split % 136.03/20.06 | | % 136.03/20.06 | Case 2: % 136.03/20.06 | | % 136.03/20.06 | | (16) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = % 136.03/20.06 | | e2) % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (1), (3), (4), (6), (8), (16) are inconsistent by sub-proof #172. % 136.03/20.06 | | % 136.03/20.06 | End of split % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #172 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) op(e1, e1) = all_6_2 % 136.03/20.06 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.06 (3) ~ (e2 = e1) % 136.03/20.06 (4) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 136.03/20.06 (5) op(e1, e0) = e1 % 136.03/20.06 (6) ~ (all_6_2 = e2) % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | BETA: splitting (4) gives: % 136.03/20.06 | % 136.03/20.06 | Case 1: % 136.03/20.06 | | % 136.03/20.06 | | (7) all_57_8 = e2 & op(e1, e1) = e2 % 136.03/20.06 | | % 136.03/20.06 | | ALPHA: (7) implies: % 136.03/20.06 | | (8) op(e1, e1) = e2 % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #767. % 136.03/20.06 | | % 136.03/20.06 | Case 2: % 136.03/20.06 | | % 136.03/20.06 | | (9) all_57_11 = e2 & op(e1, e0) = e2 % 136.03/20.06 | | % 136.03/20.06 | | ALPHA: (9) implies: % 136.03/20.06 | | (10) op(e1, e0) = e2 % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #720. % 136.03/20.06 | | % 136.03/20.06 | End of split % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #173 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) ~ (e2 = e0) % 136.03/20.06 (2) op(e3, e3) = e1 % 136.03/20.06 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.03/20.06 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.03/20.06 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.06 (5) ~ (e2 = e1) % 136.03/20.06 (6) ~ (all_56_25 = e0) % 136.03/20.06 (7) ~ (all_52_3 = e3) % 136.03/20.06 (8) op(e2, e2) = e1 % 136.03/20.06 (9) op(e3, e3) = all_56_1 % 136.03/20.06 (10) op(e3, e0) = all_56_25 % 136.03/20.06 (11) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) % 136.03/20.06 (12) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 136.03/20.06 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 136.03/20.06 (13) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & $i(all_34_0)) | ( ~ % 136.03/20.06 (all_34_1 = e1) & op(e3, e3) = all_34_1 & $i(all_34_1)) % 136.03/20.06 (14) ~ (all_52_4 = e2) % 136.03/20.06 (15) ~ (all_52_3 = e1) % 136.03/20.06 (16) op(e3, e2) = all_52_4 % 136.03/20.06 (17) op(e0, e3) = all_52_3 % 136.03/20.06 (18) op(e3, e0) = all_52_12 % 136.03/20.06 (19) op(e3, e2) = all_56_9 % 136.03/20.06 (20) op(e0, e3) = e0 % 136.03/20.06 (21) ~ (e3 = e1) % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | BETA: splitting (11) gives: % 136.03/20.06 | % 136.03/20.06 | Case 1: % 136.03/20.06 | | % 136.03/20.06 | | (22) all_57_1 = e3 & op(e3, e2) = e3 % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (12), (13), (14), % 136.03/20.06 | | (15), (16), (17), (18), (19), (20), (22) are inconsistent by % 136.03/20.06 | | sub-proof #549. % 136.03/20.06 | | % 136.03/20.06 | Case 2: % 136.03/20.06 | | % 136.03/20.06 | | (23) all_57_3 = e3 & op(e2, e2) = e3 % 136.03/20.06 | | % 136.03/20.06 | | ALPHA: (23) implies: % 136.03/20.06 | | (24) op(e2, e2) = e3 % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (4), (8), (21), (24) are inconsistent by sub-proof #325. % 136.03/20.06 | | % 136.03/20.06 | End of split % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #174 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) op(e3, e3) = e1 % 136.03/20.06 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.06 (3) ~ (e2 = e1) % 136.03/20.06 (4) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 136.03/20.06 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 136.03/20.06 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.03/20.06 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.03/20.06 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.03/20.06 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.03/20.06 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 136.03/20.06 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.03/20.06 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.06 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 136.03/20.06 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.03/20.06 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 136.03/20.06 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 136.03/20.06 = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.03/20.06 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & % 136.03/20.06 ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, % 136.03/20.06 e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 136.03/20.06 op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 136.03/20.06 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 136.03/20.06 (5) op(e2, e2) = e1 % 136.03/20.06 (6) ~ (e3 = e1) % 136.03/20.06 (7) ~ (e1 = e0) % 136.03/20.06 (8) op(e1, e3) = e3 % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | BETA: splitting (4) gives: % 136.03/20.06 | % 136.03/20.06 | Case 1: % 136.03/20.06 | | % 136.03/20.06 | | (9) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.03/20.06 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 % 136.03/20.06 | | & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 % 136.03/20.06 | | & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.03/20.06 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.03/20.06 | | all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.03/20.06 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 136.03/20.06 | | e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.03/20.06 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.03/20.06 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 136.03/20.06 | | % 136.03/20.06 | | BETA: splitting (9) gives: % 136.03/20.06 | | % 136.03/20.06 | | Case 1: % 136.03/20.06 | | | % 136.03/20.06 | | | (10) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.03/20.06 | | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = % 136.03/20.06 | | | e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.03/20.06 | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.03/20.06 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.03/20.06 | | | % 136.03/20.06 | | | ALPHA: (10) implies: % 136.03/20.06 | | | (11) op(e3, e3) = e2 % 136.03/20.06 | | | % 136.03/20.06 | | | REF_CLOSE: (1), (2), (3), (11) are inconsistent by sub-proof #743. % 136.03/20.06 | | | % 136.03/20.06 | | Case 2: % 136.03/20.06 | | | % 136.03/20.06 | | | (12) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ % 136.03/20.06 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.03/20.06 | | | op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 136.03/20.06 | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.03/20.06 | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.03/20.06 | | | $i(all_56_29) % 136.03/20.06 | | | % 136.03/20.06 | | | ALPHA: (12) implies: % 136.03/20.06 | | | (13) ~ (all_56_5 = e3) % 136.03/20.06 | | | (14) op(e1, e3) = all_56_5 % 136.03/20.06 | | | % 136.03/20.06 | | | REF_CLOSE: (2), (8), (13), (14) are inconsistent by sub-proof #724. % 136.03/20.06 | | | % 136.03/20.06 | | End of split % 136.03/20.06 | | % 136.03/20.06 | Case 2: % 136.03/20.06 | | % 136.03/20.06 | | (15) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 % 136.03/20.06 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = % 136.03/20.06 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 136.03/20.06 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 136.03/20.06 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 136.03/20.06 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.03/20.06 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.06 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.06 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 136.03/20.06 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (1), (2), (5), (6), (7), (15) are inconsistent by sub-proof #175. % 136.03/20.06 | | % 136.03/20.06 | End of split % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #175 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) op(e3, e3) = e1 % 136.03/20.06 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.06 (3) op(e2, e2) = e1 % 136.03/20.06 (4) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.06 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.03/20.06 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.06 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.06 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 136.03/20.06 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 136.03/20.06 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 136.03/20.06 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.03/20.06 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.03/20.06 $i(all_56_17) & $i(all_56_25)) % 136.03/20.06 (5) ~ (e3 = e1) % 136.03/20.06 (6) ~ (e1 = e0) % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | BETA: splitting (4) gives: % 136.03/20.06 | % 136.03/20.06 | Case 1: % 136.03/20.06 | | % 136.03/20.06 | | (7) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.06 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.03/20.06 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.06 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.06 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.03/20.06 | | % 136.03/20.06 | | ALPHA: (7) implies: % 136.03/20.06 | | (8) op(e3, e3) = e0 % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #717. % 136.03/20.06 | | % 136.03/20.06 | Case 2: % 136.03/20.06 | | % 136.03/20.06 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.03/20.06 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.06 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.06 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) % 136.03/20.06 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.03/20.06 | | % 136.03/20.06 | | ALPHA: (9) implies: % 136.03/20.06 | | (10) op(e2, e2) = e3 % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #325. % 136.03/20.06 | | % 136.03/20.06 | End of split % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #176 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) all_54_9 = all_48_0 % 136.03/20.06 (2) all_54_9 = e3 % 136.03/20.06 (3) ~ (all_48_0 = e3) % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | COMBINE_EQS: (1), (2) imply: % 136.03/20.06 | (4) all_48_0 = e3 % 136.03/20.06 | % 136.03/20.06 | SIMP: (4) implies: % 136.03/20.06 | (5) all_48_0 = e3 % 136.03/20.06 | % 136.03/20.06 | REDUCE: (3), (5) imply: % 136.03/20.06 | (6) $false % 136.03/20.06 | % 136.03/20.06 | CLOSE: (6) is inconsistent. % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #177 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) ~ (e2 = e0) % 136.03/20.06 (2) op(e3, e3) = e1 % 136.03/20.06 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.06 (4) ~ (e2 = e1) % 136.03/20.06 (5) ~ (e3 = e0) % 136.03/20.06 (6) ~ (e3 = e2) % 136.03/20.06 (7) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.03/20.06 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.03/20.06 (8) op(e0, e2) = all_52_7 % 136.03/20.06 (9) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.03/20.06 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.03/20.06 (10) ~ (all_52_7 = e1) % 136.03/20.06 (11) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) | % 136.03/20.06 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2) % 136.03/20.06 (12) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.03/20.06 (13) ~ (e3 = e1) % 136.03/20.06 (14) ~ (e1 = e0) % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | BETA: splitting (12) gives: % 136.03/20.06 | % 136.03/20.06 | Case 1: % 136.03/20.06 | | % 136.03/20.06 | | (15) all_57_12 = e1 & op(e0, e3) = e1 % 136.03/20.06 | | % 136.03/20.06 | | ALPHA: (15) implies: % 136.03/20.06 | | (16) all_57_12 = e1 % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (13), (14), (16) % 136.03/20.06 | | are inconsistent by sub-proof #583. % 136.03/20.06 | | % 136.03/20.06 | Case 2: % 136.03/20.06 | | % 136.03/20.06 | | (17) all_57_13 = e1 & op(e0, e2) = e1 % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (3), (8), (10), (17) are inconsistent by sub-proof #178. % 136.03/20.06 | | % 136.03/20.06 | End of split % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #178 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) all_57_13 = e1 & op(e0, e2) = e1 % 136.03/20.06 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.06 (3) op(e0, e2) = all_52_7 % 136.03/20.06 (4) ~ (all_52_7 = e1) % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | ALPHA: (1) implies: % 136.03/20.06 | (5) op(e0, e2) = e1 % 136.03/20.06 | % 136.03/20.06 | GROUND_INST: instantiating (2) with all_52_7, e1, e2, e0, simplifying with % 136.03/20.06 | (3), (5) gives: % 136.03/20.06 | (6) all_52_7 = e1 % 136.03/20.06 | % 136.03/20.06 | REDUCE: (4), (6) imply: % 136.03/20.06 | (7) $false % 136.03/20.06 | % 136.03/20.06 | CLOSE: (7) is inconsistent. % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #179 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) ~ (all_52_12 = e1) % 136.03/20.06 (2) op(e2, e0) = all_52_13 % 136.03/20.06 (3) ~ (all_52_13 = e1) % 136.03/20.06 (4) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.03/20.06 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.06 (6) op(e3, e0) = all_52_12 % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | BETA: splitting (4) gives: % 136.03/20.06 | % 136.03/20.06 | Case 1: % 136.03/20.06 | | % 136.03/20.06 | | (7) all_57_9 = e1 & op(e3, e0) = e1 % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (1), (5), (6), (7) are inconsistent by sub-proof #181. % 136.03/20.06 | | % 136.03/20.06 | Case 2: % 136.03/20.06 | | % 136.03/20.06 | | (8) all_57_10 = e1 & op(e2, e0) = e1 % 136.03/20.06 | | % 136.03/20.06 | | ALPHA: (8) implies: % 136.03/20.06 | | (9) op(e2, e0) = e1 % 136.03/20.06 | | % 136.03/20.06 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #180. % 136.03/20.06 | | % 136.03/20.06 | End of split % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #180 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.06 (2) op(e2, e0) = all_52_13 % 136.03/20.06 (3) op(e2, e0) = e1 % 136.03/20.06 (4) ~ (all_52_13 = e1) % 136.03/20.06 % 136.03/20.06 Begin of proof % 136.03/20.06 | % 136.03/20.06 | GROUND_INST: instantiating (1) with all_52_13, e1, e0, e2, simplifying with % 136.03/20.06 | (2), (3) gives: % 136.03/20.06 | (5) all_52_13 = e1 % 136.03/20.06 | % 136.03/20.06 | REDUCE: (4), (5) imply: % 136.03/20.06 | (6) $false % 136.03/20.06 | % 136.03/20.06 | CLOSE: (6) is inconsistent. % 136.03/20.06 | % 136.03/20.06 End of proof % 136.03/20.06 % 136.03/20.06 Sub-proof #181 shows that the following formulas are inconsistent: % 136.03/20.06 ---------------------------------------------------------------- % 136.03/20.06 (1) all_57_9 = e1 & op(e3, e0) = e1 % 136.03/20.06 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.06 (3) op(e3, e0) = all_52_12 % 136.03/20.07 (4) ~ (all_52_12 = e1) % 136.03/20.07 % 136.03/20.07 Begin of proof % 136.03/20.07 | % 136.03/20.07 | ALPHA: (1) implies: % 136.03/20.07 | (5) op(e3, e0) = e1 % 136.03/20.07 | % 136.03/20.07 | GROUND_INST: instantiating (2) with all_52_12, e1, e0, e3, simplifying with % 136.03/20.07 | (3), (5) gives: % 136.03/20.07 | (6) all_52_12 = e1 % 136.03/20.07 | % 136.03/20.07 | REDUCE: (4), (6) imply: % 136.03/20.07 | (7) $false % 136.03/20.07 | % 136.03/20.07 | CLOSE: (7) is inconsistent. % 136.03/20.07 | % 136.03/20.07 End of proof % 136.03/20.07 % 136.03/20.07 Sub-proof #182 shows that the following formulas are inconsistent: % 136.03/20.07 ---------------------------------------------------------------- % 136.03/20.07 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.07 (2) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.07 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 136.03/20.07 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.07 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 136.03/20.07 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.03/20.07 e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 136.03/20.07 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.03/20.07 = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.07 $i(all_56_21) & $i(all_56_29)) % 136.03/20.07 (3) op(e1, e1) = e1 % 136.03/20.07 (4) ~ (all_52_14 = e1) % 136.03/20.07 (5) op(e1, e0) = all_52_14 % 136.03/20.07 % 136.03/20.07 Begin of proof % 136.03/20.07 | % 136.03/20.07 | BETA: splitting (2) gives: % 136.03/20.07 | % 136.03/20.07 | Case 1: % 136.03/20.07 | | % 136.03/20.07 | | (6) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 % 136.03/20.07 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 % 136.03/20.07 | | & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.07 | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) % 136.03/20.07 | | % 136.03/20.07 | | ALPHA: (6) implies: % 136.03/20.07 | | (7) op(e1, e0) = e1 % 136.03/20.07 | | % 136.03/20.07 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #327. % 136.03/20.07 | | % 136.03/20.07 | Case 2: % 136.03/20.07 | | % 136.03/20.07 | | (8) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.03/20.07 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 136.03/20.07 | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 136.03/20.07 | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.07 | | $i(all_56_21) & $i(all_56_29) % 136.03/20.07 | | % 136.03/20.07 | | ALPHA: (8) implies: % 136.03/20.07 | | (9) ~ (all_56_21 = e1) % 136.03/20.07 | | (10) op(e1, e1) = all_56_21 % 136.03/20.07 | | % 136.03/20.07 | | REF_CLOSE: (1), (3), (9), (10) are inconsistent by sub-proof #510. % 136.03/20.07 | | % 136.03/20.07 | End of split % 136.03/20.07 | % 136.03/20.07 End of proof % 136.03/20.07 % 136.03/20.07 Sub-proof #183 shows that the following formulas are inconsistent: % 136.03/20.07 ---------------------------------------------------------------- % 136.03/20.07 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.07 (2) op(e2, e2) = e1 % 136.03/20.07 (3) ~ (all_52_4 = e3) % 136.03/20.07 (4) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) % 136.03/20.07 (5) op(e3, e2) = all_52_4 % 136.03/20.07 (6) ~ (e3 = e1) % 136.03/20.07 % 136.03/20.07 Begin of proof % 136.03/20.07 | % 136.03/20.07 | BETA: splitting (4) gives: % 136.03/20.07 | % 136.03/20.07 | Case 1: % 136.03/20.07 | | % 136.03/20.07 | | (7) all_57_1 = e3 & op(e3, e2) = e3 % 136.03/20.07 | | % 136.03/20.07 | | ALPHA: (7) implies: % 136.03/20.07 | | (8) op(e3, e2) = e3 % 136.03/20.07 | | % 136.03/20.07 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #738. % 136.03/20.07 | | % 136.03/20.07 | Case 2: % 136.03/20.07 | | % 136.03/20.07 | | (9) all_57_3 = e3 & op(e2, e2) = e3 % 136.03/20.07 | | % 136.03/20.07 | | ALPHA: (9) implies: % 136.03/20.07 | | (10) op(e2, e2) = e3 % 136.03/20.07 | | % 136.03/20.07 | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #325. % 136.03/20.07 | | % 136.03/20.07 | End of split % 136.03/20.07 | % 136.03/20.07 End of proof % 136.03/20.07 % 136.03/20.07 Sub-proof #184 shows that the following formulas are inconsistent: % 136.03/20.07 ---------------------------------------------------------------- % 136.03/20.07 (1) op(e0, e0) = e0 % 136.03/20.07 (2) op(e1, e1) = all_6_2 % 136.03/20.07 (3) ~ (e2 = e0) % 136.03/20.07 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.07 (5) ~ (e3 = e0) % 136.03/20.07 (6) op(e2, e2) = e1 % 136.03/20.07 (7) ~ (all_6_2 = e2) % 136.03/20.07 (8) ~ (e1 = e0) % 136.03/20.07 (9) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.07 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 136.03/20.07 op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.07 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.07 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 & % 136.03/20.07 all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ % 136.03/20.07 (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, % 136.03/20.07 e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.03/20.07 op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 136.03/20.07 $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 & % 136.03/20.07 $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & % 136.03/20.07 ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.03/20.07 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.03/20.07 all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) % 136.03/20.07 & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & % 136.03/20.07 all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ % 136.03/20.07 (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 136.03/20.07 op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 136.03/20.07 all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 136.03/20.07 $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & % 136.03/20.07 ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.03/20.07 (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 136.03/20.07 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.03/20.07 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & % 136.03/20.07 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.03/20.07 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 136.03/20.07 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.03/20.07 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.07 $i(all_56_21) & $i(all_56_29)))) % 136.03/20.07 % 136.03/20.07 Begin of proof % 136.03/20.07 | % 136.03/20.07 | BETA: splitting (9) gives: % 136.03/20.07 | % 136.03/20.07 | Case 1: % 136.03/20.07 | | % 136.03/20.07 | | (10) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 % 136.03/20.07 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = % 136.03/20.07 | | e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 136.03/20.07 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 136.03/20.07 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.03/20.07 | | % 136.03/20.07 | | ALPHA: (10) implies: % 136.03/20.07 | | (11) op(e2, e2) = e0 % 136.03/20.07 | | % 136.03/20.07 | | REF_CLOSE: (4), (6), (8), (11) are inconsistent by sub-proof #675. % 136.03/20.07 | | % 136.03/20.07 | Case 2: % 136.03/20.07 | | % 136.03/20.07 | | (12) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.07 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.07 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.07 | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) % 136.03/20.07 | | = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.03/20.07 | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 136.03/20.07 | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.03/20.07 | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.03/20.07 | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.03/20.07 | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.03/20.07 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.03/20.07 | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.07 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.07 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.07 | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.03/20.07 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 136.03/20.07 | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.03/20.07 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.07 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 136.03/20.07 | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 136.03/20.07 | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 136.03/20.07 | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.03/20.07 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 % 136.03/20.07 | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.03/20.07 | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.07 | | $i(all_56_21) & $i(all_56_29)))) % 136.03/20.07 | | % 136.03/20.07 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (12) are inconsistent by % 136.03/20.07 | | sub-proof #709. % 136.03/20.07 | | % 136.03/20.07 | End of split % 136.03/20.07 | % 136.03/20.07 End of proof % 136.03/20.07 % 136.03/20.07 Sub-proof #185 shows that the following formulas are inconsistent: % 136.03/20.07 ---------------------------------------------------------------- % 136.03/20.07 (1) op(e1, e0) = all_56_29 % 136.03/20.07 (2) op(e1, e1) = all_6_2 % 136.03/20.07 (3) ~ (all_52_9 = all_6_2) % 136.03/20.07 (4) ~ (all_52_13 = e0) % 136.03/20.07 (5) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 136.03/20.07 (6) ~ (all_56_5 = e3) % 136.03/20.07 (7) ~ (all_52_13 = e1) % 136.03/20.07 (8) ~ (all_6_2 = e3) % 136.03/20.07 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.07 (10) op(e2, e1) = e2 % 136.03/20.07 (11) op(e1, e3) = all_56_5 % 136.03/20.07 (12) ~ (all_52_13 = all_52_14) % 136.03/20.07 (13) all_48_2 = e1 % 136.03/20.07 (14) all_54_10 = all_6_2 % 136.03/20.07 (15) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & % 136.03/20.07 $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 & % 136.03/20.07 $i(all_48_1)) % 136.03/20.07 (16) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 136.03/20.07 (17) ~ (all_56_21 = e1) % 136.03/20.07 (18) op(e2, e1) = all_52_9 % 136.03/20.07 (19) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 136.03/20.07 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 136.03/20.07 (20) all_54_7 = all_52_13 % 136.03/20.07 (21) ~ (all_52_9 = all_52_13) % 136.03/20.07 (22) op(e1, e0) = all_52_14 % 136.03/20.07 (23) op(e1, e1) = all_56_21 % 136.03/20.07 % 136.03/20.07 Begin of proof % 136.03/20.07 | % 136.03/20.07 | GROUND_INST: instantiating (9) with all_52_14, all_56_29, e0, e1, simplifying % 136.03/20.07 | with (1), (22) gives: % 136.03/20.07 | (24) all_56_29 = all_52_14 % 136.03/20.07 | % 136.03/20.07 | GROUND_INST: instantiating (9) with all_6_2, all_56_21, e1, e1, simplifying % 136.03/20.07 | with (2), (23) gives: % 136.03/20.07 | (25) all_56_21 = all_6_2 % 136.03/20.07 | % 136.03/20.07 | GROUND_INST: instantiating (9) with all_52_9, e2, e1, e2, simplifying with % 136.03/20.07 | (10), (18) gives: % 136.03/20.07 | (26) all_52_9 = e2 % 136.03/20.07 | % 136.03/20.07 | REDUCE: (17), (25) imply: % 136.03/20.07 | (27) ~ (all_6_2 = e1) % 136.03/20.07 | % 136.03/20.07 | REDUCE: (21), (26) imply: % 136.03/20.07 | (28) ~ (all_52_13 = e2) % 136.03/20.07 | % 136.03/20.07 | SIMP: (28) implies: % 136.03/20.07 | (29) ~ (all_52_13 = e2) % 136.03/20.07 | % 136.03/20.07 | REDUCE: (3), (26) imply: % 136.03/20.07 | (30) ~ (all_6_2 = e2) % 136.03/20.07 | % 136.03/20.07 | SIMP: (30) implies: % 136.03/20.07 | (31) ~ (all_6_2 = e2) % 136.03/20.07 | % 136.03/20.07 | BETA: splitting (16) gives: % 136.03/20.07 | % 136.03/20.07 | Case 1: % 136.03/20.07 | | % 136.03/20.07 | | (32) all_54_10 = e3 % 136.03/20.07 | | % 136.03/20.07 | | REF_CLOSE: (8), (14), (32) are inconsistent by sub-proof #742. % 136.03/20.07 | | % 136.03/20.07 | Case 2: % 136.03/20.07 | | % 136.03/20.07 | | (33) ~ (all_54_10 = e3) % 136.03/20.07 | | (34) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 136.03/20.07 | | % 136.03/20.07 | | BETA: splitting (5) gives: % 136.03/20.07 | | % 136.03/20.07 | | Case 1: % 136.03/20.07 | | | % 136.03/20.07 | | | (35) all_54_7 = e3 % 136.03/20.07 | | | % 136.03/20.07 | | | COMBINE_EQS: (20), (35) imply: % 136.03/20.07 | | | (36) all_52_13 = e3 % 136.03/20.07 | | | % 136.03/20.07 | | | SIMP: (36) implies: % 136.03/20.07 | | | (37) all_52_13 = e3 % 136.03/20.07 | | | % 136.03/20.07 | | | REDUCE: (12), (37) imply: % 136.03/20.07 | | | (38) ~ (all_52_14 = e3) % 136.03/20.07 | | | % 136.03/20.07 | | | SIMP: (38) implies: % 136.03/20.07 | | | (39) ~ (all_52_14 = e3) % 136.03/20.07 | | | % 136.03/20.07 | | | BETA: splitting (34) gives: % 136.03/20.07 | | | % 136.03/20.07 | | | Case 1: % 136.03/20.07 | | | | % 136.03/20.07 | | | | (40) all_54_10 = e2 % 136.03/20.07 | | | | % 136.03/20.07 | | | | REF_CLOSE: (14), (31), (40) are inconsistent by sub-proof #741. % 136.03/20.07 | | | | % 136.03/20.07 | | | Case 2: % 136.03/20.07 | | | | % 136.03/20.07 | | | | (41) all_54_10 = e1 | all_54_10 = e0 % 136.03/20.07 | | | | % 136.03/20.07 | | | | REF_CLOSE: (2), (6), (8), (9), (11), (13), (14), (15), (19), (22), (27), % 136.03/20.07 | | | | (39), (41) are inconsistent by sub-proof #186. % 136.03/20.07 | | | | % 136.03/20.07 | | | End of split % 136.03/20.07 | | | % 136.03/20.07 | | Case 2: % 136.03/20.07 | | | % 136.03/20.07 | | | (42) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 136.03/20.07 | | | % 136.03/20.07 | | | BETA: splitting (42) gives: % 136.03/20.07 | | | % 136.03/20.07 | | | Case 1: % 136.03/20.07 | | | | % 136.03/20.07 | | | | (43) all_54_7 = e2 % 136.03/20.07 | | | | % 136.03/20.07 | | | | REF_CLOSE: (20), (29), (43) are inconsistent by sub-proof #337. % 136.03/20.07 | | | | % 136.03/20.07 | | | Case 2: % 136.03/20.07 | | | | % 136.03/20.07 | | | | (44) all_54_7 = e1 | all_54_7 = e0 % 136.03/20.07 | | | | % 136.03/20.07 | | | | REF_CLOSE: (4), (7), (20), (44) are inconsistent by sub-proof #313. % 136.03/20.07 | | | | % 136.03/20.07 | | | End of split % 136.03/20.07 | | | % 136.03/20.07 | | End of split % 136.03/20.07 | | % 136.03/20.07 | End of split % 136.03/20.07 | % 136.03/20.07 End of proof % 136.03/20.07 % 136.03/20.07 Sub-proof #186 shows that the following formulas are inconsistent: % 136.03/20.07 ---------------------------------------------------------------- % 136.03/20.07 (1) op(e1, e1) = all_6_2 % 136.03/20.07 (2) ~ (all_52_14 = e3) % 136.03/20.07 (3) ~ (all_56_5 = e3) % 136.03/20.07 (4) ~ (all_6_2 = e3) % 136.03/20.07 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.07 (6) op(e1, e3) = all_56_5 % 136.03/20.07 (7) all_48_2 = e1 % 136.03/20.07 (8) all_54_10 = all_6_2 % 136.03/20.07 (9) ~ (all_6_2 = e1) % 136.03/20.07 (10) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & % 136.03/20.07 $i(all_48_0)) | ( ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 & % 136.03/20.07 $i(all_48_1)) % 136.03/20.07 (11) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 136.03/20.07 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 136.03/20.07 (12) all_54_10 = e1 | all_54_10 = e0 % 136.03/20.07 (13) op(e1, e0) = all_52_14 % 136.03/20.07 % 136.03/20.07 Begin of proof % 136.03/20.07 | % 136.03/20.07 | BETA: splitting (11) gives: % 136.03/20.07 | % 136.03/20.07 | Case 1: % 136.03/20.07 | | % 136.03/20.07 | | (14) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = % 136.03/20.07 | | e3) % 136.03/20.07 | | % 136.03/20.07 | | BETA: splitting (14) gives: % 136.03/20.07 | | % 136.03/20.07 | | Case 1: % 136.03/20.07 | | | % 136.03/20.07 | | | (15) all_57_6 = e3 & op(e1, e3) = e3 % 136.03/20.07 | | | % 136.03/20.07 | | | ALPHA: (15) implies: % 136.03/20.07 | | | (16) op(e1, e3) = e3 % 136.03/20.07 | | | % 136.03/20.07 | | | REF_CLOSE: (3), (5), (6), (16) are inconsistent by sub-proof #724. % 136.03/20.07 | | | % 136.03/20.07 | | Case 2: % 136.03/20.07 | | | % 136.03/20.07 | | | (17) all_57_7 = e3 & op(e1, e2) = e3 % 136.03/20.07 | | | % 136.03/20.07 | | | ALPHA: (17) implies: % 136.03/20.07 | | | (18) op(e1, e2) = e3 % 136.03/20.07 | | | % 136.03/20.07 | | | BETA: splitting (12) gives: % 136.03/20.07 | | | % 136.03/20.07 | | | Case 1: % 136.03/20.07 | | | | % 136.03/20.07 | | | | (19) all_54_10 = e1 % 136.03/20.07 | | | | % 136.03/20.07 | | | | REF_CLOSE: (8), (9), (19) are inconsistent by sub-proof #736. % 136.03/20.07 | | | | % 136.03/20.07 | | | Case 2: % 136.03/20.07 | | | | % 136.03/20.07 | | | | (20) all_54_10 = e0 % 136.03/20.07 | | | | % 136.03/20.07 | | | | COMBINE_EQS: (8), (20) imply: % 136.03/20.07 | | | | (21) all_6_2 = e0 % 136.03/20.07 | | | | % 136.03/20.07 | | | | SIMP: (21) implies: % 136.03/20.07 | | | | (22) all_6_2 = e0 % 136.03/20.07 | | | | % 136.03/20.07 | | | | REDUCE: (1), (22) imply: % 136.03/20.07 | | | | (23) op(e1, e1) = e0 % 136.03/20.07 | | | | % 136.03/20.07 | | | | BETA: splitting (10) gives: % 136.03/20.07 | | | | % 136.03/20.07 | | | | Case 1: % 136.03/20.07 | | | | | % 136.03/20.07 | | | | | (24) ~ (all_48_2 = e1) % 136.03/20.07 | | | | | % 136.03/20.07 | | | | | REDUCE: (7), (24) imply: % 136.03/20.07 | | | | | (25) $false % 136.03/20.07 | | | | | % 136.03/20.07 | | | | | CLOSE: (25) is inconsistent. % 136.03/20.07 | | | | | % 136.03/20.07 | | | | Case 2: % 136.03/20.07 | | | | | % 136.03/20.07 | | | | | (26) ( ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & $i(all_48_0)) | % 136.03/20.07 | | | | | ( ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 & $i(all_48_1)) % 136.03/20.07 | | | | | % 136.03/20.07 | | | | | BETA: splitting (26) gives: % 136.03/20.07 | | | | | % 136.03/20.07 | | | | | Case 1: % 136.03/20.07 | | | | | | % 136.03/20.07 | | | | | | (27) ~ (all_48_0 = e3) & op(e1, e2) = all_48_0 & $i(all_48_0) % 136.03/20.07 | | | | | | % 136.03/20.07 | | | | | | ALPHA: (27) implies: % 136.03/20.07 | | | | | | (28) ~ (all_48_0 = e3) % 136.03/20.07 | | | | | | (29) op(e1, e2) = all_48_0 % 136.03/20.07 | | | | | | % 136.03/20.07 | | | | | | REF_CLOSE: (5), (18), (28), (29) are inconsistent by sub-proof #188. % 136.03/20.07 | | | | | | % 136.03/20.07 | | | | | Case 2: % 136.03/20.07 | | | | | | % 136.03/20.07 | | | | | | (30) ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 & $i(all_48_1) % 136.03/20.07 | | | | | | % 136.03/20.07 | | | | | | REF_CLOSE: (5), (23), (30) are inconsistent by sub-proof #187. % 136.03/20.07 | | | | | | % 136.03/20.07 | | | | | End of split % 136.03/20.07 | | | | | % 136.03/20.07 | | | | End of split % 136.03/20.07 | | | | % 136.03/20.07 | | | End of split % 136.03/20.07 | | | % 136.03/20.07 | | End of split % 136.03/20.07 | | % 136.03/20.07 | Case 2: % 136.03/20.07 | | % 136.03/20.07 | | (31) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = % 136.03/20.07 | | e3) % 136.03/20.07 | | % 136.03/20.07 | | REF_CLOSE: (1), (2), (4), (5), (13), (31) are inconsistent by sub-proof % 136.03/20.07 | | #653. % 136.03/20.07 | | % 136.03/20.07 | End of split % 136.03/20.07 | % 136.03/20.07 End of proof % 136.03/20.07 % 136.03/20.07 Sub-proof #187 shows that the following formulas are inconsistent: % 136.03/20.07 ---------------------------------------------------------------- % 136.03/20.07 (1) ~ (all_48_1 = e0) & op(e1, e1) = all_48_1 & $i(all_48_1) % 136.03/20.07 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.07 (3) op(e1, e1) = e0 % 136.03/20.07 % 136.03/20.07 Begin of proof % 136.03/20.07 | % 136.03/20.07 | ALPHA: (1) implies: % 136.03/20.07 | (4) ~ (all_48_1 = e0) % 136.03/20.07 | (5) op(e1, e1) = all_48_1 % 136.03/20.07 | % 136.03/20.07 | GROUND_INST: instantiating (2) with e0, all_48_1, e1, e1, simplifying with % 136.03/20.07 | (3), (5) gives: % 136.03/20.07 | (6) all_48_1 = e0 % 136.03/20.07 | % 136.03/20.07 | REDUCE: (4), (6) imply: % 136.03/20.07 | (7) $false % 136.03/20.07 | % 136.03/20.07 | CLOSE: (7) is inconsistent. % 136.03/20.07 | % 136.03/20.07 End of proof % 136.03/20.07 % 136.03/20.07 Sub-proof #188 shows that the following formulas are inconsistent: % 136.03/20.07 ---------------------------------------------------------------- % 136.03/20.07 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.07 (2) op(e1, e2) = all_48_0 % 136.03/20.07 (3) op(e1, e2) = e3 % 136.03/20.07 (4) ~ (all_48_0 = e3) % 136.03/20.07 % 136.03/20.07 Begin of proof % 136.03/20.07 | % 136.03/20.07 | GROUND_INST: instantiating (1) with e3, all_48_0, e2, e1, simplifying with % 136.03/20.07 | (2), (3) gives: % 136.03/20.07 | (5) all_48_0 = e3 % 136.03/20.07 | % 136.03/20.07 | REDUCE: (4), (5) imply: % 136.03/20.07 | (6) $false % 136.03/20.07 | % 136.03/20.07 | CLOSE: (6) is inconsistent. % 136.03/20.07 | % 136.03/20.07 End of proof % 136.03/20.07 % 136.03/20.07 Sub-proof #189 shows that the following formulas are inconsistent: % 136.03/20.07 ---------------------------------------------------------------- % 136.03/20.07 (1) all_54_0 = all_10_2 % 136.03/20.07 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.07 (3) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 136.03/20.07 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 136.03/20.07 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.03/20.07 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.03/20.07 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.03/20.07 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.03/20.07 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 136.03/20.07 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.03/20.07 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.07 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 136.03/20.07 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.03/20.07 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 136.03/20.07 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 136.03/20.07 = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.03/20.07 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & % 136.03/20.07 ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, % 136.03/20.07 e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 136.03/20.07 op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 136.03/20.07 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 136.03/20.07 (4) op(e2, e2) = e1 % 136.03/20.07 (5) ~ (all_10_2 = e0) % 136.03/20.07 (6) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 136.03/20.07 (7) op(e3, e3) = all_10_2 % 136.03/20.07 (8) op(e3, e3) = e3 % 136.03/20.07 (9) op(e3, e0) = all_52_12 % 136.03/20.07 (10) ~ (all_10_2 = e2) % 136.03/20.07 (11) ~ (e3 = e1) % 136.03/20.07 (12) ~ (all_10_2 = e1) % 136.03/20.07 (13) ~ (all_52_12 = e3) % 136.03/20.07 % 136.03/20.07 Begin of proof % 136.03/20.07 | % 136.03/20.07 | BETA: splitting (3) gives: % 136.03/20.07 | % 136.03/20.07 | Case 1: % 136.03/20.07 | | % 136.03/20.07 | | (14) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.03/20.07 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = % 136.03/20.07 | | e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.03/20.07 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.03/20.07 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.03/20.07 | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.03/20.07 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = % 136.03/20.07 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.03/20.07 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.03/20.07 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 136.03/20.07 | | % 136.03/20.07 | | BETA: splitting (14) gives: % 136.03/20.07 | | % 136.03/20.07 | | Case 1: % 136.03/20.07 | | | % 136.03/20.07 | | | (15) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.03/20.07 | | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = % 136.03/20.07 | | | e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.03/20.07 | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.03/20.07 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.03/20.07 | | | % 136.03/20.07 | | | ALPHA: (15) implies: % 136.03/20.07 | | | (16) op(e3, e3) = e2 % 136.03/20.07 | | | % 136.03/20.07 | | | REF_CLOSE: (1), (2), (5), (6), (7), (10), (12), (16) are inconsistent by % 136.03/20.07 | | | sub-proof #776. % 136.03/20.07 | | | % 136.03/20.07 | | Case 2: % 136.03/20.07 | | | % 136.03/20.07 | | | (17) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ % 136.03/20.07 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.03/20.07 | | | op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 136.03/20.07 | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.03/20.07 | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.03/20.07 | | | $i(all_56_29) % 136.03/20.07 | | | % 136.03/20.07 | | | ALPHA: (17) implies: % 136.03/20.07 | | | (18) op(e3, e3) = e1 % 136.03/20.07 | | | % 136.03/20.07 | | | REF_CLOSE: (2), (8), (11), (18) are inconsistent by sub-proof #775. % 136.03/20.07 | | | % 136.03/20.07 | | End of split % 136.03/20.07 | | % 136.03/20.07 | Case 2: % 136.03/20.07 | | % 136.03/20.07 | | (19) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 % 136.03/20.07 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = % 136.03/20.07 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 136.03/20.07 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 136.03/20.07 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 136.03/20.07 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.03/20.07 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.07 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.07 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 136.03/20.07 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 136.03/20.07 | | % 136.03/20.07 | | REF_CLOSE: (2), (4), (9), (11), (13), (19) are inconsistent by sub-proof % 136.03/20.07 | | #190. % 136.03/20.07 | | % 136.03/20.07 | End of split % 136.03/20.07 | % 136.03/20.07 End of proof % 136.03/20.07 % 136.03/20.07 Sub-proof #190 shows that the following formulas are inconsistent: % 136.03/20.07 ---------------------------------------------------------------- % 136.03/20.07 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.07 (2) op(e2, e2) = e1 % 136.03/20.07 (3) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.07 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.03/20.07 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.07 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.07 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 136.03/20.07 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 136.03/20.07 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 136.03/20.07 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.03/20.07 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.03/20.07 $i(all_56_17) & $i(all_56_25)) % 136.03/20.07 (4) op(e3, e0) = all_52_12 % 136.03/20.07 (5) ~ (e3 = e1) % 136.03/20.07 (6) ~ (all_52_12 = e3) % 136.03/20.07 % 136.03/20.07 Begin of proof % 136.03/20.07 | % 136.03/20.07 | BETA: splitting (3) gives: % 136.03/20.07 | % 136.03/20.07 | Case 1: % 136.03/20.07 | | % 136.03/20.07 | | (7) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.07 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.03/20.07 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.07 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.07 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.03/20.07 | | % 136.03/20.07 | | ALPHA: (7) implies: % 136.03/20.07 | | (8) op(e3, e0) = e3 % 136.03/20.07 | | % 136.03/20.07 | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #733. % 136.03/20.07 | | % 136.03/20.07 | Case 2: % 136.03/20.07 | | % 136.03/20.07 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.03/20.07 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.07 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.07 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) % 136.03/20.07 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.03/20.07 | | % 136.03/20.07 | | ALPHA: (9) implies: % 136.03/20.07 | | (10) op(e2, e2) = e3 % 136.03/20.07 | | % 136.03/20.07 | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #325. % 136.03/20.07 | | % 136.03/20.07 | End of split % 136.03/20.07 | % 136.03/20.07 End of proof % 136.03/20.07 % 136.03/20.07 Sub-proof #191 shows that the following formulas are inconsistent: % 136.03/20.07 ---------------------------------------------------------------- % 136.03/20.07 (1) ~ (all_14_1 = e0) & op(e3, e3) = all_14_1 & $i(all_14_1) % 136.03/20.07 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.07 (3) op(e3, e3) = e0 % 136.03/20.07 % 136.03/20.07 Begin of proof % 136.03/20.07 | % 136.03/20.07 | ALPHA: (1) implies: % 136.03/20.07 | (4) ~ (all_14_1 = e0) % 136.03/20.07 | (5) op(e3, e3) = all_14_1 % 136.03/20.07 | % 136.03/20.07 | GROUND_INST: instantiating (2) with e0, all_14_1, e3, e3, simplifying with % 136.03/20.07 | (3), (5) gives: % 136.03/20.07 | (6) all_14_1 = e0 % 136.03/20.07 | % 136.03/20.07 | REDUCE: (4), (6) imply: % 136.03/20.07 | (7) $false % 136.03/20.07 | % 136.03/20.07 | CLOSE: (7) is inconsistent. % 136.03/20.07 | % 136.03/20.07 End of proof % 136.03/20.07 % 136.03/20.07 Sub-proof #192 shows that the following formulas are inconsistent: % 136.03/20.07 ---------------------------------------------------------------- % 136.03/20.07 (1) all_54_1 = e1 | all_54_1 = e0 % 136.03/20.07 (2) all_54_1 = all_14_0 % 136.03/20.07 (3) ~ (all_14_0 = e1) % 136.03/20.07 (4) ~ (all_14_0 = e0) % 136.03/20.07 % 136.03/20.07 Begin of proof % 136.03/20.07 | % 136.03/20.07 | BETA: splitting (1) gives: % 136.03/20.07 | % 136.03/20.07 | Case 1: % 136.03/20.07 | | % 136.03/20.07 | | (5) all_54_1 = e1 % 136.03/20.07 | | % 136.03/20.07 | | COMBINE_EQS: (2), (5) imply: % 136.03/20.07 | | (6) all_14_0 = e1 % 136.03/20.08 | | % 136.03/20.08 | | SIMP: (6) implies: % 136.03/20.08 | | (7) all_14_0 = e1 % 136.03/20.08 | | % 136.03/20.08 | | REDUCE: (3), (7) imply: % 136.03/20.08 | | (8) $false % 136.03/20.08 | | % 136.03/20.08 | | CLOSE: (8) is inconsistent. % 136.03/20.08 | | % 136.03/20.08 | Case 2: % 136.03/20.08 | | % 136.03/20.08 | | (9) all_54_1 = e0 % 136.03/20.08 | | % 136.03/20.08 | | COMBINE_EQS: (2), (9) imply: % 136.03/20.08 | | (10) all_14_0 = e0 % 136.03/20.08 | | % 136.03/20.08 | | SIMP: (10) implies: % 136.03/20.08 | | (11) all_14_0 = e0 % 136.03/20.08 | | % 136.03/20.08 | | REDUCE: (4), (11) imply: % 136.03/20.08 | | (12) $false % 136.03/20.08 | | % 136.03/20.08 | | CLOSE: (12) is inconsistent. % 136.03/20.08 | | % 136.03/20.08 | End of split % 136.03/20.08 | % 136.03/20.08 End of proof % 136.03/20.08 % 136.03/20.08 Sub-proof #193 shows that the following formulas are inconsistent: % 136.03/20.08 ---------------------------------------------------------------- % 136.03/20.08 (1) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.03/20.08 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 136.03/20.08 (2) ~ (e2 = e0) % 136.03/20.08 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.08 (4) ~ (e2 = e1) % 136.03/20.08 (5) ~ (e3 = e0) % 136.03/20.08 (6) all_57_13 = e2 & op(e0, e2) = e2 % 136.03/20.08 (7) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 136.03/20.08 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 136.03/20.08 (8) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.03/20.08 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.03/20.08 (9) ~ (all_52_8 = e2) % 136.03/20.08 (10) op(e3, e0) = all_52_12 % 136.03/20.08 (11) ~ (all_52_12 = e2) % 136.03/20.08 (12) all_57_3 = e3 % 136.03/20.08 (13) op(e3, e1) = all_52_8 % 136.03/20.08 (14) op(e3, e3) = e0 % 136.03/20.08 (15) ~ (e3 = e1) % 136.03/20.08 (16) ~ (e1 = e0) % 136.03/20.08 % 136.03/20.08 Begin of proof % 136.03/20.08 | % 136.03/20.08 | ALPHA: (6) implies: % 136.03/20.08 | (17) all_57_13 = e2 % 136.03/20.08 | % 136.03/20.08 | BETA: splitting (7) gives: % 136.03/20.08 | % 136.03/20.08 | Case 1: % 136.03/20.08 | | % 136.03/20.08 | | (18) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = % 136.03/20.08 | | e2) % 136.03/20.08 | | % 136.03/20.08 | | BETA: splitting (18) gives: % 136.03/20.08 | | % 136.03/20.08 | | Case 1: % 136.03/20.08 | | | % 136.03/20.08 | | | (19) all_57_0 = e2 & op(e3, e3) = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | ALPHA: (19) implies: % 136.03/20.08 | | | (20) op(e3, e3) = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | REF_CLOSE: (2), (3), (14), (20) are inconsistent by sub-proof #495. % 136.03/20.08 | | | % 136.03/20.08 | | Case 2: % 136.03/20.08 | | | % 136.03/20.08 | | | (21) all_57_1 = e2 & op(e3, e2) = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | ALPHA: (21) implies: % 136.03/20.08 | | | (22) all_57_1 = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | REF_CLOSE: (1), (2), (4), (5), (8), (12), (15), (16), (17), (22) are % 136.03/20.08 | | | inconsistent by sub-proof #301. % 136.03/20.08 | | | % 136.03/20.08 | | End of split % 136.03/20.08 | | % 136.03/20.08 | Case 2: % 136.03/20.08 | | % 136.03/20.08 | | (23) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = % 136.03/20.08 | | e2) % 136.03/20.08 | | % 136.03/20.08 | | BETA: splitting (23) gives: % 136.03/20.08 | | % 136.03/20.08 | | Case 1: % 136.03/20.08 | | | % 136.03/20.08 | | | (24) all_57_4 = e2 & op(e3, e1) = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | REF_CLOSE: (3), (9), (13), (24) are inconsistent by sub-proof #442. % 136.03/20.08 | | | % 136.03/20.08 | | Case 2: % 136.03/20.08 | | | % 136.03/20.08 | | | (25) all_57_9 = e2 & op(e3, e0) = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | REF_CLOSE: (3), (10), (11), (25) are inconsistent by sub-proof #460. % 136.03/20.08 | | | % 136.03/20.08 | | End of split % 136.03/20.08 | | % 136.03/20.08 | End of split % 136.03/20.08 | % 136.03/20.08 End of proof % 136.03/20.08 % 136.03/20.08 Sub-proof #194 shows that the following formulas are inconsistent: % 136.03/20.08 ---------------------------------------------------------------- % 136.03/20.08 (1) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.08 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.03/20.08 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.08 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.08 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 136.03/20.08 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 136.03/20.08 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 136.03/20.08 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.03/20.08 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.03/20.08 $i(all_56_17) & $i(all_56_25)) % 136.03/20.08 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.08 (3) op(e0, e3) = e3 % 136.03/20.08 (4) op(e3, e2) = e2 % 136.03/20.08 % 136.03/20.08 Begin of proof % 136.03/20.08 | % 136.03/20.08 | BETA: splitting (1) gives: % 136.03/20.08 | % 136.03/20.08 | Case 1: % 136.03/20.08 | | % 136.03/20.08 | | (5) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.08 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.03/20.08 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.08 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.08 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.03/20.08 | | % 136.03/20.08 | | ALPHA: (5) implies: % 136.03/20.08 | | (6) ~ (all_56_7 = e3) % 136.03/20.08 | | (7) op(e0, e3) = all_56_7 % 136.03/20.08 | | % 136.03/20.08 | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #209. % 136.03/20.08 | | % 136.03/20.08 | Case 2: % 136.03/20.08 | | % 136.03/20.08 | | (8) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.03/20.08 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.08 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.08 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) % 136.03/20.08 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.03/20.08 | | % 136.03/20.08 | | ALPHA: (8) implies: % 136.03/20.08 | | (9) ~ (all_56_9 = e2) % 136.03/20.08 | | (10) op(e3, e2) = all_56_9 % 136.03/20.08 | | % 136.03/20.08 | | REF_CLOSE: (2), (4), (9), (10) are inconsistent by sub-proof #199. % 136.03/20.08 | | % 136.03/20.08 | End of split % 136.03/20.08 | % 136.03/20.08 End of proof % 136.03/20.08 % 136.03/20.08 Sub-proof #195 shows that the following formulas are inconsistent: % 136.03/20.08 ---------------------------------------------------------------- % 136.03/20.08 (1) all_57_2 = e1 % 136.03/20.08 (2) ~ (e2 = e0) % 136.03/20.08 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.08 (4) ~ (e2 = e1) % 136.03/20.08 (5) ~ (e3 = e0) % 136.03/20.08 (6) ~ (e3 = e2) % 136.03/20.08 (7) all_57_12 = e3 % 136.03/20.08 (8) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) % 136.03/20.08 & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, % 136.03/20.08 e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) % 136.03/20.08 = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.08 $i(all_56_21) & $i(all_56_29) % 136.03/20.08 (9) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.03/20.08 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.03/20.08 (10) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) | % 136.03/20.08 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2) % 136.03/20.08 (11) ~ (e1 = e0) % 136.03/20.08 (12) op(e2, e3) = e1 % 136.03/20.08 % 136.03/20.08 Begin of proof % 136.03/20.08 | % 136.03/20.08 | ALPHA: (8) implies: % 136.03/20.08 | (13) op(e3, e3) = e1 % 136.03/20.08 | % 136.03/20.08 | BETA: splitting (10) gives: % 136.03/20.08 | % 136.03/20.08 | Case 1: % 136.03/20.08 | | % 136.03/20.08 | | (14) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = % 136.03/20.08 | | e2) % 136.03/20.08 | | % 136.03/20.08 | | BETA: splitting (14) gives: % 136.03/20.08 | | % 136.03/20.08 | | Case 1: % 136.03/20.08 | | | % 136.03/20.08 | | | (15) all_57_0 = e2 & op(e3, e3) = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | ALPHA: (15) implies: % 136.03/20.08 | | | (16) op(e3, e3) = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | REF_CLOSE: (3), (4), (13), (16) are inconsistent by sub-proof #743. % 136.03/20.08 | | | % 136.03/20.08 | | Case 2: % 136.03/20.08 | | | % 136.03/20.08 | | | (17) all_57_2 = e2 & op(e2, e3) = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | ALPHA: (17) implies: % 136.03/20.08 | | | (18) op(e2, e3) = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | REF_CLOSE: (3), (4), (12), (18) are inconsistent by sub-proof #450. % 136.03/20.08 | | | % 136.03/20.08 | | End of split % 136.03/20.08 | | % 136.03/20.08 | Case 2: % 136.03/20.08 | | % 136.03/20.08 | | (19) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = % 136.03/20.08 | | e2) % 136.03/20.08 | | % 136.03/20.08 | | BETA: splitting (19) gives: % 136.03/20.08 | | % 136.03/20.08 | | Case 1: % 136.03/20.08 | | | % 136.03/20.08 | | | (20) all_57_6 = e2 & op(e1, e3) = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | ALPHA: (20) implies: % 136.03/20.08 | | | (21) all_57_6 = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | BETA: splitting (9) gives: % 136.03/20.08 | | | % 136.03/20.08 | | | Case 1: % 136.03/20.08 | | | | % 136.03/20.08 | | | | (22) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) % 136.03/20.08 | | | | = e0) % 136.03/20.08 | | | | % 136.03/20.08 | | | | BETA: splitting (22) gives: % 136.03/20.08 | | | | % 136.03/20.08 | | | | Case 1: % 136.03/20.08 | | | | | % 136.03/20.08 | | | | | (23) all_57_0 = e0 & op(e3, e3) = e0 % 136.03/20.08 | | | | | % 136.03/20.08 | | | | | ALPHA: (23) implies: % 136.03/20.08 | | | | | (24) op(e3, e3) = e0 % 136.03/20.08 | | | | | % 136.03/20.08 | | | | | REF_CLOSE: (3), (11), (13), (24) are inconsistent by sub-proof #717. % 136.03/20.08 | | | | | % 136.03/20.08 | | | | Case 2: % 136.03/20.08 | | | | | % 136.03/20.08 | | | | | (25) all_57_2 = e0 & op(e2, e3) = e0 % 136.03/20.08 | | | | | % 136.03/20.08 | | | | | REF_CLOSE: (1), (11), (25) are inconsistent by sub-proof #272. % 136.03/20.08 | | | | | % 136.03/20.08 | | | | End of split % 136.03/20.08 | | | | % 136.03/20.08 | | | Case 2: % 136.03/20.08 | | | | % 136.03/20.08 | | | | (26) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) % 136.03/20.08 | | | | = e0) % 136.03/20.08 | | | | % 136.03/20.08 | | | | BETA: splitting (26) gives: % 136.03/20.08 | | | | % 136.03/20.08 | | | | Case 1: % 136.03/20.08 | | | | | % 136.03/20.08 | | | | | (27) all_57_6 = e0 & op(e1, e3) = e0 % 136.03/20.08 | | | | | % 136.03/20.08 | | | | | REF_CLOSE: (2), (21), (27) are inconsistent by sub-proof #520. % 136.03/20.08 | | | | | % 136.03/20.08 | | | | Case 2: % 136.03/20.08 | | | | | % 136.03/20.08 | | | | | (28) all_57_12 = e0 & op(e0, e3) = e0 % 136.03/20.08 | | | | | % 136.03/20.08 | | | | | REF_CLOSE: (5), (7), (28) are inconsistent by sub-proof #436. % 136.03/20.08 | | | | | % 136.03/20.08 | | | | End of split % 136.03/20.08 | | | | % 136.03/20.08 | | | End of split % 136.03/20.08 | | | % 136.03/20.08 | | Case 2: % 136.03/20.08 | | | % 136.03/20.08 | | | (29) all_57_12 = e2 & op(e0, e3) = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | REF_CLOSE: (6), (7), (29) are inconsistent by sub-proof #196. % 136.03/20.08 | | | % 136.03/20.08 | | End of split % 136.03/20.08 | | % 136.03/20.08 | End of split % 136.03/20.08 | % 136.03/20.08 End of proof % 136.03/20.08 % 136.03/20.08 Sub-proof #196 shows that the following formulas are inconsistent: % 136.03/20.08 ---------------------------------------------------------------- % 136.03/20.08 (1) all_57_12 = e2 & op(e0, e3) = e2 % 136.03/20.08 (2) all_57_12 = e3 % 136.03/20.08 (3) ~ (e3 = e2) % 136.03/20.08 % 136.03/20.08 Begin of proof % 136.03/20.08 | % 136.03/20.08 | ALPHA: (1) implies: % 136.03/20.08 | (4) all_57_12 = e2 % 136.03/20.08 | % 136.03/20.08 | COMBINE_EQS: (2), (4) imply: % 136.03/20.08 | (5) e3 = e2 % 136.03/20.08 | % 136.03/20.08 | REDUCE: (3), (5) imply: % 136.03/20.08 | (6) $false % 136.03/20.08 | % 136.03/20.08 | CLOSE: (6) is inconsistent. % 136.03/20.08 | % 136.03/20.08 End of proof % 136.03/20.08 % 136.03/20.08 Sub-proof #197 shows that the following formulas are inconsistent: % 136.03/20.08 ---------------------------------------------------------------- % 136.03/20.08 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.08 (2) ~ (e3 = e0) % 136.03/20.08 (3) ~ (all_52_4 = e3) % 136.03/20.08 (4) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) % 136.03/20.08 (5) op(e3, e2) = all_52_4 % 136.03/20.08 (6) op(e3, e3) = e0 % 136.03/20.08 % 136.03/20.08 Begin of proof % 136.03/20.08 | % 136.03/20.08 | BETA: splitting (4) gives: % 136.03/20.08 | % 136.03/20.08 | Case 1: % 136.03/20.08 | | % 136.03/20.08 | | (7) all_57_0 = e3 & op(e3, e3) = e3 % 136.03/20.08 | | % 136.03/20.08 | | ALPHA: (7) implies: % 136.03/20.08 | | (8) op(e3, e3) = e3 % 136.03/20.08 | | % 136.03/20.08 | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #773. % 136.03/20.08 | | % 136.03/20.08 | Case 2: % 136.03/20.08 | | % 136.03/20.08 | | (9) all_57_1 = e3 & op(e3, e2) = e3 % 136.03/20.08 | | % 136.03/20.08 | | ALPHA: (9) implies: % 136.03/20.08 | | (10) op(e3, e2) = e3 % 136.03/20.08 | | % 136.03/20.08 | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #738. % 136.03/20.08 | | % 136.03/20.08 | End of split % 136.03/20.08 | % 136.03/20.08 End of proof % 136.03/20.08 % 136.03/20.08 Sub-proof #198 shows that the following formulas are inconsistent: % 136.03/20.08 ---------------------------------------------------------------- % 136.03/20.08 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.08 (2) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.08 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.03/20.08 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.08 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.08 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 136.03/20.08 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 136.03/20.08 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 136.03/20.08 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.03/20.08 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.03/20.08 $i(all_56_17) & $i(all_56_25)) % 136.03/20.08 (3) op(e3, e0) = all_52_12 % 136.03/20.08 (4) op(e3, e2) = e2 % 136.03/20.08 (5) ~ (all_52_12 = e3) % 136.03/20.08 % 136.03/20.08 Begin of proof % 136.03/20.08 | % 136.03/20.08 | BETA: splitting (2) gives: % 136.03/20.08 | % 136.03/20.08 | Case 1: % 136.03/20.08 | | % 136.03/20.08 | | (6) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.08 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.03/20.08 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.08 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.08 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.03/20.08 | | % 136.03/20.08 | | ALPHA: (6) implies: % 136.03/20.08 | | (7) op(e3, e0) = e3 % 136.03/20.08 | | % 136.03/20.08 | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #733. % 136.03/20.08 | | % 136.03/20.08 | Case 2: % 136.03/20.08 | | % 136.03/20.08 | | (8) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.03/20.08 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.08 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.08 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) % 136.03/20.08 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.03/20.08 | | % 136.03/20.08 | | ALPHA: (8) implies: % 136.03/20.08 | | (9) ~ (all_56_9 = e2) % 136.03/20.08 | | (10) op(e3, e2) = all_56_9 % 136.03/20.08 | | % 136.03/20.08 | | REF_CLOSE: (1), (4), (9), (10) are inconsistent by sub-proof #199. % 136.03/20.08 | | % 136.03/20.08 | End of split % 136.03/20.08 | % 136.03/20.08 End of proof % 136.03/20.08 % 136.03/20.08 Sub-proof #199 shows that the following formulas are inconsistent: % 136.03/20.08 ---------------------------------------------------------------- % 136.03/20.08 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.08 (2) op(e3, e2) = all_56_9 % 136.03/20.08 (3) op(e3, e2) = e2 % 136.03/20.08 (4) ~ (all_56_9 = e2) % 136.03/20.08 % 136.03/20.08 Begin of proof % 136.03/20.08 | % 136.03/20.08 | GROUND_INST: instantiating (1) with e2, all_56_9, e2, e3, simplifying with % 136.03/20.08 | (2), (3) gives: % 136.03/20.08 | (5) all_56_9 = e2 % 136.03/20.08 | % 136.03/20.08 | REDUCE: (4), (5) imply: % 136.03/20.08 | (6) $false % 136.03/20.08 | % 136.03/20.08 | CLOSE: (6) is inconsistent. % 136.03/20.08 | % 136.03/20.08 End of proof % 136.03/20.08 % 136.03/20.08 Sub-proof #200 shows that the following formulas are inconsistent: % 136.03/20.08 ---------------------------------------------------------------- % 136.03/20.08 (1) ~ (e2 = e0) % 136.03/20.08 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.08 (3) op(e2, e0) = e0 % 136.03/20.08 (4) op(e3, e0) = all_52_12 % 136.03/20.08 (5) ~ (all_52_12 = e2) % 136.03/20.08 (6) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 136.03/20.08 % 136.03/20.08 Begin of proof % 136.03/20.08 | % 136.03/20.08 | BETA: splitting (6) gives: % 136.03/20.08 | % 136.03/20.08 | Case 1: % 136.03/20.08 | | % 136.03/20.08 | | (7) all_57_9 = e2 & op(e3, e0) = e2 % 136.03/20.08 | | % 136.03/20.08 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #460. % 136.03/20.08 | | % 136.03/20.08 | Case 2: % 136.03/20.08 | | % 136.03/20.08 | | (8) all_57_10 = e2 & op(e2, e0) = e2 % 136.03/20.08 | | % 136.03/20.08 | | ALPHA: (8) implies: % 136.03/20.08 | | (9) op(e2, e0) = e2 % 136.03/20.08 | | % 136.03/20.08 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #451. % 136.03/20.08 | | % 136.03/20.08 | End of split % 136.03/20.08 | % 136.03/20.08 End of proof % 136.03/20.08 % 136.03/20.08 Sub-proof #201 shows that the following formulas are inconsistent: % 136.03/20.08 ---------------------------------------------------------------- % 136.03/20.08 (1) ~ (all_52_6 = e3) % 136.03/20.08 (2) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.03/20.08 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 136.03/20.08 (3) ~ (e2 = e0) % 136.03/20.08 (4) all_57_1 = e2 % 136.03/20.08 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.08 (6) ~ (e2 = e1) % 136.03/20.08 (7) ~ (e3 = e0) % 136.03/20.08 (8) ~ (e3 = e2) % 136.03/20.08 (9) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 136.03/20.08 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) % 136.03/20.08 (10) op(e1, e2) = all_52_6 % 136.03/20.08 (11) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.03/20.08 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.03/20.08 (12) all_57_11 = e3 % 136.03/20.08 (13) all_57_3 = e3 % 136.03/20.08 (14) all_57_11 = e2 % 136.03/20.08 (15) ~ (e3 = e1) % 136.03/20.08 (16) ~ (e1 = e0) % 136.03/20.08 % 136.03/20.08 Begin of proof % 136.03/20.08 | % 136.03/20.08 | COMBINE_EQS: (12), (14) imply: % 136.03/20.08 | (17) e3 = e2 % 136.03/20.08 | % 136.03/20.08 | SIMP: (17) implies: % 136.03/20.08 | (18) e3 = e2 % 136.03/20.08 | % 136.03/20.08 | COMBINE_EQS: (13), (18) imply: % 136.03/20.08 | (19) all_57_3 = e2 % 136.03/20.08 | % 136.03/20.08 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (15), % 136.03/20.08 | (16), (19) are inconsistent by sub-proof #463. % 136.03/20.08 | % 136.03/20.08 End of proof % 136.03/20.08 % 136.03/20.08 Sub-proof #202 shows that the following formulas are inconsistent: % 136.03/20.08 ---------------------------------------------------------------- % 136.03/20.08 (1) ~ (all_52_4 = e0) % 136.03/20.08 (2) all_57_1 = e2 % 136.03/20.08 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.03/20.08 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.03/20.08 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.08 (5) ~ (e2 = e1) % 136.03/20.08 (6) ~ (e3 = e0) % 136.03/20.08 (7) ~ (all_52_12 = e0) % 136.03/20.08 (8) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) % 136.03/20.08 (9) op(e3, e2) = all_52_4 % 136.03/20.08 (10) op(e3, e0) = all_52_12 % 136.03/20.08 (11) op(e3, e1) = all_52_8 % 136.03/20.08 (12) ~ (e1 = e0) % 136.03/20.08 (13) op(e3, e1) = e3 % 136.03/20.08 % 136.03/20.08 Begin of proof % 136.03/20.08 | % 136.03/20.08 | BETA: splitting (8) gives: % 136.03/20.08 | % 136.03/20.08 | Case 1: % 136.03/20.08 | | % 136.03/20.08 | | (14) all_57_0 = e1 & op(e3, e3) = e1 % 136.03/20.08 | | % 136.03/20.08 | | ALPHA: (14) implies: % 136.03/20.08 | | (15) op(e3, e3) = e1 % 136.03/20.08 | | % 136.03/20.08 | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (10), (11), (12), (13), (15) are % 136.03/20.08 | | inconsistent by sub-proof #599. % 136.03/20.08 | | % 136.03/20.08 | Case 2: % 136.03/20.08 | | % 136.03/20.08 | | (16) all_57_1 = e1 & op(e3, e2) = e1 % 136.03/20.08 | | % 136.03/20.08 | | REF_CLOSE: (2), (5), (16) are inconsistent by sub-proof #465. % 136.03/20.08 | | % 136.03/20.08 | End of split % 136.03/20.08 | % 136.03/20.08 End of proof % 136.03/20.08 % 136.03/20.08 Sub-proof #203 shows that the following formulas are inconsistent: % 136.03/20.08 ---------------------------------------------------------------- % 136.03/20.08 (1) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) % 136.03/20.08 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.08 (3) ~ (e3 = e0) % 136.03/20.08 (4) ~ (all_52_1 = e0) % 136.03/20.08 (5) op(e2, e2) = e3 % 136.03/20.08 (6) op(e2, e3) = all_52_1 % 136.03/20.08 % 136.03/20.08 Begin of proof % 136.03/20.08 | % 136.03/20.08 | BETA: splitting (1) gives: % 136.03/20.08 | % 136.03/20.08 | Case 1: % 136.03/20.08 | | % 136.03/20.08 | | (7) all_57_2 = e0 & op(e2, e3) = e0 % 136.03/20.08 | | % 136.03/20.08 | | REF_CLOSE: (2), (4), (6), (7) are inconsistent by sub-proof #225. % 136.03/20.08 | | % 136.03/20.08 | Case 2: % 136.03/20.08 | | % 136.03/20.08 | | (8) all_57_3 = e0 & op(e2, e2) = e0 % 136.03/20.08 | | % 136.03/20.08 | | ALPHA: (8) implies: % 136.03/20.08 | | (9) op(e2, e2) = e0 % 136.03/20.08 | | % 136.03/20.08 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #641. % 136.03/20.08 | | % 136.03/20.08 | End of split % 136.03/20.08 | % 136.03/20.08 End of proof % 136.03/20.08 % 136.03/20.08 Sub-proof #204 shows that the following formulas are inconsistent: % 136.03/20.08 ---------------------------------------------------------------- % 136.03/20.08 (1) ~ (all_24_1 = e2) & op(e0, e0) = all_24_1 & $i(all_24_1) % 136.03/20.08 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.08 (3) op(e0, e0) = e2 % 136.03/20.08 % 136.03/20.08 Begin of proof % 136.03/20.08 | % 136.03/20.08 | ALPHA: (1) implies: % 136.03/20.08 | (4) ~ (all_24_1 = e2) % 136.03/20.08 | (5) op(e0, e0) = all_24_1 % 136.03/20.08 | % 136.03/20.08 | GROUND_INST: instantiating (2) with e2, all_24_1, e0, e0, simplifying with % 136.03/20.08 | (3), (5) gives: % 136.03/20.08 | (6) all_24_1 = e2 % 136.03/20.08 | % 136.03/20.08 | REDUCE: (4), (6) imply: % 136.03/20.08 | (7) $false % 136.03/20.08 | % 136.03/20.08 | CLOSE: (7) is inconsistent. % 136.03/20.08 | % 136.03/20.08 End of proof % 136.03/20.08 % 136.03/20.08 Sub-proof #205 shows that the following formulas are inconsistent: % 136.03/20.08 ---------------------------------------------------------------- % 136.03/20.08 (1) ~ (all_24_0 = e1) % 136.03/20.08 (2) ~ (all_24_0 = e2) % 136.03/20.08 (3) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 136.03/20.08 (4) all_54_12 = all_24_0 % 136.03/20.08 (5) ~ (all_24_0 = e0) % 136.03/20.08 % 136.03/20.08 Begin of proof % 136.03/20.08 | % 136.03/20.08 | BETA: splitting (3) gives: % 136.03/20.08 | % 136.03/20.08 | Case 1: % 136.03/20.08 | | % 136.03/20.08 | | (6) all_54_12 = e2 % 136.03/20.08 | | % 136.03/20.08 | | COMBINE_EQS: (4), (6) imply: % 136.03/20.08 | | (7) all_24_0 = e2 % 136.03/20.08 | | % 136.03/20.08 | | REDUCE: (2), (7) imply: % 136.03/20.08 | | (8) $false % 136.03/20.08 | | % 136.03/20.08 | | CLOSE: (8) is inconsistent. % 136.03/20.08 | | % 136.03/20.08 | Case 2: % 136.03/20.08 | | % 136.03/20.08 | | (9) all_54_12 = e1 | all_54_12 = e0 % 136.03/20.08 | | % 136.03/20.08 | | BETA: splitting (9) gives: % 136.03/20.08 | | % 136.03/20.08 | | Case 1: % 136.03/20.08 | | | % 136.03/20.08 | | | (10) all_54_12 = e1 % 136.03/20.08 | | | % 136.03/20.08 | | | COMBINE_EQS: (4), (10) imply: % 136.03/20.08 | | | (11) all_24_0 = e1 % 136.03/20.08 | | | % 136.03/20.08 | | | REDUCE: (1), (11) imply: % 136.03/20.08 | | | (12) $false % 136.03/20.08 | | | % 136.03/20.08 | | | CLOSE: (12) is inconsistent. % 136.03/20.08 | | | % 136.03/20.08 | | Case 2: % 136.03/20.08 | | | % 136.03/20.08 | | | (13) all_54_12 = e0 % 136.03/20.08 | | | % 136.03/20.08 | | | COMBINE_EQS: (4), (13) imply: % 136.03/20.08 | | | (14) all_24_0 = e0 % 136.03/20.08 | | | % 136.03/20.08 | | | REDUCE: (5), (14) imply: % 136.03/20.08 | | | (15) $false % 136.03/20.08 | | | % 136.03/20.08 | | | CLOSE: (15) is inconsistent. % 136.03/20.08 | | | % 136.03/20.08 | | End of split % 136.03/20.08 | | % 136.03/20.08 | End of split % 136.03/20.08 | % 136.03/20.08 End of proof % 136.03/20.08 % 136.03/20.08 Sub-proof #206 shows that the following formulas are inconsistent: % 136.03/20.08 ---------------------------------------------------------------- % 136.03/20.08 (1) op(e3, e1) = all_28_0 % 136.03/20.08 (2) all_57_1 = e3 % 136.03/20.08 (3) ~ (e2 = e0) % 136.03/20.08 (4) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 136.03/20.08 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.03/20.08 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.08 (6) ~ (e2 = e1) % 136.03/20.08 (7) ~ (e3 = e0) % 136.03/20.08 (8) ~ (all_28_0 = e2) % 136.03/20.08 (9) ~ (e3 = e2) % 136.03/20.08 (10) op(e0, e1) = all_52_11 % 136.03/20.08 (11) ~ (all_52_11 = e3) % 136.03/20.08 (12) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 136.03/20.08 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 136.03/20.08 (13) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.03/20.08 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 136.03/20.08 e1) % 136.03/20.08 (14) all_57_12 = e3 % 136.03/20.08 (15) op(e3, e0) = all_52_12 % 136.03/20.08 (16) ~ (all_52_12 = e2) % 136.03/20.08 (17) op(e0, e0) = e2 % 136.03/20.08 (18) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.03/20.08 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.03/20.08 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.03/20.08 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.03/20.08 (19) op(e3, e3) = e0 % 136.03/20.08 (20) ~ (e3 = e1) % 136.03/20.08 (21) ~ (e1 = e0) % 136.03/20.08 % 136.03/20.08 Begin of proof % 136.03/20.08 | % 136.03/20.08 | BETA: splitting (12) gives: % 136.03/20.08 | % 136.03/20.08 | Case 1: % 136.03/20.08 | | % 136.03/20.08 | | (22) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = % 136.03/20.08 | | e2) % 136.03/20.08 | | % 136.03/20.08 | | BETA: splitting (22) gives: % 136.03/20.08 | | % 136.03/20.08 | | Case 1: % 136.03/20.08 | | | % 136.03/20.08 | | | (23) all_57_0 = e2 & op(e3, e3) = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | ALPHA: (23) implies: % 136.03/20.08 | | | (24) op(e3, e3) = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | REF_CLOSE: (3), (5), (19), (24) are inconsistent by sub-proof #495. % 136.03/20.08 | | | % 136.03/20.08 | | Case 2: % 136.03/20.08 | | | % 136.03/20.08 | | | (25) all_57_1 = e2 & op(e3, e2) = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14), % 136.03/20.08 | | | (17), (18), (20), (21), (25) are inconsistent by sub-proof % 136.03/20.08 | | | #207. % 136.03/20.08 | | | % 136.03/20.08 | | End of split % 136.03/20.08 | | % 136.03/20.08 | Case 2: % 136.03/20.08 | | % 136.03/20.08 | | (26) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = % 136.03/20.08 | | e2) % 136.03/20.08 | | % 136.03/20.08 | | BETA: splitting (26) gives: % 136.03/20.08 | | % 136.03/20.08 | | Case 1: % 136.03/20.08 | | | % 136.03/20.08 | | | (27) all_57_4 = e2 & op(e3, e1) = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | REF_CLOSE: (1), (5), (8), (27) are inconsistent by sub-proof #218. % 136.03/20.08 | | | % 136.03/20.08 | | Case 2: % 136.03/20.08 | | | % 136.03/20.08 | | | (28) all_57_9 = e2 & op(e3, e0) = e2 % 136.03/20.08 | | | % 136.03/20.08 | | | REF_CLOSE: (5), (15), (16), (28) are inconsistent by sub-proof #460. % 136.03/20.08 | | | % 136.03/20.08 | | End of split % 136.03/20.08 | | % 136.03/20.08 | End of split % 136.03/20.08 | % 136.03/20.08 End of proof % 136.03/20.08 % 136.03/20.08 Sub-proof #207 shows that the following formulas are inconsistent: % 136.03/20.08 ---------------------------------------------------------------- % 136.03/20.08 (1) all_57_1 = e3 % 136.03/20.08 (2) ~ (e2 = e0) % 136.03/20.08 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 136.03/20.08 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.03/20.08 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.08 (5) ~ (e2 = e1) % 136.03/20.08 (6) ~ (e3 = e0) % 136.03/20.08 (7) ~ (e3 = e2) % 136.03/20.08 (8) op(e0, e1) = all_52_11 % 136.03/20.08 (9) ~ (all_52_11 = e3) % 136.03/20.08 (10) all_57_1 = e2 & op(e3, e2) = e2 % 136.03/20.08 (11) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.03/20.08 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 136.03/20.08 e1) % 136.03/20.08 (12) all_57_12 = e3 % 136.03/20.08 (13) op(e0, e0) = e2 % 136.03/20.09 (14) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.03/20.09 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.03/20.09 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.03/20.09 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.03/20.09 (15) ~ (e3 = e1) % 136.03/20.09 (16) ~ (e1 = e0) % 136.03/20.09 % 136.03/20.09 Begin of proof % 136.03/20.09 | % 136.03/20.09 | ALPHA: (10) implies: % 136.03/20.09 | (17) all_57_1 = e2 % 136.03/20.09 | % 136.03/20.09 | COMBINE_EQS: (1), (17) imply: % 136.03/20.09 | (18) e3 = e2 % 136.03/20.09 | % 136.03/20.09 | COMBINE_EQS: (12), (18) imply: % 136.03/20.09 | (19) all_57_12 = e2 % 136.03/20.09 | % 136.03/20.09 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (13), (14), (15), % 136.03/20.09 | (16), (19) are inconsistent by sub-proof #458. % 136.03/20.09 | % 136.03/20.09 End of proof % 136.03/20.09 % 136.03/20.09 Sub-proof #208 shows that the following formulas are inconsistent: % 136.03/20.09 ---------------------------------------------------------------- % 136.03/20.09 (1) op(e2, e2) = all_8_2 % 136.03/20.09 (2) ~ (e2 = e0) % 136.03/20.09 (3) ~ (all_8_2 = e1) % 136.03/20.09 (4) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 136.03/20.09 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.03/20.09 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.09 (6) ~ (e2 = e1) % 136.03/20.09 (7) ~ (e3 = e0) % 136.03/20.09 (8) ~ (e3 = e2) % 136.03/20.09 (9) op(e0, e1) = all_52_11 % 136.03/20.09 (10) op(e0, e2) = all_52_7 % 136.03/20.09 (11) ~ (all_52_11 = e3) % 136.03/20.09 (12) op(e0, e3) = e3 % 136.03/20.09 (13) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 136.03/20.09 (14) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.03/20.09 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 136.03/20.09 e1) % 136.03/20.09 (15) all_54_5 = all_8_2 % 136.03/20.09 (16) all_57_12 = e3 % 136.03/20.09 (17) op(e0, e0) = e2 % 136.03/20.09 (18) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.03/20.09 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.03/20.09 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.03/20.09 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.03/20.09 (19) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.03/20.09 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.09 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 136.03/20.09 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 136.03/20.09 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 136.03/20.09 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 136.03/20.09 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.03/20.09 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.03/20.09 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.03/20.09 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.09 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 136.03/20.09 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.09 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 136.03/20.09 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.03/20.09 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 136.03/20.09 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 136.03/20.09 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.09 $i(all_56_21) & $i(all_56_29)) % 136.03/20.09 (20) ~ (e3 = e1) % 136.03/20.09 (21) ~ (all_52_7 = all_8_2) % 136.03/20.09 (22) ~ (e1 = e0) % 136.03/20.09 (23) ~ (all_8_2 = e3) % 136.03/20.09 (24) op(e0, e0) = all_56_31 % 136.03/20.09 % 136.03/20.09 Begin of proof % 136.03/20.09 | % 136.03/20.09 | GROUND_INST: instantiating (5) with e2, all_56_31, e0, e0, simplifying with % 136.03/20.09 | (17), (24) gives: % 136.03/20.09 | (25) all_56_31 = e2 % 136.03/20.09 | % 136.03/20.09 | BETA: splitting (19) gives: % 136.03/20.09 | % 136.03/20.09 | Case 1: % 136.03/20.09 | | % 136.03/20.09 | | (26) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.03/20.09 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.09 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.09 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 136.03/20.09 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 136.03/20.09 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 136.03/20.09 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.03/20.09 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.03/20.09 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.03/20.09 | | $i(all_56_27)) % 136.03/20.09 | | % 136.03/20.09 | | BETA: splitting (26) gives: % 136.03/20.09 | | % 136.03/20.09 | | Case 1: % 136.03/20.09 | | | % 136.03/20.09 | | | (27) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.03/20.09 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.09 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.09 | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 136.03/20.09 | | | & $i(all_56_17) & $i(all_56_25) % 136.03/20.09 | | | % 136.03/20.09 | | | ALPHA: (27) implies: % 136.03/20.09 | | | (28) all_56_31 = e3 % 136.03/20.09 | | | % 136.03/20.09 | | | COMBINE_EQS: (25), (28) imply: % 136.03/20.09 | | | (29) e3 = e2 % 136.03/20.09 | | | % 136.03/20.09 | | | SIMP: (29) implies: % 136.03/20.09 | | | (30) e3 = e2 % 136.03/20.09 | | | % 136.03/20.09 | | | COMBINE_EQS: (16), (30) imply: % 136.03/20.09 | | | (31) all_57_12 = e2 % 136.03/20.09 | | | % 136.03/20.09 | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (11), (14), (17), (18), % 136.03/20.09 | | | (20), (22), (31) are inconsistent by sub-proof #458. % 136.03/20.09 | | | % 136.03/20.09 | | Case 2: % 136.03/20.09 | | | % 136.03/20.09 | | | (32) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.09 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.09 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.09 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.03/20.09 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.03/20.09 | | | % 136.03/20.09 | | | ALPHA: (32) implies: % 136.03/20.09 | | | (33) ~ (all_56_11 = e2) % 136.03/20.09 | | | (34) op(e0, e2) = e0 % 136.03/20.09 | | | (35) op(e2, e2) = all_56_11 % 136.03/20.09 | | | % 136.03/20.09 | | | REF_CLOSE: (1), (3), (5), (10), (13), (15), (21), (23), (33), (34), (35) % 136.03/20.09 | | | are inconsistent by sub-proof #227. % 136.03/20.09 | | | % 136.03/20.09 | | End of split % 136.03/20.09 | | % 136.03/20.09 | Case 2: % 136.03/20.09 | | % 136.03/20.09 | | (36) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.03/20.09 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.09 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.03/20.09 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.03/20.09 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.03/20.09 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.03/20.09 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.03/20.09 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.03/20.09 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.03/20.09 | | $i(all_56_29)) % 136.03/20.09 | | % 136.03/20.09 | | BETA: splitting (36) gives: % 136.03/20.09 | | % 136.03/20.09 | | Case 1: % 136.03/20.09 | | | % 136.03/20.09 | | | (37) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.03/20.09 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.09 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.03/20.09 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.03/20.09 | | | $i(all_56_15) & $i(all_56_23) % 136.03/20.09 | | | % 136.03/20.09 | | | ALPHA: (37) implies: % 136.03/20.09 | | | (38) ~ (all_56_7 = e3) % 136.03/20.09 | | | (39) op(e0, e3) = all_56_7 % 136.03/20.09 | | | % 136.03/20.09 | | | REF_CLOSE: (5), (12), (38), (39) are inconsistent by sub-proof #209. % 136.03/20.09 | | | % 136.03/20.09 | | Case 2: % 136.03/20.09 | | | % 136.03/20.09 | | | (40) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.03/20.09 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.03/20.09 | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.03/20.09 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.03/20.09 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.03/20.09 | | | % 136.03/20.09 | | | REF_CLOSE: (6), (25), (40) are inconsistent by sub-proof #525. % 136.03/20.09 | | | % 136.03/20.09 | | End of split % 136.03/20.09 | | % 136.03/20.09 | End of split % 136.03/20.09 | % 136.03/20.09 End of proof % 136.03/20.09 % 136.03/20.09 Sub-proof #209 shows that the following formulas are inconsistent: % 136.03/20.09 ---------------------------------------------------------------- % 136.03/20.09 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.09 (2) op(e0, e3) = all_56_7 % 136.03/20.09 (3) op(e0, e3) = e3 % 136.03/20.09 (4) ~ (all_56_7 = e3) % 136.03/20.09 % 136.03/20.09 Begin of proof % 136.03/20.09 | % 136.03/20.09 | GROUND_INST: instantiating (1) with e3, all_56_7, e3, e0, simplifying with % 136.03/20.09 | (2), (3) gives: % 136.03/20.09 | (5) all_56_7 = e3 % 136.03/20.09 | % 136.03/20.09 | REDUCE: (4), (5) imply: % 136.03/20.09 | (6) $false % 136.03/20.09 | % 136.03/20.09 | CLOSE: (6) is inconsistent. % 136.03/20.09 | % 136.03/20.09 End of proof % 136.03/20.09 % 136.03/20.09 Sub-proof #210 shows that the following formulas are inconsistent: % 136.03/20.09 ---------------------------------------------------------------- % 136.03/20.09 (1) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) % 136.03/20.09 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.09 (3) ~ (e3 = e0) % 136.03/20.09 (4) ~ (all_52_1 = e3) % 136.03/20.09 (5) op(e2, e3) = all_52_1 % 136.03/20.09 (6) op(e3, e3) = e0 % 136.03/20.09 % 136.03/20.09 Begin of proof % 136.03/20.09 | % 136.03/20.09 | BETA: splitting (1) gives: % 136.03/20.09 | % 136.03/20.09 | Case 1: % 136.03/20.09 | | % 136.03/20.09 | | (7) all_57_0 = e3 & op(e3, e3) = e3 % 136.03/20.09 | | % 136.03/20.09 | | ALPHA: (7) implies: % 136.03/20.09 | | (8) op(e3, e3) = e3 % 136.03/20.09 | | % 136.03/20.09 | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #773. % 136.03/20.09 | | % 136.03/20.09 | Case 2: % 136.03/20.09 | | % 136.03/20.09 | | (9) all_57_2 = e3 & op(e2, e3) = e3 % 136.03/20.09 | | % 136.03/20.09 | | ALPHA: (9) implies: % 136.03/20.09 | | (10) op(e2, e3) = e3 % 136.03/20.09 | | % 136.03/20.09 | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #763. % 136.03/20.09 | | % 136.03/20.09 | End of split % 136.03/20.09 | % 136.03/20.09 End of proof % 136.03/20.09 % 136.03/20.09 Sub-proof #211 shows that the following formulas are inconsistent: % 136.03/20.09 ---------------------------------------------------------------- % 136.03/20.09 (1) ~ (all_28_1 = e0) & op(e3, e3) = all_28_1 & $i(all_28_1) % 136.03/20.09 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.09 (3) op(e3, e3) = e0 % 136.03/20.09 % 136.03/20.09 Begin of proof % 136.03/20.09 | % 136.03/20.09 | ALPHA: (1) implies: % 136.03/20.09 | (4) ~ (all_28_1 = e0) % 136.03/20.09 | (5) op(e3, e3) = all_28_1 % 136.03/20.09 | % 136.03/20.09 | GROUND_INST: instantiating (2) with e0, all_28_1, e3, e3, simplifying with % 136.03/20.09 | (3), (5) gives: % 136.03/20.09 | (6) all_28_1 = e0 % 136.03/20.09 | % 136.03/20.09 | REDUCE: (4), (6) imply: % 136.03/20.09 | (7) $false % 136.03/20.09 | % 136.03/20.09 | CLOSE: (7) is inconsistent. % 136.03/20.09 | % 136.03/20.09 End of proof % 136.03/20.09 % 136.03/20.09 Sub-proof #212 shows that the following formulas are inconsistent: % 136.03/20.09 ---------------------------------------------------------------- % 136.03/20.09 (1) op(e3, e1) = all_28_0 % 136.03/20.09 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) | % 136.03/20.09 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 136.03/20.09 (3) op(e1, e1) = all_6_2 % 136.03/20.09 (4) ~ (e2 = e0) % 136.03/20.09 (5) op(e3, e1) = e1 % 136.03/20.09 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.09 (7) ~ (e2 = e1) % 136.03/20.09 (8) ~ (e3 = e0) % 136.03/20.09 (9) ~ (all_28_0 = e2) % 136.03/20.09 (10) op(e1, e1) = e3 % 136.03/20.09 (11) ~ (all_6_2 = e2) % 136.03/20.09 (12) ~ (e1 = e0) % 136.03/20.09 (13) all_57_14 = e1 % 136.03/20.09 (14) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | % 136.03/20.09 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 136.03/20.09 % 136.03/20.09 Begin of proof % 136.03/20.09 | % 136.03/20.09 | BETA: splitting (2) gives: % 136.03/20.09 | % 136.03/20.09 | Case 1: % 136.03/20.09 | | % 136.03/20.09 | | (15) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = % 136.03/20.09 | | e0) % 136.03/20.09 | | % 136.03/20.09 | | BETA: splitting (15) gives: % 136.03/20.09 | | % 136.03/20.09 | | Case 1: % 136.03/20.09 | | | % 136.03/20.09 | | | (16) all_57_4 = e0 & op(e3, e1) = e0 % 136.03/20.09 | | | % 136.03/20.09 | | | ALPHA: (16) implies: % 136.03/20.09 | | | (17) op(e3, e1) = e0 % 136.03/20.09 | | | % 136.03/20.09 | | | REF_CLOSE: (5), (6), (12), (17) are inconsistent by sub-proof #343. % 136.03/20.09 | | | % 136.03/20.09 | | Case 2: % 136.03/20.09 | | | % 136.03/20.09 | | | (18) all_57_5 = e0 & op(e2, e1) = e0 % 136.03/20.09 | | | % 136.03/20.09 | | | ALPHA: (18) implies: % 136.03/20.09 | | | (19) all_57_5 = e0 % 136.03/20.09 | | | % 136.03/20.09 | | | BETA: splitting (14) gives: % 136.03/20.09 | | | % 136.03/20.09 | | | Case 1: % 136.03/20.09 | | | | % 136.03/20.09 | | | | (20) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) % 136.03/20.09 | | | | = e2) % 136.03/20.09 | | | | % 136.03/20.09 | | | | BETA: splitting (20) gives: % 136.03/20.09 | | | | % 136.03/20.09 | | | | Case 1: % 136.03/20.09 | | | | | % 136.03/20.09 | | | | | (21) all_57_4 = e2 & op(e3, e1) = e2 % 136.03/20.09 | | | | | % 136.03/20.09 | | | | | REF_CLOSE: (1), (6), (9), (21) are inconsistent by sub-proof #218. % 136.03/20.09 | | | | | % 136.03/20.09 | | | | Case 2: % 136.03/20.09 | | | | | % 136.03/20.09 | | | | | (22) all_57_5 = e2 & op(e2, e1) = e2 % 136.03/20.09 | | | | | % 136.03/20.09 | | | | | ALPHA: (22) implies: % 136.03/20.09 | | | | | (23) all_57_5 = e2 % 136.03/20.09 | | | | | % 136.03/20.09 | | | | | COMBINE_EQS: (19), (23) imply: % 136.03/20.09 | | | | | (24) e2 = e0 % 136.03/20.09 | | | | | % 136.03/20.09 | | | | | REDUCE: (4), (24) imply: % 136.03/20.09 | | | | | (25) $false % 136.03/20.09 | | | | | % 136.03/20.09 | | | | | CLOSE: (25) is inconsistent. % 136.03/20.09 | | | | | % 136.03/20.09 | | | | End of split % 136.03/20.09 | | | | % 136.03/20.09 | | | Case 2: % 136.03/20.09 | | | | % 136.03/20.09 | | | | (26) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) % 136.03/20.09 | | | | = e2) % 136.03/20.09 | | | | % 136.03/20.09 | | | | BETA: splitting (26) gives: % 136.03/20.09 | | | | % 136.03/20.09 | | | | Case 1: % 136.03/20.09 | | | | | % 136.03/20.09 | | | | | (27) all_57_8 = e2 & op(e1, e1) = e2 % 136.03/20.09 | | | | | % 136.03/20.09 | | | | | ALPHA: (27) implies: % 136.03/20.09 | | | | | (28) op(e1, e1) = e2 % 136.03/20.09 | | | | | % 136.03/20.09 | | | | | REF_CLOSE: (3), (6), (11), (28) are inconsistent by sub-proof #767. % 136.03/20.09 | | | | | % 136.03/20.09 | | | | Case 2: % 136.03/20.09 | | | | | % 136.03/20.09 | | | | | (29) all_57_14 = e2 & op(e0, e1) = e2 % 136.03/20.09 | | | | | % 136.03/20.09 | | | | | REF_CLOSE: (7), (13), (29) are inconsistent by sub-proof #213. % 136.03/20.09 | | | | | % 136.03/20.09 | | | | End of split % 136.03/20.09 | | | | % 136.03/20.09 | | | End of split % 136.03/20.09 | | | % 136.03/20.09 | | End of split % 136.03/20.09 | | % 136.03/20.09 | Case 2: % 136.03/20.09 | | % 136.03/20.09 | | (30) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = % 136.03/20.09 | | e0) % 136.03/20.09 | | % 136.03/20.09 | | BETA: splitting (30) gives: % 136.03/20.09 | | % 136.03/20.09 | | Case 1: % 136.03/20.09 | | | % 136.03/20.09 | | | (31) all_57_8 = e0 & op(e1, e1) = e0 % 136.03/20.09 | | | % 136.03/20.09 | | | ALPHA: (31) implies: % 136.03/20.09 | | | (32) op(e1, e1) = e0 % 136.03/20.09 | | | % 136.03/20.09 | | | REF_CLOSE: (6), (8), (10), (32) are inconsistent by sub-proof #753. % 136.03/20.09 | | | % 136.03/20.09 | | Case 2: % 136.03/20.09 | | | % 136.03/20.09 | | | (33) all_57_14 = e0 & op(e0, e1) = e0 % 136.03/20.09 | | | % 136.03/20.09 | | | REF_CLOSE: (12), (13), (33) are inconsistent by sub-proof #483. % 136.03/20.09 | | | % 136.03/20.09 | | End of split % 136.03/20.09 | | % 136.03/20.09 | End of split % 136.03/20.09 | % 136.03/20.09 End of proof % 136.03/20.09 % 136.03/20.09 Sub-proof #213 shows that the following formulas are inconsistent: % 136.03/20.09 ---------------------------------------------------------------- % 136.03/20.09 (1) all_57_14 = e2 & op(e0, e1) = e2 % 136.03/20.09 (2) all_57_14 = e1 % 136.03/20.09 (3) ~ (e2 = e1) % 136.03/20.09 % 136.03/20.09 Begin of proof % 136.03/20.09 | % 136.03/20.09 | ALPHA: (1) implies: % 136.03/20.09 | (4) all_57_14 = e2 % 136.03/20.09 | % 136.03/20.09 | COMBINE_EQS: (2), (4) imply: % 136.03/20.09 | (5) e2 = e1 % 136.03/20.09 | % 136.03/20.09 | REDUCE: (3), (5) imply: % 136.03/20.09 | (6) $false % 136.03/20.09 | % 136.03/20.09 | CLOSE: (6) is inconsistent. % 136.03/20.09 | % 136.03/20.09 End of proof % 136.03/20.09 % 136.03/20.09 Sub-proof #214 shows that the following formulas are inconsistent: % 136.03/20.09 ---------------------------------------------------------------- % 136.03/20.09 (1) op(e3, e1) = all_28_0 % 136.03/20.09 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) | % 136.03/20.09 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 136.03/20.09 (3) op(e1, e1) = all_6_2 % 136.03/20.09 (4) all_57_5 = e1 % 136.03/20.09 (5) ~ (e2 = e0) % 136.03/20.09 (6) op(e3, e1) = e1 % 136.03/20.09 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.09 (8) ~ (e2 = e1) % 136.03/20.09 (9) ~ (e3 = e0) % 136.03/20.09 (10) ~ (all_28_0 = e2) % 136.03/20.09 (11) op(e1, e1) = e3 % 136.03/20.09 (12) ~ (all_6_2 = e2) % 136.03/20.09 (13) ~ (e1 = e0) % 136.03/20.09 (14) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | % 136.03/20.09 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 136.03/20.09 % 136.03/20.09 Begin of proof % 136.03/20.09 | % 136.03/20.09 | BETA: splitting (2) gives: % 136.03/20.09 | % 136.03/20.09 | Case 1: % 136.03/20.09 | | % 136.03/20.09 | | (15) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = % 136.03/20.09 | | e0) % 136.03/20.09 | | % 136.03/20.09 | | BETA: splitting (15) gives: % 136.03/20.09 | | % 136.03/20.09 | | Case 1: % 136.03/20.09 | | | % 136.03/20.09 | | | (16) all_57_4 = e0 & op(e3, e1) = e0 % 136.03/20.09 | | | % 136.03/20.09 | | | ALPHA: (16) implies: % 136.03/20.09 | | | (17) op(e3, e1) = e0 % 136.03/20.09 | | | % 136.03/20.09 | | | REF_CLOSE: (6), (7), (13), (17) are inconsistent by sub-proof #343. % 136.03/20.09 | | | % 136.03/20.09 | | Case 2: % 136.03/20.09 | | | % 136.03/20.09 | | | (18) all_57_5 = e0 & op(e2, e1) = e0 % 136.03/20.09 | | | % 136.03/20.09 | | | REF_CLOSE: (4), (13), (18) are inconsistent by sub-proof #461. % 136.03/20.09 | | | % 136.03/20.09 | | End of split % 136.03/20.09 | | % 136.03/20.09 | Case 2: % 136.03/20.09 | | % 136.03/20.09 | | (19) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = % 136.03/20.09 | | e0) % 136.03/20.09 | | % 136.03/20.09 | | BETA: splitting (19) gives: % 136.03/20.09 | | % 136.03/20.09 | | Case 1: % 136.03/20.09 | | | % 136.03/20.09 | | | (20) all_57_8 = e0 & op(e1, e1) = e0 % 136.03/20.09 | | | % 136.03/20.09 | | | ALPHA: (20) implies: % 136.03/20.09 | | | (21) op(e1, e1) = e0 % 136.03/20.09 | | | % 136.03/20.09 | | | REF_CLOSE: (7), (9), (11), (21) are inconsistent by sub-proof #753. % 136.03/20.09 | | | % 136.03/20.09 | | Case 2: % 136.03/20.09 | | | % 136.03/20.09 | | | (22) all_57_14 = e0 & op(e0, e1) = e0 % 136.03/20.09 | | | % 136.03/20.09 | | | ALPHA: (22) implies: % 136.03/20.09 | | | (23) op(e0, e1) = e0 % 136.03/20.09 | | | % 136.03/20.09 | | | BETA: splitting (14) gives: % 136.03/20.09 | | | % 136.03/20.09 | | | Case 1: % 136.03/20.09 | | | | % 136.03/20.09 | | | | (24) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) % 136.03/20.09 | | | | = e2) % 136.03/20.09 | | | | % 136.03/20.09 | | | | BETA: splitting (24) gives: % 136.03/20.09 | | | | % 136.03/20.09 | | | | Case 1: % 136.03/20.09 | | | | | % 136.03/20.09 | | | | | (25) all_57_4 = e2 & op(e3, e1) = e2 % 136.03/20.09 | | | | | % 136.03/20.09 | | | | | REF_CLOSE: (1), (7), (10), (25) are inconsistent by sub-proof #218. % 136.03/20.09 | | | | | % 136.03/20.09 | | | | Case 2: % 136.03/20.09 | | | | | % 136.03/20.09 | | | | | (26) all_57_5 = e2 & op(e2, e1) = e2 % 136.03/20.09 | | | | | % 136.03/20.09 | | | | | ALPHA: (26) implies: % 136.03/20.09 | | | | | (27) all_57_5 = e2 % 136.03/20.09 | | | | | % 136.03/20.09 | | | | | REF_CLOSE: (4), (8), (27) are inconsistent by sub-proof #418. % 136.03/20.09 | | | | | % 136.03/20.09 | | | | End of split % 136.03/20.09 | | | | % 136.03/20.09 | | | Case 2: % 136.03/20.09 | | | | % 136.03/20.09 | | | | (28) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) % 136.03/20.09 | | | | = e2) % 136.03/20.09 | | | | % 136.03/20.09 | | | | REF_CLOSE: (3), (5), (7), (12), (23), (28) are inconsistent by sub-proof % 136.03/20.09 | | | | #659. % 136.03/20.09 | | | | % 136.03/20.09 | | | End of split % 136.03/20.09 | | | % 136.03/20.09 | | End of split % 136.03/20.09 | | % 136.03/20.09 | End of split % 136.03/20.09 | % 136.03/20.09 End of proof % 136.03/20.09 % 136.03/20.09 Sub-proof #215 shows that the following formulas are inconsistent: % 136.03/20.09 ---------------------------------------------------------------- % 136.03/20.09 (1) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 136.03/20.09 (2) ~ (all_52_4 = e0) % 136.03/20.09 (3) op(e2, e2) = e0 % 136.03/20.09 (4) ~ (all_52_4 = all_52_12) % 136.03/20.09 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.09 (6) ~ (e3 = e0) % 136.03/20.09 (7) ~ (all_52_4 = e2) % 136.03/20.09 (8) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.09 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.03/20.09 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.09 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.09 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 136.03/20.09 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 136.03/20.09 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 136.03/20.09 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.03/20.09 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.03/20.09 $i(all_56_17) & $i(all_56_25)) % 136.03/20.09 (9) all_54_1 = all_52_4 % 136.03/20.09 (10) op(e3, e0) = all_52_12 % 136.03/20.09 (11) ~ (all_52_4 = e1) % 136.03/20.09 % 136.03/20.09 Begin of proof % 136.03/20.09 | % 136.03/20.09 | BETA: splitting (8) gives: % 136.03/20.09 | % 136.03/20.09 | Case 1: % 136.03/20.09 | | % 136.03/20.09 | | (12) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 % 136.03/20.09 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = % 136.03/20.09 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 136.03/20.09 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 136.03/20.09 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.03/20.09 | | % 136.03/20.09 | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (11), (12) are inconsistent % 136.03/20.09 | | by sub-proof #217. % 136.03/20.09 | | % 136.03/20.09 | Case 2: % 136.03/20.09 | | % 136.03/20.09 | | (13) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.03/20.09 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.09 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.09 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) % 136.03/20.09 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.03/20.09 | | % 136.03/20.09 | | ALPHA: (13) implies: % 136.03/20.09 | | (14) op(e2, e2) = e3 % 136.03/20.09 | | % 136.03/20.09 | | REF_CLOSE: (3), (5), (6), (14) are inconsistent by sub-proof #641. % 136.03/20.09 | | % 136.03/20.09 | End of split % 136.03/20.09 | % 136.03/20.09 End of proof % 136.03/20.09 % 136.03/20.09 Sub-proof #216 shows that the following formulas are inconsistent: % 136.03/20.09 ---------------------------------------------------------------- % 136.03/20.09 (1) all_54_3 = all_52_12 % 136.03/20.09 (2) all_54_3 = e3 % 136.03/20.09 (3) ~ (all_52_12 = e3) % 136.03/20.09 % 136.03/20.09 Begin of proof % 136.03/20.09 | % 136.03/20.09 | COMBINE_EQS: (1), (2) imply: % 136.03/20.09 | (4) all_52_12 = e3 % 136.03/20.09 | % 136.03/20.09 | SIMP: (4) implies: % 136.03/20.09 | (5) all_52_12 = e3 % 136.03/20.09 | % 136.03/20.09 | REDUCE: (3), (5) imply: % 136.03/20.09 | (6) $false % 136.03/20.09 | % 136.03/20.09 | CLOSE: (6) is inconsistent. % 136.03/20.09 | % 136.03/20.09 End of proof % 136.03/20.09 % 136.03/20.09 Sub-proof #217 shows that the following formulas are inconsistent: % 136.03/20.09 ---------------------------------------------------------------- % 136.03/20.09 (1) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) % 136.03/20.09 & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 136.03/20.09 e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) % 136.03/20.09 = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 136.03/20.09 $i(all_56_23) & $i(all_56_31) % 136.03/20.09 (2) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 136.03/20.09 (3) ~ (all_52_4 = e0) % 136.03/20.09 (4) ~ (all_52_4 = all_52_12) % 136.03/20.09 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.09 (6) ~ (all_52_4 = e2) % 136.03/20.09 (7) all_54_1 = all_52_4 % 136.03/20.09 (8) op(e3, e0) = all_52_12 % 136.03/20.09 (9) ~ (all_52_4 = e1) % 136.03/20.09 % 136.03/20.09 Begin of proof % 136.03/20.09 | % 136.03/20.09 | ALPHA: (1) implies: % 136.03/20.09 | (10) op(e3, e0) = e3 % 136.03/20.09 | % 136.03/20.09 | BETA: splitting (2) gives: % 136.03/20.09 | % 136.03/20.09 | Case 1: % 136.03/20.09 | | % 136.03/20.09 | | (11) all_54_1 = e3 % 136.03/20.09 | | % 136.03/20.09 | | COMBINE_EQS: (7), (11) imply: % 136.03/20.09 | | (12) all_52_4 = e3 % 136.03/20.09 | | % 136.03/20.09 | | SIMP: (12) implies: % 136.03/20.09 | | (13) all_52_4 = e3 % 136.03/20.09 | | % 136.03/20.09 | | REDUCE: (4), (13) imply: % 136.03/20.09 | | (14) ~ (all_52_12 = e3) % 136.03/20.09 | | % 136.03/20.09 | | SIMP: (14) implies: % 136.03/20.09 | | (15) ~ (all_52_12 = e3) % 136.03/20.09 | | % 136.03/20.09 | | REF_CLOSE: (5), (8), (10), (15) are inconsistent by sub-proof #733. % 136.03/20.09 | | % 136.03/20.09 | Case 2: % 136.03/20.09 | | % 136.03/20.09 | | (16) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 136.03/20.09 | | % 136.03/20.09 | | REF_CLOSE: (3), (6), (7), (9), (16) are inconsistent by sub-proof #701. % 136.03/20.09 | | % 136.03/20.09 | End of split % 136.03/20.09 | % 136.03/20.09 End of proof % 136.03/20.09 % 136.03/20.09 Sub-proof #218 shows that the following formulas are inconsistent: % 136.03/20.09 ---------------------------------------------------------------- % 136.03/20.09 (1) all_57_4 = e2 & op(e3, e1) = e2 % 136.03/20.09 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.09 (3) op(e3, e1) = all_28_0 % 136.03/20.09 (4) ~ (all_28_0 = e2) % 136.03/20.09 % 136.03/20.09 Begin of proof % 136.03/20.09 | % 136.03/20.09 | ALPHA: (1) implies: % 136.03/20.09 | (5) op(e3, e1) = e2 % 136.03/20.09 | % 136.03/20.09 | GROUND_INST: instantiating (2) with e2, all_28_0, e1, e3, simplifying with % 136.03/20.09 | (3), (5) gives: % 136.03/20.09 | (6) all_28_0 = e2 % 136.03/20.09 | % 136.03/20.09 | REDUCE: (4), (6) imply: % 136.03/20.09 | (7) $false % 136.03/20.09 | % 136.03/20.09 | CLOSE: (7) is inconsistent. % 136.03/20.09 | % 136.03/20.09 End of proof % 136.03/20.09 % 136.03/20.09 Sub-proof #219 shows that the following formulas are inconsistent: % 136.03/20.09 ---------------------------------------------------------------- % 136.03/20.09 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.09 (2) op(e0, e3) = all_52_3 % 136.03/20.09 (3) op(e0, e3) = e0 % 136.03/20.09 (4) ~ (all_52_3 = e0) % 136.03/20.09 % 136.03/20.09 Begin of proof % 136.03/20.09 | % 136.03/20.09 | GROUND_INST: instantiating (1) with all_52_3, e0, e3, e0, simplifying with % 136.03/20.09 | (2), (3) gives: % 136.03/20.09 | (5) all_52_3 = e0 % 136.03/20.09 | % 136.03/20.09 | REDUCE: (4), (5) imply: % 136.03/20.09 | (6) $false % 136.03/20.09 | % 136.03/20.09 | CLOSE: (6) is inconsistent. % 136.03/20.09 | % 136.03/20.09 End of proof % 136.03/20.09 % 136.03/20.09 Sub-proof #220 shows that the following formulas are inconsistent: % 136.03/20.09 ---------------------------------------------------------------- % 136.03/20.09 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.09 (2) op(e0, e0) = e1 % 136.03/20.09 (3) op(e0, e0) = e0 % 136.03/20.09 (4) ~ (e1 = e0) % 136.03/20.09 % 136.03/20.09 Begin of proof % 136.03/20.09 | % 136.03/20.09 | GROUND_INST: instantiating (1) with e0, e1, e0, e0, simplifying with (2), (3) % 136.03/20.09 | gives: % 136.03/20.09 | (5) e1 = e0 % 136.03/20.09 | % 136.03/20.09 | REDUCE: (4), (5) imply: % 136.03/20.09 | (6) $false % 136.03/20.09 | % 136.03/20.09 | CLOSE: (6) is inconsistent. % 136.03/20.09 | % 136.03/20.09 End of proof % 136.03/20.09 % 136.03/20.09 Sub-proof #221 shows that the following formulas are inconsistent: % 136.03/20.09 ---------------------------------------------------------------- % 136.03/20.09 (1) all_57_14 = e1 % 136.03/20.10 (2) all_57_14 = e0 % 136.03/20.10 (3) ~ (e1 = e0) % 136.03/20.10 % 136.03/20.10 Begin of proof % 136.03/20.10 | % 136.03/20.10 | COMBINE_EQS: (1), (2) imply: % 136.03/20.10 | (4) e1 = e0 % 136.03/20.10 | % 136.03/20.10 | SIMP: (4) implies: % 136.03/20.10 | (5) e1 = e0 % 136.03/20.10 | % 136.03/20.10 | REDUCE: (3), (5) imply: % 136.03/20.10 | (6) $false % 136.03/20.10 | % 136.03/20.10 | CLOSE: (6) is inconsistent. % 136.03/20.10 | % 136.03/20.10 End of proof % 136.03/20.10 % 136.03/20.10 Sub-proof #222 shows that the following formulas are inconsistent: % 136.03/20.10 ---------------------------------------------------------------- % 136.03/20.10 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 136.03/20.10 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 136.03/20.10 (2) op(e1, e1) = all_6_2 % 136.03/20.10 (3) ~ (all_52_4 = e0) % 136.03/20.10 (4) ~ (e2 = e0) % 136.03/20.10 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.03/20.10 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.03/20.10 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.10 (7) ~ (e2 = e1) % 136.03/20.10 (8) ~ (e3 = e0) % 136.03/20.10 (9) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 136.03/20.10 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 136.03/20.10 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) % 136.03/20.10 = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & $i(all_56_11) & % 136.03/20.10 $i(all_56_19) & $i(all_56_27) % 136.03/20.10 (10) ~ (e3 = e2) % 136.03/20.10 (11) all_57_14 = e0 % 136.03/20.10 (12) ~ (all_52_12 = e0) % 136.03/20.10 (13) ~ (all_6_2 = e2) % 136.03/20.10 (14) op(e3, e2) = all_52_4 % 136.03/20.10 (15) op(e3, e0) = all_52_12 % 136.03/20.10 (16) op(e0, e1) = e0 % 136.03/20.10 (17) ~ (e3 = e1) % 136.03/20.10 (18) ~ (e1 = e0) % 136.03/20.10 (19) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) | % 136.03/20.10 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) % 136.03/20.10 (20) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | % 136.03/20.10 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 136.03/20.10 % 136.03/20.10 Begin of proof % 136.03/20.10 | % 136.03/20.10 | ALPHA: (9) implies: % 136.03/20.10 | (21) op(e3, e3) = e2 % 136.03/20.10 | % 136.03/20.10 | BETA: splitting (5) gives: % 136.03/20.10 | % 136.03/20.10 | Case 1: % 136.03/20.10 | | % 136.03/20.10 | | (22) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = % 136.03/20.10 | | e0) % 136.03/20.10 | | % 136.03/20.10 | | REF_CLOSE: (3), (4), (6), (14), (21), (22) are inconsistent by sub-proof % 136.03/20.10 | | #421. % 136.03/20.10 | | % 136.03/20.10 | Case 2: % 136.03/20.10 | | % 136.03/20.10 | | (23) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = % 136.03/20.10 | | e0) % 136.03/20.10 | | % 136.03/20.10 | | BETA: splitting (23) gives: % 136.03/20.10 | | % 136.03/20.10 | | Case 1: % 136.03/20.10 | | | % 136.03/20.10 | | | (24) all_57_4 = e0 & op(e3, e1) = e0 % 136.03/20.10 | | | % 136.03/20.10 | | | ALPHA: (24) implies: % 136.03/20.10 | | | (25) all_57_4 = e0 % 136.03/20.10 | | | % 136.03/20.10 | | | BETA: splitting (20) gives: % 136.03/20.10 | | | % 136.03/20.10 | | | Case 1: % 136.03/20.10 | | | | % 136.03/20.10 | | | | (26) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) % 136.03/20.10 | | | | = e2) % 136.03/20.10 | | | | % 136.03/20.10 | | | | BETA: splitting (26) gives: % 136.03/20.10 | | | | % 136.03/20.10 | | | | Case 1: % 136.03/20.10 | | | | | % 136.03/20.10 | | | | | (27) all_57_4 = e2 & op(e3, e1) = e2 % 136.03/20.10 | | | | | % 136.03/20.10 | | | | | REF_CLOSE: (4), (25), (27) are inconsistent by sub-proof #689. % 136.03/20.10 | | | | | % 136.03/20.10 | | | | Case 2: % 136.03/20.10 | | | | | % 136.03/20.10 | | | | | (28) all_57_5 = e2 & op(e2, e1) = e2 % 136.03/20.10 | | | | | % 136.03/20.10 | | | | | ALPHA: (28) implies: % 136.03/20.10 | | | | | (29) all_57_5 = e2 % 136.03/20.10 | | | | | % 136.03/20.10 | | | | | BETA: splitting (19) gives: % 136.03/20.10 | | | | | % 136.03/20.10 | | | | | Case 1: % 136.03/20.10 | | | | | | % 136.03/20.10 | | | | | | (30) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, % 136.03/20.10 | | | | | | e1) = e3) % 136.03/20.10 | | | | | | % 136.03/20.10 | | | | | | BETA: splitting (30) gives: % 136.03/20.10 | | | | | | % 136.03/20.10 | | | | | | Case 1: % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | | (31) all_57_4 = e3 & op(e3, e1) = e3 % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | | ALPHA: (31) implies: % 136.03/20.10 | | | | | | | (32) all_57_4 = e3 % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | | COMBINE_EQS: (25), (32) imply: % 136.03/20.10 | | | | | | | (33) e3 = e0 % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | | REDUCE: (8), (33) imply: % 136.03/20.10 | | | | | | | (34) $false % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | | CLOSE: (34) is inconsistent. % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | Case 2: % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | | (35) all_57_5 = e3 & op(e2, e1) = e3 % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | | ALPHA: (35) implies: % 136.03/20.10 | | | | | | | (36) all_57_5 = e3 % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | | REF_CLOSE: (10), (29), (36) are inconsistent by sub-proof #501. % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | End of split % 136.03/20.10 | | | | | | % 136.03/20.10 | | | | | Case 2: % 136.03/20.10 | | | | | | % 136.03/20.10 | | | | | | (37) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, % 136.03/20.10 | | | | | | e1) = e3) % 136.03/20.10 | | | | | | % 136.03/20.10 | | | | | | BETA: splitting (37) gives: % 136.03/20.10 | | | | | | % 136.03/20.10 | | | | | | Case 1: % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | | (38) all_57_8 = e3 & op(e1, e1) = e3 % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | | ALPHA: (38) implies: % 136.03/20.10 | | | | | | | (39) op(e1, e1) = e3 % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | | REF_CLOSE: (1), (2), (6), (7), (11), (17), (18), (25), (29), (39) % 136.03/20.10 | | | | | | | are inconsistent by sub-proof #230. % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | Case 2: % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | | (40) all_57_14 = e3 & op(e0, e1) = e3 % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | | ALPHA: (40) implies: % 136.03/20.10 | | | | | | | (41) all_57_14 = e3 % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | | REF_CLOSE: (8), (11), (41) are inconsistent by sub-proof #400. % 136.03/20.10 | | | | | | | % 136.03/20.10 | | | | | | End of split % 136.03/20.10 | | | | | | % 136.03/20.10 | | | | | End of split % 136.03/20.10 | | | | | % 136.03/20.10 | | | | End of split % 136.03/20.10 | | | | % 136.03/20.10 | | | Case 2: % 136.03/20.10 | | | | % 136.03/20.10 | | | | (42) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) % 136.03/20.10 | | | | = e2) % 136.03/20.10 | | | | % 136.03/20.10 | | | | REF_CLOSE: (2), (4), (6), (13), (16), (42) are inconsistent by sub-proof % 136.03/20.10 | | | | #659. % 136.03/20.10 | | | | % 136.03/20.10 | | | End of split % 136.03/20.10 | | | % 136.03/20.10 | | Case 2: % 136.03/20.10 | | | % 136.03/20.10 | | | (43) all_57_9 = e0 & op(e3, e0) = e0 % 136.03/20.10 | | | % 136.03/20.10 | | | REF_CLOSE: (6), (12), (15), (43) are inconsistent by sub-proof #618. % 136.03/20.10 | | | % 136.03/20.10 | | End of split % 136.03/20.10 | | % 136.03/20.10 | End of split % 136.03/20.10 | % 136.03/20.10 End of proof % 136.03/20.10 % 136.03/20.10 Sub-proof #223 shows that the following formulas are inconsistent: % 136.03/20.10 ---------------------------------------------------------------- % 136.03/20.10 (1) op(e0, e0) = e0 % 136.03/20.10 (2) op(e2, e2) = e0 % 136.03/20.10 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.10 (4) ~ (e3 = e0) % 136.03/20.10 (5) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.10 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.03/20.10 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.10 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.10 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 136.03/20.10 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 136.03/20.10 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 136.03/20.10 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.03/20.10 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.03/20.10 $i(all_56_17) & $i(all_56_25)) % 136.03/20.10 % 136.03/20.10 Begin of proof % 136.03/20.10 | % 136.03/20.10 | BETA: splitting (5) gives: % 136.03/20.10 | % 136.03/20.10 | Case 1: % 136.03/20.10 | | % 136.03/20.10 | | (6) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.03/20.10 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.03/20.10 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.03/20.10 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.03/20.10 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.03/20.10 | | % 136.03/20.10 | | ALPHA: (6) implies: % 136.03/20.10 | | (7) ~ (all_56_31 = e0) % 136.03/20.10 | | (8) op(e0, e0) = all_56_31 % 136.03/20.10 | | % 136.03/20.10 | | REF_CLOSE: (1), (3), (7), (8) are inconsistent by sub-proof #712. % 136.03/20.10 | | % 136.03/20.10 | Case 2: % 136.03/20.10 | | % 136.03/20.10 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.03/20.10 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.10 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.10 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) % 136.03/20.10 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.03/20.10 | | % 136.03/20.10 | | ALPHA: (9) implies: % 136.03/20.10 | | (10) op(e2, e2) = e3 % 136.03/20.10 | | % 136.03/20.10 | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #641. % 136.03/20.10 | | % 136.03/20.10 | End of split % 136.03/20.10 | % 136.03/20.10 End of proof % 136.03/20.10 % 136.03/20.10 Sub-proof #224 shows that the following formulas are inconsistent: % 136.03/20.10 ---------------------------------------------------------------- % 136.03/20.10 (1) all_57_4 = e0 & op(e3, e1) = e0 % 136.03/20.10 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.10 (3) op(e3, e1) = all_52_8 % 136.03/20.10 (4) ~ (all_52_8 = e0) % 136.03/20.10 % 136.03/20.10 Begin of proof % 136.03/20.10 | % 136.03/20.10 | ALPHA: (1) implies: % 136.03/20.10 | (5) op(e3, e1) = e0 % 136.03/20.10 | % 136.03/20.10 | GROUND_INST: instantiating (2) with all_52_8, e0, e1, e3, simplifying with % 136.03/20.10 | (3), (5) gives: % 136.03/20.10 | (6) all_52_8 = e0 % 136.03/20.10 | % 136.03/20.10 | REDUCE: (4), (6) imply: % 136.03/20.10 | (7) $false % 136.03/20.10 | % 136.03/20.10 | CLOSE: (7) is inconsistent. % 136.03/20.10 | % 136.03/20.10 End of proof % 136.03/20.10 % 136.03/20.10 Sub-proof #225 shows that the following formulas are inconsistent: % 136.03/20.10 ---------------------------------------------------------------- % 136.03/20.10 (1) all_57_2 = e0 & op(e2, e3) = e0 % 136.03/20.10 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.10 (3) op(e2, e3) = all_52_1 % 136.03/20.10 (4) ~ (all_52_1 = e0) % 136.03/20.10 % 136.03/20.10 Begin of proof % 136.03/20.10 | % 136.03/20.10 | ALPHA: (1) implies: % 136.03/20.10 | (5) op(e2, e3) = e0 % 136.03/20.10 | % 136.03/20.10 | GROUND_INST: instantiating (2) with all_52_1, e0, e3, e2, simplifying with % 136.03/20.10 | (3), (5) gives: % 136.03/20.10 | (6) all_52_1 = e0 % 136.03/20.10 | % 136.03/20.10 | REDUCE: (4), (6) imply: % 136.03/20.10 | (7) $false % 136.03/20.10 | % 136.03/20.10 | CLOSE: (7) is inconsistent. % 136.03/20.10 | % 136.03/20.10 End of proof % 136.03/20.10 % 136.03/20.10 Sub-proof #226 shows that the following formulas are inconsistent: % 136.03/20.10 ---------------------------------------------------------------- % 136.03/20.10 (1) op(e2, e2) = all_8_2 % 136.03/20.10 (2) op(e1, e1) = all_6_2 % 136.03/20.10 (3) op(e0, e0) = e3 % 136.03/20.10 (4) ~ (all_8_2 = e1) % 136.03/20.10 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.10 (6) ~ (all_46_2 = e0) | ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 & % 136.03/20.10 $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0) = all_46_1 & % 136.03/20.10 $i(all_46_1)) % 136.03/20.10 (7) ~ (all_52_11 = all_6_2) % 136.03/20.10 (8) op(e0, e1) = all_52_11 % 136.03/20.10 (9) op(e0, e2) = all_52_7 % 136.03/20.10 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 136.03/20.10 (11) ~ (all_52_11 = e3) % 136.03/20.10 (12) ~ (all_6_2 = e2) % 136.03/20.10 (13) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 136.03/20.10 (14) all_54_5 = all_8_2 % 136.03/20.10 (15) op(e0, e3) = all_52_3 % 136.03/20.10 (16) all_46_2 = all_6_2 % 136.03/20.10 (17) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.03/20.10 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.03/20.10 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.03/20.10 e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 136.03/20.10 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 136.03/20.10 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 136.03/20.10 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 136.03/20.10 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 136.03/20.10 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 % 136.03/20.10 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.03/20.10 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.10 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.10 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.10 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.03/20.10 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.03/20.10 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.03/20.10 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.10 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.03/20.10 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.03/20.10 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.03/20.10 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.03/20.10 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.03/20.10 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.03/20.10 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.03/20.10 $i(all_56_29)))) % 136.03/20.10 (18) all_54_14 = all_52_11 % 136.03/20.10 (19) ~ (e3 = e1) % 136.03/20.10 (20) ~ (all_52_7 = all_8_2) % 136.03/20.10 (21) ~ (all_8_2 = e3) % 136.03/20.10 (22) ~ (all_52_3 = e0) % 136.03/20.10 % 136.03/20.10 Begin of proof % 136.03/20.10 | % 136.03/20.10 | BETA: splitting (17) gives: % 136.03/20.10 | % 136.03/20.10 | Case 1: % 136.03/20.10 | | % 136.03/20.10 | | (23) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.03/20.10 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.03/20.10 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.03/20.10 | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) % 136.03/20.10 | | & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.03/20.10 | | % 136.03/20.10 | | ALPHA: (23) implies: % 136.03/20.10 | | (24) op(e1, e1) = e2 % 136.03/20.10 | | % 136.03/20.10 | | REF_CLOSE: (2), (5), (12), (24) are inconsistent by sub-proof #767. % 136.03/20.10 | | % 136.03/20.10 | Case 2: % 136.03/20.10 | | % 136.03/20.10 | | (25) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 % 136.03/20.10 | | = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 136.03/20.10 | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) % 136.03/20.10 | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.03/20.10 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.03/20.10 | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 % 136.03/20.10 | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 136.03/20.10 | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.03/20.10 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.03/20.10 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.03/20.10 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 % 136.03/20.10 | | = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.03/20.10 | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, % 136.03/20.10 | | e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 136.03/20.10 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 136.03/20.10 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.03/20.10 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.03/20.10 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.03/20.10 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.03/20.10 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29))) % 136.03/20.10 | | % 136.03/20.10 | | ALPHA: (25) implies: % 136.03/20.10 | | (26) op(e0, e0) = all_56_31 % 136.03/20.10 | | (27) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.03/20.10 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.03/20.10 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.03/20.10 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 136.03/20.10 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 136.03/20.10 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 136.03/20.10 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.03/20.10 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.03/20.10 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.03/20.10 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 136.03/20.10 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 % 136.03/20.10 | | = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 136.03/20.10 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.03/20.10 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & % 136.03/20.10 | | all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.03/20.10 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 136.03/20.10 | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.03/20.10 | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.10 | | $i(all_56_21) & $i(all_56_29)) % 136.03/20.10 | | % 136.03/20.10 | | GROUND_INST: instantiating (5) with e3, all_56_31, e0, e0, simplifying with % 136.03/20.10 | | (3), (26) gives: % 136.03/20.10 | | (28) all_56_31 = e3 % 136.03/20.10 | | % 136.03/20.10 | | BETA: splitting (27) gives: % 136.03/20.10 | | % 136.03/20.10 | | Case 1: % 136.03/20.10 | | | % 136.03/20.10 | | | (29) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.03/20.10 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.03/20.10 | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.03/20.10 | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.03/20.10 | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.03/20.10 | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.10 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.10 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.10 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.03/20.10 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 136.03/20.10 | | | % 136.03/20.10 | | | BETA: splitting (29) gives: % 136.03/20.10 | | | % 136.03/20.10 | | | Case 1: % 136.03/20.10 | | | | % 136.03/20.10 | | | | (30) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.03/20.10 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.03/20.10 | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.03/20.10 | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.03/20.10 | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.03/20.10 | | | | % 136.03/20.10 | | | | ALPHA: (30) implies: % 136.03/20.10 | | | | (31) op(e0, e3) = e0 % 136.03/20.10 | | | | % 136.03/20.10 | | | | GROUND_INST: instantiating (5) with all_52_3, e0, e3, e0, simplifying % 136.03/20.10 | | | | with (15), (31) gives: % 136.03/20.10 | | | | (32) all_52_3 = e0 % 136.03/20.10 | | | | % 136.03/20.10 | | | | REDUCE: (22), (32) imply: % 136.03/20.10 | | | | (33) $false % 136.03/20.10 | | | | % 136.03/20.10 | | | | CLOSE: (33) is inconsistent. % 136.03/20.10 | | | | % 136.03/20.10 | | | Case 2: % 136.03/20.10 | | | | % 136.03/20.10 | | | | (34) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.03/20.10 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.03/20.10 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.03/20.10 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.03/20.10 | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.03/20.10 | | | | % 136.03/20.10 | | | | ALPHA: (34) implies: % 136.03/20.10 | | | | (35) ~ (all_56_11 = e2) % 136.03/20.10 | | | | (36) op(e0, e2) = e0 % 136.03/20.10 | | | | (37) op(e2, e2) = all_56_11 % 136.03/20.10 | | | | % 136.03/20.10 | | | | REF_CLOSE: (1), (4), (5), (9), (13), (14), (20), (21), (35), (36), (37) % 136.03/20.10 | | | | are inconsistent by sub-proof #227. % 136.03/20.10 | | | | % 136.03/20.10 | | | End of split % 136.03/20.10 | | | % 136.03/20.10 | | Case 2: % 136.03/20.10 | | | % 136.03/20.10 | | | (38) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.03/20.10 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.10 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 136.03/20.10 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.03/20.10 | | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = % 136.03/20.10 | | | e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 136.03/20.10 | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 136.03/20.10 | | | = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.03/20.10 | | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.03/20.10 | | | $i(all_56_29)) % 136.03/20.10 | | | % 136.03/20.10 | | | BETA: splitting (38) gives: % 136.03/20.10 | | | % 136.03/20.10 | | | Case 1: % 136.03/20.10 | | | | % 136.03/20.10 | | | | (39) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.03/20.10 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.03/20.10 | | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 136.03/20.10 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.03/20.10 | | | | $i(all_56_15) & $i(all_56_23) % 136.03/20.10 | | | | % 136.03/20.10 | | | | ALPHA: (39) implies: % 136.03/20.10 | | | | (40) ~ (all_56_23 = e1) % 136.03/20.10 | | | | (41) op(e0, e1) = all_56_23 % 136.03/20.10 | | | | (42) op(e1, e1) = e0 % 136.03/20.10 | | | | % 136.03/20.10 | | | | GROUND_INST: instantiating (5) with all_52_11, all_56_23, e1, e0, % 136.03/20.10 | | | | simplifying with (8), (41) gives: % 136.03/20.10 | | | | (43) all_56_23 = all_52_11 % 136.03/20.10 | | | | % 136.03/20.10 | | | | REF_CLOSE: (2), (3), (5), (6), (7), (10), (11), (16), (18), (40), (41), % 136.03/20.10 | | | | (42), (43) are inconsistent by sub-proof #608. % 136.03/20.10 | | | | % 136.03/20.10 | | | Case 2: % 136.03/20.10 | | | | % 136.03/20.10 | | | | (44) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.03/20.10 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.03/20.10 | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.03/20.10 | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.03/20.10 | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.03/20.10 | | | | % 136.03/20.10 | | | | REF_CLOSE: (19), (28), (44) are inconsistent by sub-proof #752. % 136.03/20.10 | | | | % 136.03/20.10 | | | End of split % 136.03/20.10 | | | % 136.03/20.10 | | End of split % 136.03/20.10 | | % 136.03/20.10 | End of split % 136.03/20.10 | % 136.03/20.10 End of proof % 136.03/20.10 % 136.03/20.10 Sub-proof #227 shows that the following formulas are inconsistent: % 136.03/20.10 ---------------------------------------------------------------- % 136.03/20.10 (1) op(e2, e2) = all_8_2 % 136.03/20.10 (2) ~ (all_8_2 = e1) % 136.03/20.10 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.10 (4) op(e0, e2) = all_52_7 % 136.03/20.10 (5) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 136.03/20.10 (6) all_54_5 = all_8_2 % 136.03/20.10 (7) op(e0, e2) = e0 % 136.03/20.10 (8) ~ (all_56_11 = e2) % 136.03/20.10 (9) ~ (all_52_7 = all_8_2) % 136.03/20.10 (10) ~ (all_8_2 = e3) % 136.03/20.10 (11) op(e2, e2) = all_56_11 % 136.03/20.10 % 136.03/20.10 Begin of proof % 136.03/20.10 | % 136.03/20.10 | GROUND_INST: instantiating (3) with all_52_7, e0, e2, e0, simplifying with % 136.03/20.10 | (4), (7) gives: % 136.03/20.10 | (12) all_52_7 = e0 % 136.03/20.10 | % 136.03/20.10 | GROUND_INST: instantiating (3) with all_8_2, all_56_11, e2, e2, simplifying % 136.03/20.10 | with (1), (11) gives: % 136.03/20.10 | (13) all_56_11 = all_8_2 % 136.03/20.10 | % 136.03/20.10 | REDUCE: (8), (13) imply: % 136.03/20.10 | (14) ~ (all_8_2 = e2) % 136.03/20.10 | % 136.03/20.10 | REDUCE: (9), (12) imply: % 136.03/20.10 | (15) ~ (all_8_2 = e0) % 136.03/20.10 | % 136.03/20.10 | SIMP: (15) implies: % 136.03/20.10 | (16) ~ (all_8_2 = e0) % 136.03/20.10 | % 136.03/20.10 | BETA: splitting (5) gives: % 136.03/20.10 | % 136.03/20.10 | Case 1: % 136.03/20.10 | | % 136.03/20.10 | | (17) all_54_5 = e3 % 136.03/20.10 | | % 136.03/20.10 | | COMBINE_EQS: (6), (17) imply: % 136.03/20.10 | | (18) all_8_2 = e3 % 136.03/20.10 | | % 136.03/20.10 | | REDUCE: (10), (18) imply: % 136.03/20.10 | | (19) $false % 136.03/20.10 | | % 136.03/20.10 | | CLOSE: (19) is inconsistent. % 136.03/20.10 | | % 136.03/20.10 | Case 2: % 136.03/20.10 | | % 136.03/20.10 | | (20) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0 % 136.03/20.10 | | % 136.03/20.10 | | BETA: splitting (20) gives: % 136.03/20.10 | | % 136.03/20.10 | | Case 1: % 136.03/20.10 | | | % 136.03/20.10 | | | (21) all_54_5 = e2 % 136.03/20.10 | | | % 136.03/20.10 | | | COMBINE_EQS: (6), (21) imply: % 136.03/20.10 | | | (22) all_8_2 = e2 % 136.03/20.10 | | | % 136.03/20.10 | | | REDUCE: (14), (22) imply: % 136.03/20.10 | | | (23) $false % 136.03/20.10 | | | % 136.03/20.10 | | | CLOSE: (23) is inconsistent. % 136.03/20.10 | | | % 136.03/20.10 | | Case 2: % 136.03/20.10 | | | % 136.03/20.10 | | | (24) all_54_5 = e1 | all_54_5 = e0 % 136.03/20.10 | | | % 136.03/20.10 | | | REF_CLOSE: (2), (6), (16), (24) are inconsistent by sub-proof #624. % 136.03/20.10 | | | % 136.03/20.10 | | End of split % 136.03/20.10 | | % 136.03/20.10 | End of split % 136.03/20.10 | % 136.03/20.10 End of proof % 136.03/20.10 % 136.03/20.10 Sub-proof #228 shows that the following formulas are inconsistent: % 136.03/20.10 ---------------------------------------------------------------- % 136.03/20.10 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.10 (2) op(e2, e2) = all_8_2 % 136.03/20.10 (3) op(e2, e2) = e3 % 136.03/20.10 (4) ~ (all_8_2 = e3) % 136.03/20.10 % 136.03/20.10 Begin of proof % 136.03/20.10 | % 136.03/20.10 | GROUND_INST: instantiating (1) with all_8_2, e3, e2, e2, simplifying with (2), % 136.03/20.10 | (3) gives: % 136.03/20.10 | (5) all_8_2 = e3 % 136.03/20.10 | % 136.03/20.10 | REDUCE: (4), (5) imply: % 136.03/20.10 | (6) $false % 136.03/20.10 | % 136.03/20.10 | CLOSE: (6) is inconsistent. % 136.03/20.10 | % 136.03/20.10 End of proof % 136.03/20.10 % 136.03/20.10 Sub-proof #229 shows that the following formulas are inconsistent: % 136.03/20.10 ---------------------------------------------------------------- % 136.03/20.10 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 136.03/20.10 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 136.03/20.10 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.03/20.10 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.03/20.10 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.03/20.10 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.03/20.10 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 136.03/20.10 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.03/20.10 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.03/20.10 $i(all_56_21) & $i(all_56_29)) % 136.03/20.10 (2) ~ (e2 = e0) % 136.03/20.10 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.10 (4) op(e3, e3) = e0 % 136.03/20.10 (5) ~ (e1 = e0) % 136.03/20.10 % 136.03/20.10 Begin of proof % 136.03/20.10 | % 136.03/20.10 | BETA: splitting (1) gives: % 136.03/20.10 | % 136.03/20.10 | Case 1: % 136.03/20.10 | | % 136.03/20.10 | | (6) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.03/20.10 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.03/20.10 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.03/20.10 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.03/20.10 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.03/20.10 | | % 136.03/20.10 | | ALPHA: (6) implies: % 136.03/20.10 | | (7) op(e3, e3) = e2 % 136.03/20.10 | | % 136.03/20.10 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #495. % 136.03/20.10 | | % 136.03/20.10 | Case 2: % 136.03/20.10 | | % 136.03/20.10 | | (8) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.03/20.10 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 136.03/20.10 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.03/20.10 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.03/20.10 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.03/20.10 | | % 136.03/20.10 | | ALPHA: (8) implies: % 136.03/20.10 | | (9) op(e3, e3) = e1 % 136.03/20.10 | | % 136.03/20.10 | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #717. % 136.03/20.10 | | % 136.03/20.10 | End of split % 136.03/20.10 | % 136.03/20.10 End of proof % 136.03/20.10 % 136.03/20.10 Sub-proof #230 shows that the following formulas are inconsistent: % 136.03/20.10 ---------------------------------------------------------------- % 136.03/20.10 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 136.03/20.10 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 136.03/20.10 (2) op(e1, e1) = all_6_2 % 136.03/20.10 (3) all_57_5 = e2 % 136.03/20.11 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.11 (5) ~ (e2 = e1) % 136.03/20.11 (6) all_57_14 = e0 % 136.03/20.11 (7) op(e1, e1) = e3 % 136.03/20.11 (8) all_57_4 = e0 % 136.03/20.11 (9) ~ (e3 = e1) % 136.03/20.11 (10) ~ (e1 = e0) % 136.03/20.11 % 136.03/20.11 Begin of proof % 136.03/20.11 | % 136.03/20.11 | BETA: splitting (1) gives: % 136.03/20.11 | % 136.03/20.11 | Case 1: % 136.03/20.11 | | % 136.03/20.11 | | (11) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = % 136.03/20.11 | | e1) % 136.03/20.11 | | % 136.03/20.11 | | BETA: splitting (11) gives: % 136.03/20.11 | | % 136.03/20.11 | | Case 1: % 136.03/20.11 | | | % 136.03/20.11 | | | (12) all_57_4 = e1 & op(e3, e1) = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | REF_CLOSE: (8), (10), (12) are inconsistent by sub-proof #419. % 136.03/20.11 | | | % 136.03/20.11 | | Case 2: % 136.03/20.11 | | | % 136.03/20.11 | | | (13) all_57_5 = e1 & op(e2, e1) = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | REF_CLOSE: (3), (5), (13) are inconsistent by sub-proof #500. % 136.03/20.11 | | | % 136.03/20.11 | | End of split % 136.03/20.11 | | % 136.03/20.11 | Case 2: % 136.03/20.11 | | % 136.03/20.11 | | (14) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = % 136.03/20.11 | | e1) % 136.03/20.11 | | % 136.03/20.11 | | BETA: splitting (14) gives: % 136.03/20.11 | | % 136.03/20.11 | | Case 1: % 136.03/20.11 | | | % 136.03/20.11 | | | (15) all_57_8 = e1 & op(e1, e1) = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | ALPHA: (15) implies: % 136.03/20.11 | | | (16) op(e1, e1) = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | REF_CLOSE: (2), (4), (7), (9), (16) are inconsistent by sub-proof #662. % 136.03/20.11 | | | % 136.03/20.11 | | Case 2: % 136.03/20.11 | | | % 136.03/20.11 | | | (17) all_57_14 = e1 & op(e0, e1) = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | REF_CLOSE: (6), (10), (17) are inconsistent by sub-proof #231. % 136.03/20.11 | | | % 136.03/20.11 | | End of split % 136.03/20.11 | | % 136.03/20.11 | End of split % 136.03/20.11 | % 136.03/20.11 End of proof % 136.03/20.11 % 136.03/20.11 Sub-proof #231 shows that the following formulas are inconsistent: % 136.03/20.11 ---------------------------------------------------------------- % 136.03/20.11 (1) all_57_14 = e1 & op(e0, e1) = e1 % 136.03/20.11 (2) all_57_14 = e0 % 136.03/20.11 (3) ~ (e1 = e0) % 136.03/20.11 % 136.03/20.11 Begin of proof % 136.03/20.11 | % 136.03/20.11 | ALPHA: (1) implies: % 136.03/20.11 | (4) all_57_14 = e1 % 136.03/20.11 | % 136.03/20.11 | COMBINE_EQS: (2), (4) imply: % 136.03/20.11 | (5) e1 = e0 % 136.03/20.11 | % 136.03/20.11 | REDUCE: (3), (5) imply: % 136.03/20.11 | (6) $false % 136.03/20.11 | % 136.03/20.11 | CLOSE: (6) is inconsistent. % 136.03/20.11 | % 136.03/20.11 End of proof % 136.03/20.11 % 136.03/20.11 Sub-proof #232 shows that the following formulas are inconsistent: % 136.03/20.11 ---------------------------------------------------------------- % 136.03/20.11 (1) ~ (all_52_11 = e1) % 136.03/20.11 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.11 (3) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 136.03/20.11 (4) ~ (all_4_2 = e2) % 136.03/20.11 (5) ~ (all_52_11 = all_4_2) % 136.03/20.11 (6) op(e0, e1) = all_52_11 % 136.03/20.11 (7) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 136.03/20.11 (8) ~ (all_52_11 = e3) % 136.03/20.11 (9) ~ (all_4_2 = e1) % 136.03/20.11 (10) all_54_15 = all_4_2 % 136.03/20.11 (11) op(e0, e1) = e0 % 136.03/20.11 (12) all_54_14 = all_52_11 % 136.03/20.11 % 136.03/20.11 Begin of proof % 136.03/20.11 | % 136.03/20.11 | BETA: splitting (3) gives: % 136.03/20.11 | % 136.03/20.11 | Case 1: % 136.03/20.11 | | % 136.03/20.11 | | (13) all_54_15 = e2 % 136.03/20.11 | | % 136.03/20.11 | | REF_CLOSE: (4), (10), (13) are inconsistent by sub-proof #748. % 136.03/20.11 | | % 136.03/20.11 | Case 2: % 136.03/20.11 | | % 136.03/20.11 | | (14) all_54_15 = e1 | all_54_15 = e0 % 136.03/20.11 | | % 136.03/20.11 | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (14) are % 136.03/20.11 | | inconsistent by sub-proof #233. % 136.03/20.11 | | % 136.03/20.11 | End of split % 136.03/20.11 | % 136.03/20.11 End of proof % 136.03/20.11 % 136.03/20.11 Sub-proof #233 shows that the following formulas are inconsistent: % 136.03/20.11 ---------------------------------------------------------------- % 136.03/20.11 (1) ~ (all_52_11 = e1) % 136.03/20.11 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.11 (3) ~ (all_52_11 = all_4_2) % 136.03/20.11 (4) op(e0, e1) = all_52_11 % 136.03/20.11 (5) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 136.03/20.11 (6) ~ (all_52_11 = e3) % 136.03/20.11 (7) ~ (all_4_2 = e1) % 136.03/20.11 (8) all_54_15 = all_4_2 % 136.03/20.11 (9) all_54_15 = e1 | all_54_15 = e0 % 136.03/20.11 (10) op(e0, e1) = e0 % 136.03/20.11 (11) all_54_14 = all_52_11 % 136.03/20.11 % 136.03/20.11 Begin of proof % 136.03/20.11 | % 136.03/20.11 | BETA: splitting (9) gives: % 136.03/20.11 | % 136.03/20.11 | Case 1: % 136.03/20.11 | | % 136.03/20.11 | | (12) all_54_15 = e1 % 136.03/20.11 | | % 136.03/20.11 | | REF_CLOSE: (7), (8), (12) are inconsistent by sub-proof #747. % 136.03/20.11 | | % 136.03/20.11 | Case 2: % 136.03/20.11 | | % 136.03/20.11 | | (13) all_54_15 = e0 % 136.03/20.11 | | % 136.03/20.11 | | COMBINE_EQS: (8), (13) imply: % 136.03/20.11 | | (14) all_4_2 = e0 % 136.03/20.11 | | % 136.03/20.11 | | SIMP: (14) implies: % 136.03/20.11 | | (15) all_4_2 = e0 % 136.03/20.11 | | % 136.03/20.11 | | REDUCE: (3), (15) imply: % 136.03/20.11 | | (16) ~ (all_52_11 = e0) % 136.03/20.11 | | % 136.03/20.11 | | BETA: splitting (5) gives: % 136.03/20.11 | | % 136.03/20.11 | | Case 1: % 136.03/20.11 | | | % 136.03/20.11 | | | (17) all_54_14 = e3 % 136.03/20.11 | | | % 136.03/20.11 | | | REF_CLOSE: (6), (11), (17) are inconsistent by sub-proof #760. % 136.03/20.11 | | | % 136.03/20.11 | | Case 2: % 136.03/20.11 | | | % 136.03/20.11 | | | (18) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 136.03/20.11 | | | % 136.03/20.11 | | | REF_CLOSE: (1), (2), (4), (10), (11), (16), (18) are inconsistent by % 136.03/20.11 | | | sub-proof #351. % 136.03/20.11 | | | % 136.03/20.11 | | End of split % 136.03/20.11 | | % 136.03/20.11 | End of split % 136.03/20.11 | % 136.03/20.11 End of proof % 136.03/20.11 % 136.03/20.11 Sub-proof #234 shows that the following formulas are inconsistent: % 136.03/20.11 ---------------------------------------------------------------- % 136.03/20.11 (1) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 136.03/20.11 (2) op(e3, e3) = e2 % 136.03/20.11 (3) ~ (all_52_4 = all_36_0) % 136.03/20.11 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.11 (5) ~ (e2 = e1) % 136.03/20.11 (6) all_57_9 = e3 % 136.03/20.11 (7) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 136.03/20.11 (8) ~ (all_36_0 = e2) % 136.03/20.11 (9) ~ (all_52_4 = e3) % 136.03/20.11 (10) all_54_2 = all_36_0 % 136.03/20.11 (11) ~ (all_52_4 = e2) % 136.03/20.11 (12) all_54_1 = all_52_4 % 136.03/20.11 (13) op(e3, e2) = all_52_4 % 136.03/20.11 (14) ~ (all_36_0 = e0) % 136.03/20.11 (15) all_57_4 = e0 % 136.03/20.11 (16) ~ (e3 = e1) % 136.03/20.11 (17) ~ (e1 = e0) % 136.03/20.11 (18) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 136.03/20.11 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 136.03/20.11 % 136.03/20.11 Begin of proof % 136.03/20.11 | % 136.03/20.11 | BETA: splitting (18) gives: % 136.03/20.11 | % 136.03/20.11 | Case 1: % 136.03/20.11 | | % 136.03/20.11 | | (19) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = % 136.03/20.11 | | e1) % 136.03/20.11 | | % 136.03/20.11 | | BETA: splitting (19) gives: % 136.03/20.11 | | % 136.03/20.11 | | Case 1: % 136.03/20.11 | | | % 136.03/20.11 | | | (20) all_57_0 = e1 & op(e3, e3) = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | ALPHA: (20) implies: % 136.03/20.11 | | | (21) op(e3, e3) = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | REF_CLOSE: (2), (4), (5), (21) are inconsistent by sub-proof #743. % 136.03/20.11 | | | % 136.03/20.11 | | Case 2: % 136.03/20.11 | | | % 136.03/20.11 | | | (22) all_57_1 = e1 & op(e3, e2) = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | ALPHA: (22) implies: % 136.03/20.11 | | | (23) op(e3, e2) = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14), % 136.03/20.11 | | | (23) are inconsistent by sub-proof #235. % 136.03/20.11 | | | % 136.03/20.11 | | End of split % 136.03/20.11 | | % 136.03/20.11 | Case 2: % 136.03/20.11 | | % 136.03/20.11 | | (24) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = % 136.03/20.11 | | e1) % 136.03/20.11 | | % 136.03/20.11 | | BETA: splitting (24) gives: % 136.03/20.11 | | % 136.03/20.11 | | Case 1: % 136.03/20.11 | | | % 136.03/20.11 | | | (25) all_57_4 = e1 & op(e3, e1) = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | ALPHA: (25) implies: % 136.03/20.11 | | | (26) all_57_4 = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | COMBINE_EQS: (15), (26) imply: % 136.03/20.11 | | | (27) e1 = e0 % 136.03/20.11 | | | % 136.03/20.11 | | | REDUCE: (17), (27) imply: % 136.03/20.11 | | | (28) $false % 136.03/20.11 | | | % 136.03/20.11 | | | CLOSE: (28) is inconsistent. % 136.03/20.11 | | | % 136.03/20.11 | | Case 2: % 136.03/20.11 | | | % 136.03/20.11 | | | (29) all_57_9 = e1 & op(e3, e0) = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | ALPHA: (29) implies: % 136.03/20.11 | | | (30) all_57_9 = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | REF_CLOSE: (6), (16), (30) are inconsistent by sub-proof #690. % 136.03/20.11 | | | % 136.03/20.11 | | End of split % 136.03/20.11 | | % 136.03/20.11 | End of split % 136.03/20.11 | % 136.03/20.11 End of proof % 136.03/20.11 % 136.03/20.11 Sub-proof #235 shows that the following formulas are inconsistent: % 136.03/20.11 ---------------------------------------------------------------- % 136.03/20.11 (1) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 136.03/20.11 (2) op(e3, e2) = e1 % 136.03/20.11 (3) ~ (all_52_4 = all_36_0) % 136.03/20.11 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.11 (5) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 136.03/20.11 (6) ~ (all_36_0 = e2) % 136.03/20.11 (7) ~ (all_52_4 = e3) % 136.03/20.11 (8) all_54_2 = all_36_0 % 136.03/20.11 (9) ~ (all_52_4 = e2) % 136.03/20.11 (10) all_54_1 = all_52_4 % 136.03/20.11 (11) op(e3, e2) = all_52_4 % 136.03/20.11 (12) ~ (all_36_0 = e0) % 136.03/20.11 % 136.03/20.11 Begin of proof % 136.03/20.11 | % 136.03/20.11 | BETA: splitting (5) gives: % 136.03/20.11 | % 136.03/20.11 | Case 1: % 136.03/20.11 | | % 136.03/20.11 | | (13) all_54_2 = e2 % 136.03/20.11 | | % 136.03/20.11 | | REF_CLOSE: (6), (8), (13) are inconsistent by sub-proof #244. % 136.03/20.11 | | % 136.03/20.11 | Case 2: % 136.03/20.11 | | % 136.03/20.11 | | (14) all_54_2 = e1 | all_54_2 = e0 % 136.03/20.11 | | % 136.03/20.11 | | BETA: splitting (14) gives: % 136.03/20.11 | | % 136.03/20.11 | | Case 1: % 136.03/20.11 | | | % 136.03/20.11 | | | (15) all_54_2 = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | COMBINE_EQS: (8), (15) imply: % 136.03/20.11 | | | (16) all_36_0 = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | SIMP: (16) implies: % 136.03/20.11 | | | (17) all_36_0 = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | REDUCE: (3), (17) imply: % 136.03/20.11 | | | (18) ~ (all_52_4 = e1) % 136.03/20.11 | | | % 136.03/20.11 | | | BETA: splitting (1) gives: % 136.03/20.11 | | | % 136.03/20.11 | | | Case 1: % 136.03/20.11 | | | | % 136.03/20.11 | | | | (19) all_54_1 = e3 % 136.03/20.11 | | | | % 136.03/20.11 | | | | COMBINE_EQS: (10), (19) imply: % 136.03/20.11 | | | | (20) all_52_4 = e3 % 136.03/20.11 | | | | % 136.03/20.11 | | | | REDUCE: (7), (20) imply: % 136.03/20.11 | | | | (21) $false % 136.03/20.11 | | | | % 136.03/20.11 | | | | CLOSE: (21) is inconsistent. % 136.03/20.11 | | | | % 136.03/20.11 | | | Case 2: % 136.03/20.11 | | | | % 136.03/20.11 | | | | (22) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0 % 136.03/20.11 | | | | % 136.03/20.11 | | | | BETA: splitting (22) gives: % 136.03/20.11 | | | | % 136.03/20.11 | | | | Case 1: % 136.03/20.11 | | | | | % 136.03/20.11 | | | | | (23) all_54_1 = e2 % 136.03/20.11 | | | | | % 136.03/20.11 | | | | | REF_CLOSE: (9), (10), (23) are inconsistent by sub-proof #739. % 136.03/20.11 | | | | | % 136.03/20.11 | | | | Case 2: % 136.03/20.11 | | | | | % 136.03/20.11 | | | | | (24) all_54_1 = e1 | all_54_1 = e0 % 136.03/20.11 | | | | | % 136.03/20.11 | | | | | REF_CLOSE: (2), (4), (10), (11), (18), (24) are inconsistent by % 136.03/20.11 | | | | | sub-proof #729. % 136.03/20.11 | | | | | % 136.03/20.11 | | | | End of split % 136.03/20.11 | | | | % 136.03/20.11 | | | End of split % 136.03/20.11 | | | % 136.03/20.11 | | Case 2: % 136.03/20.11 | | | % 136.03/20.11 | | | (25) all_54_2 = e0 % 136.03/20.11 | | | % 136.03/20.11 | | | REF_CLOSE: (8), (12), (25) are inconsistent by sub-proof #242. % 136.03/20.11 | | | % 136.03/20.11 | | End of split % 136.03/20.11 | | % 136.03/20.11 | End of split % 136.03/20.11 | % 136.03/20.11 End of proof % 136.03/20.11 % 136.03/20.11 Sub-proof #236 shows that the following formulas are inconsistent: % 136.03/20.11 ---------------------------------------------------------------- % 136.03/20.11 (1) op(e3, e3) = e2 % 136.03/20.11 (2) ~ (e2 = e0) % 136.03/20.11 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.03/20.11 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.03/20.11 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.11 (5) ~ (e2 = e1) % 136.03/20.11 (6) ~ (e3 = e0) % 136.03/20.11 (7) all_57_9 = e3 % 136.03/20.11 (8) ~ (e3 = e2) % 136.03/20.11 (9) ~ (all_52_4 = e3) % 136.03/20.11 (10) all_57_3 = e2 & op(e2, e2) = e2 % 136.03/20.11 (11) op(e3, e2) = all_52_4 % 136.03/20.11 (12) all_57_3 = e3 % 136.03/20.11 (13) ~ (e3 = e1) % 136.03/20.11 (14) ~ (e1 = e0) % 136.03/20.11 (15) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.03/20.11 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.03/20.11 (16) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 136.03/20.11 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 136.03/20.11 % 136.03/20.11 Begin of proof % 136.03/20.11 | % 136.03/20.11 | ALPHA: (10) implies: % 136.03/20.11 | (17) all_57_3 = e2 % 136.03/20.11 | % 136.03/20.11 | COMBINE_EQS: (12), (17) imply: % 136.03/20.11 | (18) e3 = e2 % 136.03/20.11 | % 136.03/20.11 | SIMP: (18) implies: % 136.03/20.11 | (19) e3 = e2 % 136.03/20.11 | % 136.03/20.11 | COMBINE_EQS: (7), (19) imply: % 136.03/20.11 | (20) all_57_9 = e2 % 136.03/20.11 | % 136.03/20.11 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (13), (14), (15), % 136.03/20.11 | (16), (20) are inconsistent by sub-proof #250. % 136.03/20.11 | % 136.03/20.11 End of proof % 136.03/20.11 % 136.03/20.11 Sub-proof #237 shows that the following formulas are inconsistent: % 136.03/20.11 ---------------------------------------------------------------- % 136.03/20.11 (1) op(e3, e3) = e2 % 136.03/20.11 (2) ~ (e2 = e0) % 136.03/20.11 (3) all_57_1 = e2 % 136.03/20.11 (4) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.03/20.11 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.03/20.11 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.11 (6) ~ (e2 = e1) % 136.03/20.11 (7) ~ (e3 = e0) % 136.03/20.11 (8) all_57_9 = e3 % 136.03/20.11 (9) ~ (e3 = e2) % 136.03/20.11 (10) ~ (all_52_4 = e3) % 136.03/20.11 (11) op(e3, e2) = all_52_4 % 136.03/20.11 (12) ~ (e3 = e1) % 136.03/20.11 (13) ~ (e1 = e0) % 136.03/20.11 (14) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.03/20.11 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.03/20.11 (15) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 136.03/20.11 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 136.03/20.11 % 136.03/20.11 Begin of proof % 136.03/20.11 | % 136.03/20.11 | BETA: splitting (4) gives: % 136.03/20.11 | % 136.03/20.11 | Case 1: % 136.03/20.11 | | % 136.03/20.11 | | (16) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = % 136.03/20.11 | | e0) % 136.03/20.11 | | % 136.03/20.11 | | REF_CLOSE: (1), (2), (3), (5), (16) are inconsistent by sub-proof #240. % 136.03/20.11 | | % 136.03/20.11 | Case 2: % 136.03/20.11 | | % 136.03/20.11 | | (17) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = % 136.03/20.11 | | e0) % 136.03/20.11 | | % 136.03/20.11 | | BETA: splitting (17) gives: % 136.03/20.11 | | % 136.03/20.11 | | Case 1: % 136.03/20.11 | | | % 136.03/20.11 | | | (18) all_57_4 = e0 & op(e3, e1) = e0 % 136.03/20.11 | | | % 136.03/20.11 | | | ALPHA: (18) implies: % 136.03/20.11 | | | (19) all_57_4 = e0 % 136.03/20.11 | | | % 136.03/20.11 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), % 136.03/20.11 | | | (14), (15), (19) are inconsistent by sub-proof #238. % 136.03/20.11 | | | % 136.03/20.11 | | Case 2: % 136.03/20.11 | | | % 136.03/20.11 | | | (20) all_57_9 = e0 & op(e3, e0) = e0 % 136.03/20.11 | | | % 136.03/20.11 | | | REF_CLOSE: (7), (8), (20) are inconsistent by sub-proof #299. % 136.03/20.11 | | | % 136.03/20.11 | | End of split % 136.03/20.11 | | % 136.03/20.11 | End of split % 136.03/20.11 | % 136.03/20.11 End of proof % 136.03/20.11 % 136.03/20.11 Sub-proof #238 shows that the following formulas are inconsistent: % 136.03/20.11 ---------------------------------------------------------------- % 136.03/20.11 (1) op(e3, e3) = e2 % 136.03/20.11 (2) ~ (e2 = e0) % 136.03/20.11 (3) all_57_1 = e2 % 136.03/20.11 (4) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.03/20.11 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.03/20.11 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.11 (6) ~ (e2 = e1) % 136.03/20.11 (7) ~ (e3 = e0) % 136.03/20.11 (8) ~ (e3 = e2) % 136.03/20.11 (9) ~ (all_52_4 = e3) % 136.03/20.11 (10) op(e3, e2) = all_52_4 % 136.03/20.11 (11) all_57_4 = e0 % 136.03/20.11 (12) ~ (e3 = e1) % 136.03/20.11 (13) ~ (e1 = e0) % 136.03/20.11 (14) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.03/20.11 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.03/20.11 (15) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 136.03/20.11 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 136.03/20.11 % 136.03/20.11 Begin of proof % 136.03/20.11 | % 136.03/20.11 | BETA: splitting (15) gives: % 136.03/20.11 | % 136.03/20.11 | Case 1: % 136.03/20.11 | | % 136.03/20.11 | | (16) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = % 136.03/20.11 | | e1) % 136.03/20.11 | | % 136.03/20.11 | | REF_CLOSE: (1), (3), (5), (6), (16) are inconsistent by sub-proof #239. % 136.03/20.11 | | % 136.03/20.11 | Case 2: % 136.03/20.11 | | % 136.03/20.11 | | (17) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = % 136.03/20.11 | | e1) % 136.03/20.11 | | % 136.03/20.11 | | BETA: splitting (17) gives: % 136.03/20.11 | | % 136.03/20.11 | | Case 1: % 136.03/20.11 | | | % 136.03/20.11 | | | (18) all_57_4 = e1 & op(e3, e1) = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | REF_CLOSE: (11), (13), (18) are inconsistent by sub-proof #419. % 136.03/20.11 | | | % 136.03/20.11 | | Case 2: % 136.03/20.11 | | | % 136.03/20.11 | | | (19) all_57_9 = e1 & op(e3, e0) = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | ALPHA: (19) implies: % 136.03/20.11 | | | (20) all_57_9 = e1 % 136.03/20.11 | | | % 136.03/20.11 | | | BETA: splitting (14) gives: % 136.03/20.11 | | | % 136.03/20.11 | | | Case 1: % 136.03/20.11 | | | | % 136.03/20.11 | | | | (21) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) % 136.03/20.11 | | | | = e3) % 136.03/20.11 | | | | % 136.03/20.11 | | | | REF_CLOSE: (1), (5), (8), (9), (10), (21) are inconsistent by sub-proof % 136.03/20.11 | | | | #282. % 136.03/20.11 | | | | % 136.03/20.11 | | | Case 2: % 136.03/20.11 | | | | % 136.03/20.11 | | | | (22) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) % 136.03/20.11 | | | | = e3) % 136.03/20.11 | | | | % 136.03/20.11 | | | | BETA: splitting (22) gives: % 136.03/20.11 | | | | % 136.03/20.11 | | | | Case 1: % 136.03/20.11 | | | | | % 136.03/20.11 | | | | | (23) all_57_4 = e3 & op(e3, e1) = e3 % 136.03/20.11 | | | | | % 136.03/20.11 | | | | | ALPHA: (23) implies: % 136.03/20.11 | | | | | (24) all_57_4 = e3 % 136.03/20.11 | | | | | % 136.03/20.11 | | | | | BETA: splitting (4) gives: % 136.03/20.11 | | | | | % 136.03/20.11 | | | | | Case 1: % 136.03/20.11 | | | | | | % 136.03/20.11 | | | | | | (25) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, % 136.03/20.11 | | | | | | e2) = e0) % 136.03/20.11 | | | | | | % 136.03/20.11 | | | | | | REF_CLOSE: (1), (2), (3), (5), (25) are inconsistent by sub-proof % 136.03/20.11 | | | | | | #240. % 136.03/20.11 | | | | | | % 136.03/20.11 | | | | | Case 2: % 136.03/20.11 | | | | | | % 136.03/20.11 | | | | | | (26) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, % 136.03/20.11 | | | | | | e0) = e0) % 136.03/20.11 | | | | | | % 136.03/20.11 | | | | | | BETA: splitting (26) gives: % 136.03/20.11 | | | | | | % 136.03/20.11 | | | | | | Case 1: % 136.03/20.11 | | | | | | | % 136.03/20.11 | | | | | | | (27) all_57_4 = e0 & op(e3, e1) = e0 % 136.03/20.11 | | | | | | | % 136.03/20.11 | | | | | | | REF_CLOSE: (7), (24), (27) are inconsistent by sub-proof #384. % 136.03/20.11 | | | | | | | % 136.03/20.11 | | | | | | Case 2: % 136.03/20.11 | | | | | | | % 136.03/20.11 | | | | | | | (28) all_57_9 = e0 & op(e3, e0) = e0 % 136.03/20.11 | | | | | | | % 136.03/20.11 | | | | | | | REF_CLOSE: (13), (20), (28) are inconsistent by sub-proof #687. % 136.03/20.11 | | | | | | | % 136.03/20.11 | | | | | | End of split % 136.03/20.11 | | | | | | % 136.03/20.11 | | | | | End of split % 136.03/20.11 | | | | | % 136.03/20.11 | | | | Case 2: % 136.03/20.11 | | | | | % 136.03/20.11 | | | | | (29) all_57_9 = e3 & op(e3, e0) = e3 % 136.03/20.11 | | | | | % 136.03/20.11 | | | | | ALPHA: (29) implies: % 136.03/20.11 | | | | | (30) all_57_9 = e3 % 136.03/20.11 | | | | | % 136.03/20.11 | | | | | REF_CLOSE: (12), (20), (30) are inconsistent by sub-proof #690. % 136.03/20.11 | | | | | % 136.03/20.11 | | | | End of split % 136.03/20.11 | | | | % 136.03/20.11 | | | End of split % 136.03/20.11 | | | % 136.03/20.11 | | End of split % 136.03/20.11 | | % 136.03/20.11 | End of split % 136.03/20.11 | % 136.03/20.11 End of proof % 136.03/20.11 % 136.03/20.11 Sub-proof #239 shows that the following formulas are inconsistent: % 136.03/20.11 ---------------------------------------------------------------- % 136.03/20.11 (1) op(e3, e3) = e2 % 136.03/20.11 (2) all_57_1 = e2 % 136.03/20.11 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.11 (4) ~ (e2 = e1) % 136.03/20.11 (5) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) % 136.03/20.11 % 136.03/20.11 Begin of proof % 136.03/20.11 | % 136.03/20.11 | BETA: splitting (5) gives: % 136.03/20.11 | % 136.03/20.11 | Case 1: % 136.03/20.11 | | % 136.03/20.11 | | (6) all_57_0 = e1 & op(e3, e3) = e1 % 136.03/20.11 | | % 136.03/20.11 | | ALPHA: (6) implies: % 136.03/20.11 | | (7) op(e3, e3) = e1 % 136.03/20.11 | | % 136.03/20.11 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #743. % 136.03/20.11 | | % 136.03/20.11 | Case 2: % 136.03/20.11 | | % 136.03/20.11 | | (8) all_57_1 = e1 & op(e3, e2) = e1 % 136.03/20.11 | | % 136.03/20.11 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #465. % 136.03/20.11 | | % 136.03/20.11 | End of split % 136.03/20.11 | % 136.03/20.11 End of proof % 136.03/20.11 % 136.03/20.11 Sub-proof #240 shows that the following formulas are inconsistent: % 136.03/20.11 ---------------------------------------------------------------- % 136.03/20.11 (1) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) % 136.03/20.11 (2) op(e3, e3) = e2 % 136.03/20.11 (3) ~ (e2 = e0) % 136.03/20.11 (4) all_57_1 = e2 % 136.03/20.11 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.11 % 136.03/20.11 Begin of proof % 136.03/20.11 | % 136.03/20.11 | BETA: splitting (1) gives: % 136.03/20.11 | % 136.03/20.11 | Case 1: % 136.03/20.11 | | % 136.03/20.11 | | (6) all_57_0 = e0 & op(e3, e3) = e0 % 136.03/20.11 | | % 136.03/20.11 | | ALPHA: (6) implies: % 136.03/20.11 | | (7) op(e3, e3) = e0 % 136.03/20.11 | | % 136.03/20.11 | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #495. % 136.03/20.11 | | % 136.03/20.11 | Case 2: % 136.03/20.11 | | % 136.03/20.11 | | (8) all_57_1 = e0 & op(e3, e2) = e0 % 136.03/20.11 | | % 136.03/20.11 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #466. % 136.03/20.11 | | % 136.03/20.11 | End of split % 136.03/20.11 | % 136.03/20.11 End of proof % 136.03/20.11 % 136.03/20.11 Sub-proof #241 shows that the following formulas are inconsistent: % 136.03/20.11 ---------------------------------------------------------------- % 136.03/20.11 (1) op(e3, e3) = e2 % 136.03/20.11 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.11 (3) ~ (e2 = e1) % 136.03/20.11 (4) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) % 136.03/20.11 (5) op(e3, e2) = e0 % 136.03/20.11 (6) ~ (e1 = e0) % 136.03/20.11 % 136.03/20.11 Begin of proof % 136.03/20.11 | % 136.03/20.11 | BETA: splitting (4) gives: % 136.03/20.11 | % 136.03/20.11 | Case 1: % 136.03/20.11 | | % 136.03/20.11 | | (7) all_57_0 = e1 & op(e3, e3) = e1 % 136.03/20.11 | | % 136.03/20.11 | | ALPHA: (7) implies: % 136.03/20.11 | | (8) op(e3, e3) = e1 % 136.03/20.11 | | % 136.03/20.11 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #743. % 136.03/20.11 | | % 136.03/20.11 | Case 2: % 136.03/20.11 | | % 136.03/20.11 | | (9) all_57_1 = e1 & op(e3, e2) = e1 % 136.03/20.11 | | % 136.03/20.11 | | ALPHA: (9) implies: % 136.03/20.11 | | (10) op(e3, e2) = e1 % 136.03/20.11 | | % 136.03/20.11 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #730. % 136.03/20.11 | | % 136.03/20.11 | End of split % 136.03/20.11 | % 136.03/20.11 End of proof % 136.03/20.11 % 136.03/20.11 Sub-proof #242 shows that the following formulas are inconsistent: % 136.03/20.11 ---------------------------------------------------------------- % 136.03/20.11 (1) all_54_2 = all_36_0 % 136.03/20.11 (2) all_54_2 = e0 % 136.03/20.11 (3) ~ (all_36_0 = e0) % 136.03/20.11 % 136.03/20.11 Begin of proof % 136.03/20.11 | % 136.03/20.11 | COMBINE_EQS: (1), (2) imply: % 136.03/20.11 | (4) all_36_0 = e0 % 136.03/20.11 | % 136.03/20.11 | SIMP: (4) implies: % 136.03/20.11 | (5) all_36_0 = e0 % 136.03/20.11 | % 136.03/20.11 | REDUCE: (3), (5) imply: % 136.03/20.11 | (6) $false % 136.03/20.11 | % 136.03/20.11 | CLOSE: (6) is inconsistent. % 136.03/20.11 | % 136.03/20.11 End of proof % 136.03/20.11 % 136.03/20.11 Sub-proof #243 shows that the following formulas are inconsistent: % 136.03/20.11 ---------------------------------------------------------------- % 136.03/20.11 (1) ~ (all_52_1 = all_52_2) % 136.03/20.11 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.11 (3) ~ (all_52_1 = e0) % 136.03/20.11 (4) all_54_4 = e1 | all_54_4 = e0 % 136.03/20.11 (5) op(e1, e3) = e1 % 136.03/20.11 (6) op(e1, e3) = all_52_2 % 136.03/20.11 (7) all_54_4 = all_52_1 % 136.03/20.11 % 136.03/20.11 Begin of proof % 136.03/20.11 | % 136.03/20.11 | BETA: splitting (4) gives: % 136.03/20.11 | % 136.03/20.11 | Case 1: % 136.03/20.11 | | % 136.03/20.11 | | (8) all_54_4 = e1 % 136.03/20.11 | | % 136.03/20.11 | | COMBINE_EQS: (7), (8) imply: % 136.03/20.11 | | (9) all_52_1 = e1 % 136.03/20.11 | | % 136.03/20.11 | | REDUCE: (1), (9) imply: % 136.03/20.11 | | (10) ~ (all_52_2 = e1) % 136.03/20.11 | | % 136.03/20.11 | | SIMP: (10) implies: % 136.03/20.11 | | (11) ~ (all_52_2 = e1) % 136.03/20.11 | | % 136.03/20.11 | | REF_CLOSE: (2), (5), (6), (11) are inconsistent by sub-proof #725. % 136.03/20.11 | | % 136.03/20.11 | Case 2: % 136.03/20.11 | | % 136.03/20.11 | | (12) all_54_4 = e0 % 136.03/20.11 | | % 136.03/20.11 | | COMBINE_EQS: (7), (12) imply: % 136.03/20.11 | | (13) all_52_1 = e0 % 136.03/20.11 | | % 136.03/20.11 | | REDUCE: (3), (13) imply: % 136.03/20.11 | | (14) $false % 136.03/20.11 | | % 136.03/20.11 | | CLOSE: (14) is inconsistent. % 136.03/20.11 | | % 136.03/20.11 | End of split % 136.03/20.11 | % 136.03/20.11 End of proof % 136.03/20.11 % 136.03/20.11 Sub-proof #244 shows that the following formulas are inconsistent: % 136.03/20.11 ---------------------------------------------------------------- % 136.03/20.11 (1) all_54_2 = all_36_0 % 136.03/20.11 (2) all_54_2 = e2 % 136.03/20.11 (3) ~ (all_36_0 = e2) % 136.03/20.11 % 136.03/20.11 Begin of proof % 136.03/20.11 | % 136.03/20.11 | COMBINE_EQS: (1), (2) imply: % 136.03/20.11 | (4) all_36_0 = e2 % 136.03/20.11 | % 136.03/20.11 | SIMP: (4) implies: % 136.03/20.11 | (5) all_36_0 = e2 % 136.03/20.11 | % 136.03/20.11 | REDUCE: (3), (5) imply: % 136.03/20.11 | (6) $false % 136.03/20.11 | % 136.03/20.11 | CLOSE: (6) is inconsistent. % 136.03/20.11 | % 136.03/20.11 End of proof % 136.03/20.11 % 136.03/20.11 Sub-proof #245 shows that the following formulas are inconsistent: % 136.03/20.11 ---------------------------------------------------------------- % 136.03/20.11 (1) ~ (e2 = e1) % 136.03/20.11 (2) all_57_13 = e2 % 136.03/20.11 (3) all_57_12 = e3 % 136.03/20.11 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.03/20.11 (5) ~ (e3 = e1) % 136.03/20.11 % 136.03/20.11 Begin of proof % 136.03/20.11 | % 136.03/20.11 | BETA: splitting (4) gives: % 136.03/20.11 | % 136.03/20.11 | Case 1: % 136.03/20.11 | | % 136.03/20.11 | | (6) all_57_12 = e1 & op(e0, e3) = e1 % 136.03/20.11 | | % 136.03/20.11 | | ALPHA: (6) implies: % 136.03/20.11 | | (7) all_57_12 = e1 % 136.03/20.11 | | % 136.03/20.11 | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #591. % 136.03/20.11 | | % 136.03/20.11 | Case 2: % 136.03/20.11 | | % 136.03/20.11 | | (8) all_57_13 = e1 & op(e0, e2) = e1 % 136.03/20.11 | | % 136.03/20.11 | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #248. % 136.03/20.11 | | % 136.03/20.11 | End of split % 136.03/20.11 | % 136.03/20.11 End of proof % 136.03/20.11 % 136.03/20.11 Sub-proof #246 shows that the following formulas are inconsistent: % 136.03/20.11 ---------------------------------------------------------------- % 136.03/20.11 (1) op(e1, e1) = all_6_2 % 136.03/20.11 (2) op(e0, e0) = e3 % 136.03/20.11 (3) op(e3, e3) = e2 % 136.03/20.11 (4) ~ (e2 = e0) % 136.03/20.11 (5) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) | % 136.03/20.11 (all_57_14 = e0 & op(e0, e1) = e0) % 136.03/20.11 (6) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.03/20.11 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.03/20.11 (7) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 136.03/20.11 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.03/20.11 (8) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 136.03/20.11 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 136.03/20.11 (9) ~ (all_52_7 = e3) % 136.03/20.11 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.03/20.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.03/20.11 (11) ~ (e2 = e1) % 136.03/20.11 (12) ~ (e3 = e0) % 136.03/20.11 (13) all_57_9 = e3 % 136.03/20.11 (14) ~ (e3 = e2) % 136.03/20.11 (15) all_57_6 = e3 % 136.03/20.12 (16) op(e2, e2) = e3 % 136.03/20.12 (17) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.03/20.12 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.03/20.12 (18) op(e0, e2) = all_52_7 % 136.03/20.12 (19) ~ (all_52_4 = e3) % 136.03/20.12 (20) ~ (all_6_2 = e2) % 136.03/20.12 (21) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.03/20.12 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 136.03/20.12 e1) % 136.03/20.12 (22) all_57_13 = e2 % 136.03/20.12 (23) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) | % 136.03/20.12 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2) % 136.03/20.12 (24) op(e3, e2) = all_52_4 % 136.03/20.12 (25) all_57_14 = e3 % 136.03/20.12 (26) all_57_3 = e3 % 136.03/20.12 (27) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.03/20.12 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.03/20.12 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.03/20.12 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.03/20.12 (28) ~ (e3 = e1) % 136.03/20.12 (29) ~ (e1 = e0) % 136.03/20.12 (30) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.03/20.12 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.03/20.12 (31) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.03/20.12 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 136.03/20.12 (32) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.03/20.12 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.03/20.12 (33) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 136.03/20.12 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 136.03/20.12 (34) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | % 136.03/20.12 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 136.03/20.12 % 136.03/20.12 Begin of proof % 136.03/20.12 | % 136.03/20.12 | BETA: splitting (34) gives: % 136.03/20.12 | % 136.03/20.12 | Case 1: % 136.03/20.12 | | % 136.03/20.12 | | (35) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = % 136.03/20.12 | | e2) % 136.03/20.12 | | % 136.03/20.12 | | BETA: splitting (35) gives: % 136.03/20.12 | | % 136.03/20.12 | | Case 1: % 136.03/20.12 | | | % 136.03/20.12 | | | (36) all_57_4 = e2 & op(e3, e1) = e2 % 136.03/20.12 | | | % 136.03/20.12 | | | ALPHA: (36) implies: % 136.03/20.12 | | | (37) all_57_4 = e2 % 136.03/20.12 | | | % 136.03/20.12 | | | REF_CLOSE: (3), (4), (6), (10), (11), (12), (13), (28), (29), (33), (37) % 136.03/20.12 | | | are inconsistent by sub-proof #279. % 136.03/20.12 | | | % 136.03/20.12 | | Case 2: % 136.03/20.12 | | | % 136.03/20.12 | | | (38) all_57_5 = e2 & op(e2, e1) = e2 % 136.03/20.12 | | | % 136.03/20.12 | | | ALPHA: (38) implies: % 136.03/20.12 | | | (39) all_57_5 = e2 % 136.03/20.12 | | | % 136.03/20.12 | | | BETA: splitting (5) gives: % 136.03/20.12 | | | % 136.03/20.12 | | | Case 1: % 136.03/20.12 | | | | % 136.03/20.12 | | | | (40) all_57_12 = e0 & op(e0, e3) = e0 % 136.03/20.12 | | | | % 136.03/20.12 | | | | BETA: splitting (8) gives: % 136.03/20.12 | | | | % 136.03/20.12 | | | | Case 1: % 136.03/20.12 | | | | | % 136.03/20.12 | | | | | (41) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, % 136.03/20.12 | | | | | e3) = e1) % 136.03/20.12 | | | | | % 136.03/20.12 | | | | | BETA: splitting (41) gives: % 136.03/20.12 | | | | | % 136.03/20.12 | | | | | Case 1: % 136.03/20.12 | | | | | | % 136.03/20.12 | | | | | | (42) all_57_0 = e1 & op(e3, e3) = e1 % 136.03/20.12 | | | | | | % 136.03/20.12 | | | | | | ALPHA: (42) implies: % 136.03/20.12 | | | | | | (43) op(e3, e3) = e1 % 136.03/20.12 | | | | | | % 136.03/20.12 | | | | | | REF_CLOSE: (3), (10), (11), (43) are inconsistent by sub-proof #743. % 136.03/20.12 | | | | | | % 136.03/20.12 | | | | | Case 2: % 136.03/20.12 | | | | | | % 136.03/20.12 | | | | | | (44) all_57_2 = e1 & op(e2, e3) = e1 % 136.03/20.12 | | | | | | % 136.03/20.12 | | | | | | ALPHA: (44) implies: % 136.03/20.12 | | | | | | (45) all_57_2 = e1 % 136.03/20.12 | | | | | | % 136.03/20.12 | | | | | | BETA: splitting (21) gives: % 136.03/20.12 | | | | | | % 136.03/20.12 | | | | | | Case 1: % 136.03/20.12 | | | | | | | % 136.03/20.12 | | | | | | | (46) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & % 136.03/20.12 | | | | | | | op(e0, e2) = e1) % 136.03/20.12 | | | | | | | % 136.03/20.12 | | | | | | | BETA: splitting (46) gives: % 136.03/20.12 | | | | | | | % 136.03/20.12 | | | | | | | Case 1: % 136.03/20.12 | | | | | | | | % 136.03/20.12 | | | | | | | | (47) all_57_12 = e1 & op(e0, e3) = e1 % 136.03/20.12 | | | | | | | | % 136.03/20.12 | | | | | | | | ALPHA: (47) implies: % 136.03/20.12 | | | | | | | | (48) all_57_12 = e1 % 136.03/20.12 | | | | | | | | % 136.03/20.12 | | | | | | | | REF_CLOSE: (4), (5), (12), (22), (25), (29), (48) are % 136.03/20.12 | | | | | | | | inconsistent by sub-proof #399. % 136.03/20.12 | | | | | | | | % 136.03/20.12 | | | | | | | Case 2: % 136.03/20.12 | | | | | | | | % 136.03/20.12 | | | | | | | | (49) all_57_13 = e1 & op(e0, e2) = e1 % 136.03/20.12 | | | | | | | | % 136.03/20.12 | | | | | | | | REF_CLOSE: (11), (22), (49) are inconsistent by sub-proof #248. % 136.03/20.12 | | | | | | | | % 136.03/20.12 | | | | | | | End of split % 136.03/20.12 | | | | | | | % 136.03/20.12 | | | | | | Case 2: % 136.03/20.12 | | | | | | | % 136.03/20.12 | | | | | | | (50) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & % 136.03/20.12 | | | | | | | op(e0, e0) = e1) % 136.03/20.12 | | | | | | | % 136.03/20.12 | | | | | | | BETA: splitting (50) gives: % 136.03/20.12 | | | | | | | % 136.03/20.12 | | | | | | | Case 1: % 136.03/20.12 | | | | | | | | % 136.03/20.12 | | | | | | | | (51) all_57_14 = e1 & op(e0, e1) = e1 % 136.03/20.12 | | | | | | | | % 136.03/20.12 | | | | | | | | REF_CLOSE: (25), (28), (51) are inconsistent by sub-proof #247. % 136.03/20.12 | | | | | | | | % 136.03/20.12 | | | | | | | Case 2: % 136.03/20.12 | | | | | | | | % 136.03/20.12 | | | | | | | | (52) all_57_15 = e1 & op(e0, e0) = e1 % 136.03/20.12 | | | | | | | | % 136.03/20.12 | | | | | | | | ALPHA: (52) implies: % 136.03/20.12 | | | | | | | | (53) all_57_15 = e1 % 136.03/20.12 | | | | | | | | (54) op(e0, e0) = e1 % 136.03/20.12 | | | | | | | | % 136.03/20.12 | | | | | | | | BETA: splitting (31) gives: % 136.03/20.12 | | | | | | | | % 136.03/20.12 | | | | | | | | Case 1: % 136.03/20.12 | | | | | | | | | % 136.03/20.12 | | | | | | | | | (55) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & % 136.03/20.12 | | | | | | | | | op(e2, e2) = e0) % 136.03/20.12 | | | | | | | | | % 136.03/20.12 | | | | | | | | | BETA: splitting (55) gives: % 136.03/20.12 | | | | | | | | | % 136.03/20.12 | | | | | | | | | Case 1: % 136.03/20.12 | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | (56) all_57_2 = e0 & op(e2, e3) = e0 % 136.03/20.12 | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | REF_CLOSE: (29), (45), (56) are inconsistent by sub-proof % 136.03/20.12 | | | | | | | | | | #272. % 136.03/20.12 | | | | | | | | | | % 136.03/20.12 | | | | | | | | | Case 2: % 136.03/20.12 | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | (57) all_57_3 = e0 & op(e2, e2) = e0 % 136.03/20.12 | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | REF_CLOSE: (12), (26), (57) are inconsistent by sub-proof % 136.03/20.12 | | | | | | | | | | #302. % 136.03/20.12 | | | | | | | | | | % 136.03/20.12 | | | | | | | | | End of split % 136.03/20.12 | | | | | | | | | % 136.03/20.12 | | | | | | | | Case 2: % 136.03/20.12 | | | | | | | | | % 136.03/20.12 | | | | | | | | | (58) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & % 136.03/20.12 | | | | | | | | | op(e2, e0) = e0) % 136.03/20.12 | | | | | | | | | % 136.03/20.12 | | | | | | | | | BETA: splitting (58) gives: % 136.03/20.12 | | | | | | | | | % 136.03/20.12 | | | | | | | | | Case 1: % 136.03/20.12 | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | (59) all_57_5 = e0 & op(e2, e1) = e0 % 136.03/20.12 | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | REF_CLOSE: (4), (39), (59) are inconsistent by sub-proof % 136.03/20.12 | | | | | | | | | | #277. % 136.03/20.12 | | | | | | | | | | % 136.03/20.12 | | | | | | | | | Case 2: % 136.03/20.12 | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | (60) all_57_10 = e0 & op(e2, e0) = e0 % 136.03/20.12 | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | ALPHA: (60) implies: % 136.03/20.12 | | | | | | | | | | (61) all_57_10 = e0 % 136.03/20.12 | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | BETA: splitting (23) gives: % 136.03/20.12 | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | Case 1: % 136.03/20.12 | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | (62) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 136.03/20.12 | | | | | | | | | | | e2 & op(e2, e0) = e2) % 136.03/20.12 | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | BETA: splitting (62) gives: % 136.03/20.12 | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | Case 1: % 136.03/20.12 | | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | | (63) all_57_9 = e2 & op(e3, e0) = e2 % 136.03/20.12 | | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | | ALPHA: (63) implies: % 136.03/20.12 | | | | | | | | | | | | (64) all_57_9 = e2 % 136.03/20.12 | | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (10), (11), (12), (14), (19), (24), % 136.03/20.12 | | | | | | | | | | | | (28), (29), (32), (33), (64) are inconsistent by % 136.03/20.12 | | | | | | | | | | | | sub-proof #250. % 136.03/20.12 | | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | Case 2: % 136.03/20.12 | | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | | (65) all_57_10 = e2 & op(e2, e0) = e2 % 136.03/20.12 | | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | | ALPHA: (65) implies: % 136.03/20.12 | | | | | | | | | | | | (66) all_57_10 = e2 % 136.03/20.12 | | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | | REF_CLOSE: (4), (12), (26), (29), (31), (39), (45), (66) are % 136.03/20.12 | | | | | | | | | | | | inconsistent by sub-proof #271. % 136.03/20.12 | | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | End of split % 136.03/20.12 | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | Case 2: % 136.03/20.12 | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | (67) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 136.03/20.12 | | | | | | | | | | | e2 & op(e0, e0) = e2) % 136.03/20.12 | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | BETA: splitting (67) gives: % 136.03/20.12 | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | Case 1: % 136.03/20.12 | | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | | (68) all_57_11 = e2 & op(e1, e0) = e2 % 136.03/20.12 | | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | | ALPHA: (68) implies: % 136.03/20.12 | | | | | | | | | | | | (69) all_57_11 = e2 % 136.03/20.12 | | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | | BETA: splitting (30) gives: % 136.03/20.12 | | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | | Case 1: % 136.03/20.12 | | | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | | | (70) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 136.03/20.12 | | | | | | | | | | | | | & op(e2, e2) = e1) % 136.03/20.12 | | | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | | | BETA: splitting (70) gives: % 136.03/20.12 | | | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | | | Case 1: % 136.03/20.12 | | | | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | | | | % 136.03/20.12 | | | | | | | | | | | | | | ALPHA: (40) implies: % 136.03/20.12 | | | | | | | | | | | | | | (71) all_57_12 = e0 % 136.03/20.12 | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with e1, e3, e0, e0, % 136.14/20.12 | | | | | | | | | | | | | | simplifying with (2), (54) gives: % 136.14/20.12 | | | | | | | | | | | | | | (72) e3 = e1 % 136.14/20.12 | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | COMBINE_EQS: (15), (72) imply: % 136.14/20.12 | | | | | | | | | | | | | | (73) all_57_6 = e1 % 136.14/20.12 | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | BETA: splitting (17) gives: % 136.14/20.12 | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | Case 1: % 136.14/20.12 | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | (74) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 % 136.14/20.12 | | | | | | | | | | | | | | | & op(e2, e3) = e3) % 136.14/20.12 | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | BETA: splitting (74) gives: % 136.14/20.12 | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | Case 1: % 136.14/20.12 | | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | | (75) all_57_0 = e3 & op(e3, e3) = e3 % 136.14/20.12 | | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | | ALPHA: (75) implies: % 136.14/20.12 | | | | | | | | | | | | | | | | (76) op(e3, e3) = e3 % 136.14/20.12 | | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (10), (14), (76) are inconsistent by % 136.14/20.12 | | | | | | | | | | | | | | | | sub-proof #778. % 136.14/20.12 | | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | Case 2: % 136.14/20.12 | | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | | (77) all_57_2 = e3 & op(e2, e3) = e3 % 136.14/20.12 | | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | | ALPHA: (77) implies: % 136.14/20.12 | | | | | | | | | | | | | | | | (78) all_57_2 = e3 % 136.14/20.12 | | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | | REF_CLOSE: (11), (26), (28), (29), (30), (39), (61), (78) are % 136.14/20.12 | | | | | | | | | | | | | | | | inconsistent by sub-proof #369. % 136.14/20.12 | | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | End of split % 136.14/20.12 | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | Case 2: % 136.14/20.12 | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | (79) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = % 136.14/20.12 | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3) % 136.14/20.12 | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 136.14/20.12 | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | Case 1: % 136.14/20.12 | | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | | (80) all_57_6 = e3 & op(e1, e3) = e3 % 136.14/20.12 | | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | | REF_CLOSE: (15), (28), (73) are inconsistent by sub-proof % 136.14/20.12 | | | | | | | | | | | | | | | | #575. % 136.14/20.12 | | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | Case 2: % 136.14/20.12 | | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | | (81) all_57_12 = e3 & op(e0, e3) = e3 % 136.14/20.12 | | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | | ALPHA: (81) implies: % 136.14/20.12 | | | | | | | | | | | | | | | | (82) all_57_12 = e3 % 136.14/20.12 | | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | | REF_CLOSE: (12), (71), (82) are inconsistent by sub-proof % 136.14/20.12 | | | | | | | | | | | | | | | | #492. % 136.14/20.12 | | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | End of split % 136.14/20.12 | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | End of split % 136.14/20.12 | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | Case 2: % 136.14/20.12 | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | (83) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.12 | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | ALPHA: (83) implies: % 136.14/20.12 | | | | | | | | | | | | | | (84) op(e2, e2) = e1 % 136.14/20.12 | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | REF_CLOSE: (10), (16), (28), (84) are inconsistent by % 136.14/20.12 | | | | | | | | | | | | | | sub-proof #325. % 136.14/20.12 | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | End of split % 136.14/20.12 | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | Case 2: % 136.14/20.12 | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | (85) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 136.14/20.12 | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 136.14/20.12 | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | BETA: splitting (85) gives: % 136.14/20.12 | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | Case 1: % 136.14/20.12 | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | (86) all_57_5 = e1 & op(e2, e1) = e1 % 136.14/20.12 | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | REF_CLOSE: (11), (39), (86) are inconsistent by sub-proof % 136.14/20.12 | | | | | | | | | | | | | | #500. % 136.14/20.12 | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | Case 2: % 136.14/20.12 | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | (87) all_57_10 = e1 & op(e2, e0) = e1 % 136.14/20.12 | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | ALPHA: (87) implies: % 136.14/20.12 | | | | | | | | | | | | | | (88) all_57_10 = e1 % 136.14/20.12 | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | BETA: splitting (27) gives: % 136.14/20.12 | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | Case 1: % 136.14/20.12 | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | (89) all_57_15 = e0 & op(e0, e0) = e0 % 136.14/20.12 | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | REF_CLOSE: (29), (53), (89) are inconsistent by sub-proof % 136.14/20.12 | | | | | | | | | | | | | | | #412. % 136.14/20.12 | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | Case 2: % 136.14/20.12 | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | (90) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 136.14/20.12 | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 136.14/20.12 | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 136.14/20.12 | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 136.14/20.12 | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 136.14/20.12 | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | | REF_CLOSE: (4), (12), (13), (29), (69), (88), (90) are % 136.14/20.12 | | | | | | | | | | | | | | | inconsistent by sub-proof #637. % 136.14/20.12 | | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | | End of split % 136.14/20.12 | | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | | End of split % 136.14/20.12 | | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | End of split % 136.14/20.12 | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | Case 2: % 136.14/20.12 | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | (91) all_57_15 = e2 & op(e0, e0) = e2 % 136.14/20.12 | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | ALPHA: (91) implies: % 136.14/20.12 | | | | | | | | | | | | (92) op(e0, e0) = e2 % 136.14/20.12 | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | | REF_CLOSE: (10), (11), (54), (92) are inconsistent by % 136.14/20.12 | | | | | | | | | | | | sub-proof #636. % 136.14/20.12 | | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | | End of split % 136.14/20.12 | | | | | | | | | | | % 136.14/20.12 | | | | | | | | | | End of split % 136.14/20.12 | | | | | | | | | | % 136.14/20.12 | | | | | | | | | End of split % 136.14/20.12 | | | | | | | | | % 136.14/20.12 | | | | | | | | End of split % 136.14/20.12 | | | | | | | | % 136.14/20.12 | | | | | | | End of split % 136.14/20.12 | | | | | | | % 136.14/20.12 | | | | | | End of split % 136.14/20.12 | | | | | | % 136.14/20.12 | | | | | End of split % 136.14/20.12 | | | | | % 136.14/20.12 | | | | Case 2: % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | (93) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, % 136.14/20.12 | | | | | e3) = e1) % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | BETA: splitting (93) gives: % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | Case 1: % 136.14/20.12 | | | | | | % 136.14/20.12 | | | | | | (94) all_57_6 = e1 & op(e1, e3) = e1 % 136.14/20.12 | | | | | | % 136.14/20.12 | | | | | | REF_CLOSE: (15), (28), (94) are inconsistent by sub-proof #645. % 136.14/20.12 | | | | | | % 136.14/20.12 | | | | | Case 2: % 136.14/20.12 | | | | | | % 136.14/20.12 | | | | | | (95) all_57_12 = e1 & op(e0, e3) = e1 % 136.14/20.12 | | | | | | % 136.14/20.12 | | | | | | ALPHA: (95) implies: % 136.14/20.12 | | | | | | (96) all_57_12 = e1 % 136.14/20.12 | | | | | | % 136.14/20.12 | | | | | | REF_CLOSE: (4), (5), (12), (22), (25), (29), (96) are inconsistent % 136.14/20.12 | | | | | | by sub-proof #399. % 136.14/20.12 | | | | | | % 136.14/20.12 | | | | | End of split % 136.14/20.12 | | | | | % 136.14/20.12 | | | | End of split % 136.14/20.12 | | | | % 136.14/20.12 | | | Case 2: % 136.14/20.12 | | | | % 136.14/20.12 | | | | (97) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 136.14/20.12 | | | | e1) = e0) % 136.14/20.12 | | | | % 136.14/20.12 | | | | BETA: splitting (97) gives: % 136.14/20.12 | | | | % 136.14/20.12 | | | | Case 1: % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | (98) all_57_13 = e0 & op(e0, e2) = e0 % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | REF_CLOSE: (4), (22), (98) are inconsistent by sub-proof #411. % 136.14/20.12 | | | | | % 136.14/20.12 | | | | Case 2: % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | (99) all_57_14 = e0 & op(e0, e1) = e0 % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | REF_CLOSE: (12), (25), (99) are inconsistent by sub-proof #252. % 136.14/20.12 | | | | | % 136.14/20.12 | | | | End of split % 136.14/20.12 | | | | % 136.14/20.12 | | | End of split % 136.14/20.12 | | | % 136.14/20.12 | | End of split % 136.14/20.12 | | % 136.14/20.12 | Case 2: % 136.14/20.12 | | % 136.14/20.12 | | (100) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = % 136.14/20.12 | | e2) % 136.14/20.12 | | % 136.14/20.12 | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (10), (11), (12), (13), (14), (18), % 136.14/20.12 | | (19), (20), (21), (22), (24), (27), (28), (29), (32), (33), (100) % 136.14/20.12 | | are inconsistent by sub-proof #249. % 136.14/20.12 | | % 136.14/20.12 | End of split % 136.14/20.12 | % 136.14/20.12 End of proof % 136.14/20.12 % 136.14/20.12 Sub-proof #247 shows that the following formulas are inconsistent: % 136.14/20.12 ---------------------------------------------------------------- % 136.14/20.12 (1) all_57_14 = e1 & op(e0, e1) = e1 % 136.14/20.12 (2) all_57_14 = e3 % 136.14/20.12 (3) ~ (e3 = e1) % 136.14/20.12 % 136.14/20.12 Begin of proof % 136.14/20.12 | % 136.14/20.12 | ALPHA: (1) implies: % 136.14/20.12 | (4) all_57_14 = e1 % 136.14/20.12 | % 136.14/20.12 | COMBINE_EQS: (2), (4) imply: % 136.14/20.12 | (5) e3 = e1 % 136.14/20.12 | % 136.14/20.12 | REDUCE: (3), (5) imply: % 136.14/20.12 | (6) $false % 136.14/20.12 | % 136.14/20.12 | CLOSE: (6) is inconsistent. % 136.14/20.12 | % 136.14/20.12 End of proof % 136.14/20.12 % 136.14/20.12 Sub-proof #248 shows that the following formulas are inconsistent: % 136.14/20.12 ---------------------------------------------------------------- % 136.14/20.12 (1) all_57_13 = e1 & op(e0, e2) = e1 % 136.14/20.12 (2) all_57_13 = e2 % 136.14/20.12 (3) ~ (e2 = e1) % 136.14/20.12 % 136.14/20.12 Begin of proof % 136.14/20.12 | % 136.14/20.12 | ALPHA: (1) implies: % 136.14/20.12 | (4) all_57_13 = e1 % 136.14/20.12 | % 136.14/20.12 | COMBINE_EQS: (2), (4) imply: % 136.14/20.12 | (5) e2 = e1 % 136.14/20.12 | % 136.14/20.12 | REDUCE: (3), (5) imply: % 136.14/20.12 | (6) $false % 136.14/20.12 | % 136.14/20.12 | CLOSE: (6) is inconsistent. % 136.14/20.12 | % 136.14/20.12 End of proof % 136.14/20.12 % 136.14/20.12 Sub-proof #249 shows that the following formulas are inconsistent: % 136.14/20.12 ---------------------------------------------------------------- % 136.14/20.12 (1) op(e1, e1) = all_6_2 % 136.14/20.12 (2) op(e3, e3) = e2 % 136.14/20.12 (3) ~ (e2 = e0) % 136.14/20.12 (4) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.14/20.12 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.12 (5) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 136.14/20.12 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.12 (6) ~ (all_52_7 = e3) % 136.14/20.12 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.12 (8) ~ (e2 = e1) % 136.14/20.12 (9) ~ (e3 = e0) % 136.14/20.12 (10) all_57_9 = e3 % 136.14/20.12 (11) ~ (e3 = e2) % 136.14/20.12 (12) op(e0, e2) = all_52_7 % 136.14/20.12 (13) ~ (all_52_4 = e3) % 136.14/20.12 (14) ~ (all_6_2 = e2) % 136.14/20.12 (15) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.12 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 136.14/20.12 e1) % 136.14/20.12 (16) all_57_13 = e2 % 136.14/20.12 (17) op(e3, e2) = all_52_4 % 136.14/20.12 (18) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.12 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.14/20.12 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.12 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.12 (19) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 136.14/20.12 (20) ~ (e3 = e1) % 136.14/20.12 (21) ~ (e1 = e0) % 136.14/20.12 (22) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.14/20.12 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.14/20.12 (23) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 136.14/20.12 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 136.14/20.12 % 136.14/20.12 Begin of proof % 136.14/20.12 | % 136.14/20.12 | BETA: splitting (19) gives: % 136.14/20.12 | % 136.14/20.12 | Case 1: % 136.14/20.12 | | % 136.14/20.12 | | (24) all_57_8 = e2 & op(e1, e1) = e2 % 136.14/20.12 | | % 136.14/20.12 | | ALPHA: (24) implies: % 136.14/20.12 | | (25) op(e1, e1) = e2 % 136.14/20.12 | | % 136.14/20.12 | | REF_CLOSE: (1), (7), (14), (25) are inconsistent by sub-proof #767. % 136.14/20.12 | | % 136.14/20.12 | Case 2: % 136.14/20.12 | | % 136.14/20.12 | | (26) all_57_14 = e2 & op(e0, e1) = e2 % 136.14/20.12 | | % 136.14/20.12 | | ALPHA: (26) implies: % 136.14/20.12 | | (27) all_57_14 = e2 % 136.14/20.12 | | % 136.14/20.12 | | BETA: splitting (5) gives: % 136.14/20.12 | | % 136.14/20.12 | | Case 1: % 136.14/20.12 | | | % 136.14/20.12 | | | (28) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) % 136.14/20.12 | | | = e3) % 136.14/20.12 | | | % 136.14/20.12 | | | BETA: splitting (28) gives: % 136.14/20.12 | | | % 136.14/20.12 | | | Case 1: % 136.14/20.12 | | | | % 136.14/20.12 | | | | (29) all_57_12 = e3 & op(e0, e3) = e3 % 136.14/20.12 | | | | % 136.14/20.12 | | | | ALPHA: (29) implies: % 136.14/20.12 | | | | (30) all_57_12 = e3 % 136.14/20.12 | | | | % 136.14/20.12 | | | | REF_CLOSE: (3), (8), (9), (15), (16), (18), (20), (21), (27), (30) are % 136.14/20.12 | | | | inconsistent by sub-proof #409. % 136.14/20.12 | | | | % 136.14/20.12 | | | Case 2: % 136.14/20.12 | | | | % 136.14/20.12 | | | | (31) all_57_13 = e3 & op(e0, e2) = e3 % 136.14/20.12 | | | | % 136.14/20.12 | | | | REF_CLOSE: (6), (7), (12), (31) are inconsistent by sub-proof #556. % 136.14/20.12 | | | | % 136.14/20.12 | | | End of split % 136.14/20.12 | | | % 136.14/20.12 | | Case 2: % 136.14/20.12 | | | % 136.14/20.12 | | | (32) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) % 136.14/20.12 | | | = e3) % 136.14/20.12 | | | % 136.14/20.12 | | | BETA: splitting (32) gives: % 136.14/20.12 | | | % 136.14/20.12 | | | Case 1: % 136.14/20.12 | | | | % 136.14/20.12 | | | | (33) all_57_14 = e3 & op(e0, e1) = e3 % 136.14/20.12 | | | | % 136.14/20.12 | | | | ALPHA: (33) implies: % 136.14/20.12 | | | | (34) all_57_14 = e3 % 136.14/20.12 | | | | % 136.14/20.12 | | | | COMBINE_EQS: (27), (34) imply: % 136.14/20.12 | | | | (35) e3 = e2 % 136.14/20.12 | | | | % 136.14/20.12 | | | | SIMP: (35) implies: % 136.14/20.12 | | | | (36) e3 = e2 % 136.14/20.12 | | | | % 136.14/20.12 | | | | COMBINE_EQS: (10), (36) imply: % 136.14/20.12 | | | | (37) all_57_9 = e2 % 136.14/20.12 | | | | % 136.14/20.12 | | | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (11), (13), (17), (20), (21), % 136.14/20.12 | | | | (22), (23), (37) are inconsistent by sub-proof #250. % 136.14/20.12 | | | | % 136.14/20.12 | | | Case 2: % 136.14/20.12 | | | | % 136.14/20.12 | | | | (38) all_57_15 = e3 & op(e0, e0) = e3 % 136.14/20.12 | | | | % 136.14/20.12 | | | | REF_CLOSE: (3), (8), (9), (15), (16), (18), (20), (21), (27), (38) are % 136.14/20.12 | | | | inconsistent by sub-proof #402. % 136.14/20.12 | | | | % 136.14/20.12 | | | End of split % 136.14/20.12 | | | % 136.14/20.12 | | End of split % 136.14/20.12 | | % 136.14/20.12 | End of split % 136.14/20.12 | % 136.14/20.12 End of proof % 136.14/20.12 % 136.14/20.12 Sub-proof #250 shows that the following formulas are inconsistent: % 136.14/20.12 ---------------------------------------------------------------- % 136.14/20.12 (1) op(e3, e3) = e2 % 136.14/20.12 (2) ~ (e2 = e0) % 136.14/20.12 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.14/20.12 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.12 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.12 (5) ~ (e2 = e1) % 136.14/20.12 (6) ~ (e3 = e0) % 136.14/20.12 (7) ~ (e3 = e2) % 136.14/20.12 (8) all_57_9 = e2 % 136.14/20.12 (9) ~ (all_52_4 = e3) % 136.14/20.12 (10) op(e3, e2) = all_52_4 % 136.14/20.12 (11) ~ (e3 = e1) % 136.14/20.12 (12) ~ (e1 = e0) % 136.14/20.12 (13) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.14/20.12 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.14/20.12 (14) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 136.14/20.12 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 136.14/20.12 % 136.14/20.12 Begin of proof % 136.14/20.12 | % 136.14/20.12 | BETA: splitting (13) gives: % 136.14/20.12 | % 136.14/20.12 | Case 1: % 136.14/20.12 | | % 136.14/20.12 | | (15) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = % 136.14/20.12 | | e3) % 136.14/20.12 | | % 136.14/20.12 | | REF_CLOSE: (1), (4), (7), (9), (10), (15) are inconsistent by sub-proof % 136.14/20.12 | | #282. % 136.14/20.12 | | % 136.14/20.12 | Case 2: % 136.14/20.12 | | % 136.14/20.12 | | (16) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = % 136.14/20.12 | | e3) % 136.14/20.12 | | % 136.14/20.12 | | BETA: splitting (16) gives: % 136.14/20.12 | | % 136.14/20.12 | | Case 1: % 136.14/20.12 | | | % 136.14/20.12 | | | (17) all_57_4 = e3 & op(e3, e1) = e3 % 136.14/20.12 | | | % 136.14/20.12 | | | ALPHA: (17) implies: % 136.14/20.12 | | | (18) all_57_4 = e3 % 136.14/20.12 | | | % 136.14/20.12 | | | BETA: splitting (3) gives: % 136.14/20.12 | | | % 136.14/20.12 | | | Case 1: % 136.14/20.12 | | | | % 136.14/20.12 | | | | (19) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) % 136.14/20.12 | | | | = e0) % 136.14/20.12 | | | | % 136.14/20.12 | | | | BETA: splitting (19) gives: % 136.14/20.12 | | | | % 136.14/20.12 | | | | Case 1: % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | (20) all_57_0 = e0 & op(e3, e3) = e0 % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | ALPHA: (20) implies: % 136.14/20.12 | | | | | (21) op(e3, e3) = e0 % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | REF_CLOSE: (1), (2), (4), (21) are inconsistent by sub-proof #495. % 136.14/20.12 | | | | | % 136.14/20.12 | | | | Case 2: % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | (22) all_57_1 = e0 & op(e3, e2) = e0 % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | ALPHA: (22) implies: % 136.14/20.12 | | | | | (23) all_57_1 = e0 % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | BETA: splitting (14) gives: % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | Case 1: % 136.14/20.12 | | | | | | % 136.14/20.12 | | | | | | (24) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, % 136.14/20.12 | | | | | | e2) = e1) % 136.14/20.12 | | | | | | % 136.14/20.12 | | | | | | REF_CLOSE: (1), (4), (5), (12), (23), (24) are inconsistent by % 136.14/20.12 | | | | | | sub-proof #281. % 136.14/20.12 | | | | | | % 136.14/20.12 | | | | | Case 2: % 136.14/20.12 | | | | | | % 136.14/20.12 | | | | | | (25) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, % 136.14/20.12 | | | | | | e0) = e1) % 136.14/20.12 | | | | | | % 136.14/20.12 | | | | | | BETA: splitting (25) gives: % 136.14/20.12 | | | | | | % 136.14/20.12 | | | | | | Case 1: % 136.14/20.12 | | | | | | | % 136.14/20.12 | | | | | | | (26) all_57_4 = e1 & op(e3, e1) = e1 % 136.14/20.12 | | | | | | | % 136.14/20.12 | | | | | | | REF_CLOSE: (11), (18), (26) are inconsistent by sub-proof #382. % 136.14/20.12 | | | | | | | % 136.14/20.12 | | | | | | Case 2: % 136.14/20.12 | | | | | | | % 136.14/20.12 | | | | | | | (27) all_57_9 = e1 & op(e3, e0) = e1 % 136.14/20.12 | | | | | | | % 136.14/20.12 | | | | | | | ALPHA: (27) implies: % 136.14/20.12 | | | | | | | (28) all_57_9 = e1 % 136.14/20.12 | | | | | | | % 136.14/20.12 | | | | | | | COMBINE_EQS: (8), (28) imply: % 136.14/20.12 | | | | | | | (29) e2 = e1 % 136.14/20.12 | | | | | | | % 136.14/20.12 | | | | | | | REDUCE: (5), (29) imply: % 136.14/20.12 | | | | | | | (30) $false % 136.14/20.12 | | | | | | | % 136.14/20.12 | | | | | | | CLOSE: (30) is inconsistent. % 136.14/20.12 | | | | | | | % 136.14/20.12 | | | | | | End of split % 136.14/20.12 | | | | | | % 136.14/20.12 | | | | | End of split % 136.14/20.12 | | | | | % 136.14/20.12 | | | | End of split % 136.14/20.12 | | | | % 136.14/20.12 | | | Case 2: % 136.14/20.12 | | | | % 136.14/20.12 | | | | (31) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) % 136.14/20.12 | | | | = e0) % 136.14/20.12 | | | | % 136.14/20.12 | | | | BETA: splitting (31) gives: % 136.14/20.12 | | | | % 136.14/20.12 | | | | Case 1: % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | (32) all_57_4 = e0 & op(e3, e1) = e0 % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | REF_CLOSE: (6), (18), (32) are inconsistent by sub-proof #384. % 136.14/20.12 | | | | | % 136.14/20.12 | | | | Case 2: % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | (33) all_57_9 = e0 & op(e3, e0) = e0 % 136.14/20.12 | | | | | % 136.14/20.12 | | | | | REF_CLOSE: (2), (8), (33) are inconsistent by sub-proof #657. % 136.14/20.12 | | | | | % 136.14/20.12 | | | | End of split % 136.14/20.12 | | | | % 136.14/20.12 | | | End of split % 136.14/20.12 | | | % 136.14/20.12 | | Case 2: % 136.14/20.12 | | | % 136.14/20.12 | | | (34) all_57_9 = e3 & op(e3, e0) = e3 % 136.14/20.12 | | | % 136.14/20.12 | | | REF_CLOSE: (7), (8), (34) are inconsistent by sub-proof #612. % 136.14/20.12 | | | % 136.14/20.12 | | End of split % 136.14/20.12 | | % 136.14/20.12 | End of split % 136.14/20.12 | % 136.14/20.12 End of proof % 136.14/20.12 % 136.14/20.12 Sub-proof #251 shows that the following formulas are inconsistent: % 136.14/20.12 ---------------------------------------------------------------- % 136.14/20.12 (1) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) | % 136.14/20.12 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1) % 136.14/20.12 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) | % 136.14/20.12 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 136.14/20.12 (3) all_57_4 = e3 & op(e3, e1) = e3 % 136.14/20.12 (4) op(e1, e1) = all_6_2 % 136.14/20.12 (5) op(e3, e3) = e2 % 136.14/20.12 (6) ~ (e2 = e0) % 136.14/20.12 (7) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.14/20.12 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.12 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.12 (9) ~ (e2 = e1) % 136.14/20.12 (10) ~ (e3 = e0) % 136.14/20.12 (11) ~ (e3 = e2) % 136.14/20.12 (12) ~ (all_52_4 = e3) % 136.14/20.12 (13) ~ (all_6_2 = e2) % 136.14/20.12 (14) op(e3, e2) = all_52_4 % 136.14/20.12 (15) all_57_14 = e3 % 136.14/20.12 (16) ~ (e3 = e1) % 136.14/20.12 (17) ~ (e1 = e0) % 136.14/20.12 (18) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.14/20.12 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.14/20.12 (19) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 136.14/20.12 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 136.14/20.12 (20) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | % 136.14/20.12 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 136.14/20.12 % 136.14/20.12 Begin of proof % 136.14/20.12 | % 136.14/20.12 | ALPHA: (3) implies: % 136.14/20.12 | (21) all_57_4 = e3 % 136.14/20.12 | % 136.14/20.12 | BETA: splitting (20) gives: % 136.14/20.12 | % 136.14/20.12 | Case 1: % 136.14/20.12 | | % 136.14/20.12 | | (22) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = % 136.14/20.12 | | e2) % 136.14/20.12 | | % 136.14/20.12 | | BETA: splitting (22) gives: % 136.14/20.12 | | % 136.14/20.12 | | Case 1: % 136.14/20.12 | | | % 136.14/20.12 | | | (23) all_57_4 = e2 & op(e3, e1) = e2 % 136.14/20.12 | | | % 136.14/20.12 | | | ALPHA: (23) implies: % 136.14/20.12 | | | (24) all_57_4 = e2 % 136.14/20.12 | | | % 136.14/20.12 | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (14), (16), (17), % 136.14/20.12 | | | (18), (19), (24) are inconsistent by sub-proof #278. % 136.14/20.12 | | | % 136.14/20.12 | | Case 2: % 136.14/20.12 | | | % 136.14/20.12 | | | (25) all_57_5 = e2 & op(e2, e1) = e2 % 136.14/20.12 | | | % 136.14/20.12 | | | ALPHA: (25) implies: % 136.14/20.12 | | | (26) all_57_5 = e2 % 136.14/20.12 | | | % 136.14/20.12 | | | BETA: splitting (2) gives: % 136.14/20.12 | | | % 136.14/20.12 | | | Case 1: % 136.14/20.12 | | | | % 136.14/20.13 | | | | (27) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) % 136.14/20.13 | | | | = e0) % 136.14/20.13 | | | | % 136.14/20.13 | | | | BETA: splitting (27) gives: % 136.14/20.13 | | | | % 136.14/20.13 | | | | Case 1: % 136.14/20.13 | | | | | % 136.14/20.13 | | | | | (28) all_57_4 = e0 & op(e3, e1) = e0 % 136.14/20.13 | | | | | % 136.14/20.13 | | | | | REF_CLOSE: (10), (21), (28) are inconsistent by sub-proof #384. % 136.14/20.13 | | | | | % 136.14/20.13 | | | | Case 2: % 136.14/20.13 | | | | | % 136.14/20.13 | | | | | (29) all_57_5 = e0 & op(e2, e1) = e0 % 136.14/20.13 | | | | | % 136.14/20.13 | | | | | REF_CLOSE: (6), (26), (29) are inconsistent by sub-proof #277. % 136.14/20.13 | | | | | % 136.14/20.13 | | | | End of split % 136.14/20.13 | | | | % 136.14/20.13 | | | Case 2: % 136.14/20.13 | | | | % 136.14/20.13 | | | | (30) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) % 136.14/20.13 | | | | = e0) % 136.14/20.13 | | | | % 136.14/20.13 | | | | BETA: splitting (30) gives: % 136.14/20.13 | | | | % 136.14/20.13 | | | | Case 1: % 136.14/20.13 | | | | | % 136.14/20.13 | | | | | (31) all_57_8 = e0 & op(e1, e1) = e0 % 136.14/20.13 | | | | | % 136.14/20.13 | | | | | ALPHA: (31) implies: % 136.14/20.13 | | | | | (32) op(e1, e1) = e0 % 136.14/20.13 | | | | | % 136.14/20.13 | | | | | BETA: splitting (1) gives: % 136.14/20.13 | | | | | % 136.14/20.13 | | | | | Case 1: % 136.14/20.13 | | | | | | % 136.14/20.13 | | | | | | (33) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, % 136.14/20.13 | | | | | | e1) = e1) % 136.14/20.13 | | | | | | % 136.14/20.13 | | | | | | BETA: splitting (33) gives: % 136.14/20.13 | | | | | | % 136.14/20.13 | | | | | | Case 1: % 136.14/20.13 | | | | | | | % 136.14/20.13 | | | | | | | (34) all_57_4 = e1 & op(e3, e1) = e1 % 136.14/20.13 | | | | | | | % 136.14/20.13 | | | | | | | REF_CLOSE: (16), (21), (34) are inconsistent by sub-proof #382. % 136.14/20.13 | | | | | | | % 136.14/20.13 | | | | | | Case 2: % 136.14/20.13 | | | | | | | % 136.14/20.13 | | | | | | | (35) all_57_5 = e1 & op(e2, e1) = e1 % 136.14/20.13 | | | | | | | % 136.14/20.13 | | | | | | | ALPHA: (35) implies: % 136.14/20.13 | | | | | | | (36) all_57_5 = e1 % 136.14/20.13 | | | | | | | % 136.14/20.13 | | | | | | | REF_CLOSE: (9), (26), (36) are inconsistent by sub-proof #418. % 136.14/20.13 | | | | | | | % 136.14/20.13 | | | | | | End of split % 136.14/20.13 | | | | | | % 136.14/20.13 | | | | | Case 2: % 136.14/20.13 | | | | | | % 136.14/20.13 | | | | | | (37) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, % 136.14/20.13 | | | | | | e1) = e1) % 136.14/20.13 | | | | | | % 136.14/20.13 | | | | | | BETA: splitting (37) gives: % 136.14/20.13 | | | | | | % 136.14/20.13 | | | | | | Case 1: % 136.14/20.13 | | | | | | | % 136.14/20.13 | | | | | | | (38) all_57_8 = e1 & op(e1, e1) = e1 % 136.14/20.13 | | | | | | | % 136.14/20.13 | | | | | | | ALPHA: (38) implies: % 136.14/20.13 | | | | | | | (39) op(e1, e1) = e1 % 136.14/20.13 | | | | | | | % 136.14/20.13 | | | | | | | REF_CLOSE: (8), (17), (32), (39) are inconsistent by sub-proof % 136.14/20.13 | | | | | | | #721. % 136.14/20.13 | | | | | | | % 136.14/20.13 | | | | | | Case 2: % 136.14/20.13 | | | | | | | % 136.14/20.13 | | | | | | | (40) all_57_14 = e1 & op(e0, e1) = e1 % 136.14/20.13 | | | | | | | % 136.14/20.13 | | | | | | | ALPHA: (40) implies: % 136.14/20.13 | | | | | | | (41) all_57_14 = e1 % 136.14/20.13 | | | | | | | % 136.14/20.13 | | | | | | | REF_CLOSE: (15), (16), (41) are inconsistent by sub-proof #561. % 136.14/20.13 | | | | | | | % 136.14/20.13 | | | | | | End of split % 136.14/20.13 | | | | | | % 136.14/20.13 | | | | | End of split % 136.14/20.13 | | | | | % 136.14/20.13 | | | | Case 2: % 136.14/20.13 | | | | | % 136.14/20.13 | | | | | (42) all_57_14 = e0 & op(e0, e1) = e0 % 136.14/20.13 | | | | | % 136.14/20.13 | | | | | REF_CLOSE: (10), (15), (42) are inconsistent by sub-proof #252. % 136.14/20.13 | | | | | % 136.14/20.13 | | | | End of split % 136.14/20.13 | | | | % 136.14/20.13 | | | End of split % 136.14/20.13 | | | % 136.14/20.13 | | End of split % 136.14/20.13 | | % 136.14/20.13 | Case 2: % 136.14/20.13 | | % 136.14/20.13 | | (43) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = % 136.14/20.13 | | e2) % 136.14/20.13 | | % 136.14/20.13 | | BETA: splitting (43) gives: % 136.14/20.13 | | % 136.14/20.13 | | Case 1: % 136.14/20.13 | | | % 136.14/20.13 | | | (44) all_57_8 = e2 & op(e1, e1) = e2 % 136.14/20.13 | | | % 136.14/20.13 | | | ALPHA: (44) implies: % 136.14/20.13 | | | (45) op(e1, e1) = e2 % 136.14/20.13 | | | % 136.14/20.13 | | | REF_CLOSE: (4), (8), (13), (45) are inconsistent by sub-proof #767. % 136.14/20.13 | | | % 136.14/20.13 | | Case 2: % 136.14/20.13 | | | % 136.14/20.13 | | | (46) all_57_14 = e2 & op(e0, e1) = e2 % 136.14/20.13 | | | % 136.14/20.13 | | | ALPHA: (46) implies: % 136.14/20.13 | | | (47) all_57_14 = e2 % 136.14/20.13 | | | % 136.14/20.13 | | | COMBINE_EQS: (15), (47) imply: % 136.14/20.13 | | | (48) e3 = e2 % 136.14/20.13 | | | % 136.14/20.13 | | | COMBINE_EQS: (21), (48) imply: % 136.14/20.13 | | | (49) all_57_4 = e2 % 136.14/20.13 | | | % 136.14/20.13 | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (14), (16), (17), % 136.14/20.13 | | | (18), (19), (49) are inconsistent by sub-proof #278. % 136.14/20.13 | | | % 136.14/20.13 | | End of split % 136.14/20.13 | | % 136.14/20.13 | End of split % 136.14/20.13 | % 136.14/20.13 End of proof % 136.14/20.13 % 136.14/20.13 Sub-proof #252 shows that the following formulas are inconsistent: % 136.14/20.13 ---------------------------------------------------------------- % 136.14/20.13 (1) all_57_14 = e0 & op(e0, e1) = e0 % 136.14/20.13 (2) all_57_14 = e3 % 136.14/20.13 (3) ~ (e3 = e0) % 136.14/20.13 % 136.14/20.13 Begin of proof % 136.14/20.13 | % 136.14/20.13 | ALPHA: (1) implies: % 136.14/20.13 | (4) all_57_14 = e0 % 136.14/20.13 | % 136.14/20.13 | COMBINE_EQS: (2), (4) imply: % 136.14/20.13 | (5) e3 = e0 % 136.14/20.13 | % 136.14/20.13 | REDUCE: (3), (5) imply: % 136.14/20.13 | (6) $false % 136.14/20.13 | % 136.14/20.13 | CLOSE: (6) is inconsistent. % 136.14/20.13 | % 136.14/20.13 End of proof % 136.14/20.13 % 136.14/20.13 Sub-proof #253 shows that the following formulas are inconsistent: % 136.14/20.13 ---------------------------------------------------------------- % 136.14/20.13 (1) all_56_31 = e3 % 136.14/20.13 (2) all_56_31 = e1 % 136.14/20.13 (3) ~ (e3 = e1) % 136.14/20.13 % 136.14/20.13 Begin of proof % 136.14/20.13 | % 136.14/20.13 | COMBINE_EQS: (1), (2) imply: % 136.14/20.13 | (4) e3 = e1 % 136.14/20.13 | % 136.14/20.13 | SIMP: (4) implies: % 136.14/20.13 | (5) e3 = e1 % 136.14/20.13 | % 136.14/20.13 | REDUCE: (3), (5) imply: % 136.14/20.13 | (6) $false % 136.14/20.13 | % 136.14/20.13 | CLOSE: (6) is inconsistent. % 136.14/20.13 | % 136.14/20.13 End of proof % 136.14/20.13 % 136.14/20.13 Sub-proof #254 shows that the following formulas are inconsistent: % 136.14/20.13 ---------------------------------------------------------------- % 136.14/20.13 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 136.14/20.13 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 136.14/20.13 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.14/20.13 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.14/20.13 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.14/20.13 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.13 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 136.14/20.13 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.14/20.13 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.13 $i(all_56_21) & $i(all_56_29)) % 136.14/20.13 (2) op(e3, e3) = e2 % 136.14/20.13 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.13 (4) ~ (e2 = e1) % 136.14/20.13 (5) ~ (all_52_4 = e3) % 136.14/20.13 (6) op(e3, e2) = all_52_4 % 136.14/20.13 % 136.14/20.13 Begin of proof % 136.14/20.13 | % 136.14/20.13 | BETA: splitting (1) gives: % 136.14/20.13 | % 136.14/20.13 | Case 1: % 136.14/20.13 | | % 136.14/20.13 | | (7) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.14/20.13 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.14/20.13 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.14/20.13 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.14/20.13 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.14/20.13 | | % 136.14/20.13 | | ALPHA: (7) implies: % 136.14/20.13 | | (8) op(e3, e2) = e3 % 136.14/20.13 | | % 136.14/20.13 | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #738. % 136.14/20.13 | | % 136.14/20.13 | Case 2: % 136.14/20.13 | | % 136.14/20.13 | | (9) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.14/20.13 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 136.14/20.13 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.14/20.13 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.14/20.13 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.14/20.13 | | % 136.14/20.13 | | ALPHA: (9) implies: % 136.14/20.13 | | (10) op(e3, e3) = e1 % 136.14/20.13 | | % 136.14/20.13 | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #743. % 136.14/20.13 | | % 136.14/20.13 | End of split % 136.14/20.13 | % 136.14/20.13 End of proof % 136.14/20.13 % 136.14/20.13 Sub-proof #255 shows that the following formulas are inconsistent: % 136.14/20.13 ---------------------------------------------------------------- % 136.14/20.13 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.13 (2) ~ (e3 = e0) % 136.14/20.13 (3) ~ (e3 = e2) % 136.14/20.13 (4) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.13 (5) op(e0, e0) = e2 % 136.14/20.13 (6) all_57_11 = e0 % 136.14/20.13 % 136.14/20.13 Begin of proof % 136.14/20.13 | % 136.14/20.13 | BETA: splitting (4) gives: % 136.14/20.13 | % 136.14/20.13 | Case 1: % 136.14/20.13 | | % 136.14/20.13 | | (7) all_57_11 = e3 & op(e1, e0) = e3 % 136.14/20.13 | | % 136.14/20.13 | | REF_CLOSE: (2), (6), (7) are inconsistent by sub-proof #256. % 136.14/20.13 | | % 136.14/20.13 | Case 2: % 136.14/20.13 | | % 136.14/20.13 | | (8) all_57_15 = e3 & op(e0, e0) = e3 % 136.14/20.13 | | % 136.14/20.13 | | ALPHA: (8) implies: % 136.14/20.13 | | (9) op(e0, e0) = e3 % 136.14/20.13 | | % 136.14/20.13 | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #634. % 136.14/20.13 | | % 136.14/20.13 | End of split % 136.14/20.13 | % 136.14/20.13 End of proof % 136.14/20.13 % 136.14/20.13 Sub-proof #256 shows that the following formulas are inconsistent: % 136.14/20.13 ---------------------------------------------------------------- % 136.14/20.13 (1) all_57_11 = e3 & op(e1, e0) = e3 % 136.14/20.13 (2) all_57_11 = e0 % 136.14/20.13 (3) ~ (e3 = e0) % 136.14/20.13 % 136.14/20.13 Begin of proof % 136.14/20.13 | % 136.14/20.13 | ALPHA: (1) implies: % 136.14/20.13 | (4) all_57_11 = e3 % 136.14/20.13 | % 136.14/20.13 | COMBINE_EQS: (2), (4) imply: % 136.14/20.13 | (5) e3 = e0 % 136.14/20.13 | % 136.14/20.13 | REDUCE: (3), (5) imply: % 136.14/20.13 | (6) $false % 136.14/20.13 | % 136.14/20.13 | CLOSE: (6) is inconsistent. % 136.14/20.13 | % 136.14/20.13 End of proof % 136.14/20.13 % 136.14/20.13 Sub-proof #257 shows that the following formulas are inconsistent: % 136.14/20.13 ---------------------------------------------------------------- % 136.14/20.13 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.13 (2) ~ (e2 = e1) % 136.14/20.13 (3) all_57_9 = e3 % 136.14/20.13 (4) op(e2, e0) = e0 % 136.14/20.13 (5) op(e0, e0) = e2 % 136.14/20.13 (6) all_57_11 = e0 % 136.14/20.13 (7) ~ (e3 = e1) % 136.14/20.13 (8) ~ (e1 = e0) % 136.14/20.13 (9) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) | % 136.14/20.13 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.13 % 136.14/20.13 Begin of proof % 136.14/20.13 | % 136.14/20.13 | BETA: splitting (9) gives: % 136.14/20.13 | % 136.14/20.13 | Case 1: % 136.14/20.13 | | % 136.14/20.13 | | (10) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = % 136.14/20.13 | | e1) % 136.14/20.13 | | % 136.14/20.13 | | BETA: splitting (10) gives: % 136.14/20.13 | | % 136.14/20.13 | | Case 1: % 136.14/20.13 | | | % 136.14/20.13 | | | (11) all_57_9 = e1 & op(e3, e0) = e1 % 136.14/20.13 | | | % 136.14/20.13 | | | ALPHA: (11) implies: % 136.14/20.13 | | | (12) all_57_9 = e1 % 136.14/20.13 | | | % 136.14/20.13 | | | REF_CLOSE: (3), (7), (12) are inconsistent by sub-proof #690. % 136.14/20.13 | | | % 136.14/20.13 | | Case 2: % 136.14/20.13 | | | % 136.14/20.13 | | | (13) all_57_10 = e1 & op(e2, e0) = e1 % 136.14/20.13 | | | % 136.14/20.13 | | | ALPHA: (13) implies: % 136.14/20.13 | | | (14) op(e2, e0) = e1 % 136.14/20.13 | | | % 136.14/20.13 | | | REF_CLOSE: (1), (4), (8), (14) are inconsistent by sub-proof #695. % 136.14/20.13 | | | % 136.14/20.13 | | End of split % 136.14/20.13 | | % 136.14/20.13 | Case 2: % 136.14/20.13 | | % 136.14/20.13 | | (15) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = % 136.14/20.13 | | e1) % 136.14/20.13 | | % 136.14/20.13 | | BETA: splitting (15) gives: % 136.14/20.13 | | % 136.14/20.13 | | Case 1: % 136.14/20.13 | | | % 136.14/20.13 | | | (16) all_57_11 = e1 & op(e1, e0) = e1 % 136.14/20.13 | | | % 136.14/20.13 | | | ALPHA: (16) implies: % 136.14/20.13 | | | (17) all_57_11 = e1 % 136.14/20.13 | | | % 136.14/20.13 | | | COMBINE_EQS: (6), (17) imply: % 136.14/20.13 | | | (18) e1 = e0 % 136.14/20.13 | | | % 136.14/20.13 | | | SIMP: (18) implies: % 136.14/20.13 | | | (19) e1 = e0 % 136.14/20.13 | | | % 136.14/20.13 | | | REDUCE: (8), (19) imply: % 136.14/20.13 | | | (20) $false % 136.14/20.13 | | | % 136.14/20.13 | | | CLOSE: (20) is inconsistent. % 136.14/20.13 | | | % 136.14/20.13 | | Case 2: % 136.14/20.13 | | | % 136.14/20.13 | | | (21) all_57_15 = e1 & op(e0, e0) = e1 % 136.14/20.13 | | | % 136.14/20.13 | | | ALPHA: (21) implies: % 136.14/20.13 | | | (22) op(e0, e0) = e1 % 136.14/20.13 | | | % 136.14/20.13 | | | REF_CLOSE: (1), (2), (5), (22) are inconsistent by sub-proof #636. % 136.14/20.13 | | | % 136.14/20.13 | | End of split % 136.14/20.13 | | % 136.14/20.13 | End of split % 136.14/20.13 | % 136.14/20.13 End of proof % 136.14/20.13 % 136.14/20.13 Sub-proof #258 shows that the following formulas are inconsistent: % 136.14/20.13 ---------------------------------------------------------------- % 136.14/20.13 (1) all_54_11 = all_52_14 % 136.14/20.13 (2) all_54_11 = e0 % 136.14/20.13 (3) ~ (all_52_14 = e0) % 136.14/20.13 % 136.14/20.13 Begin of proof % 136.14/20.13 | % 136.14/20.13 | COMBINE_EQS: (1), (2) imply: % 136.14/20.13 | (4) all_52_14 = e0 % 136.14/20.13 | % 136.14/20.13 | SIMP: (4) implies: % 136.14/20.13 | (5) all_52_14 = e0 % 136.14/20.13 | % 136.14/20.13 | REDUCE: (3), (5) imply: % 136.14/20.13 | (6) $false % 136.14/20.13 | % 136.14/20.13 | CLOSE: (6) is inconsistent. % 136.14/20.13 | % 136.14/20.13 End of proof % 136.14/20.13 % 136.14/20.13 Sub-proof #259 shows that the following formulas are inconsistent: % 136.14/20.13 ---------------------------------------------------------------- % 136.14/20.13 (1) all_54_11 = all_52_14 % 136.14/20.13 (2) all_54_11 = e2 % 136.14/20.13 (3) ~ (all_52_14 = e2) % 136.14/20.13 % 136.14/20.13 Begin of proof % 136.14/20.13 | % 136.14/20.13 | COMBINE_EQS: (1), (2) imply: % 136.14/20.13 | (4) all_52_14 = e2 % 136.14/20.13 | % 136.14/20.13 | SIMP: (4) implies: % 136.14/20.13 | (5) all_52_14 = e2 % 136.14/20.13 | % 136.14/20.13 | REDUCE: (3), (5) imply: % 136.14/20.13 | (6) $false % 136.14/20.13 | % 136.14/20.13 | CLOSE: (6) is inconsistent. % 136.14/20.13 | % 136.14/20.13 End of proof % 136.14/20.13 % 136.14/20.13 Sub-proof #260 shows that the following formulas are inconsistent: % 136.14/20.13 ---------------------------------------------------------------- % 136.14/20.13 (1) all_54_11 = all_52_14 % 136.14/20.13 (2) all_54_11 = e3 % 136.14/20.13 (3) ~ (all_52_14 = e3) % 136.14/20.13 % 136.14/20.13 Begin of proof % 136.14/20.13 | % 136.14/20.13 | COMBINE_EQS: (1), (2) imply: % 136.14/20.13 | (4) all_52_14 = e3 % 136.14/20.13 | % 136.14/20.13 | SIMP: (4) implies: % 136.14/20.13 | (5) all_52_14 = e3 % 136.14/20.13 | % 136.14/20.13 | REDUCE: (3), (5) imply: % 136.14/20.13 | (6) $false % 136.14/20.13 | % 136.14/20.13 | CLOSE: (6) is inconsistent. % 136.14/20.13 | % 136.14/20.13 End of proof % 136.14/20.13 % 136.14/20.13 Sub-proof #261 shows that the following formulas are inconsistent: % 136.14/20.13 ---------------------------------------------------------------- % 136.14/20.13 (1) ~ (all_52_12 = e1) % 136.14/20.13 (2) all_54_0 = all_10_2 % 136.14/20.13 (3) op(e1, e1) = all_6_2 % 136.14/20.13 (4) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 136.14/20.13 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 136.14/20.13 (5) ~ (all_52_9 = all_6_2) % 136.14/20.13 (6) op(e2, e0) = all_52_13 % 136.14/20.13 (7) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & % 136.14/20.13 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & % 136.14/20.13 $i(all_40_1)) % 136.14/20.13 (8) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 136.14/20.13 (9) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 136.14/20.13 (10) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.13 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 136.14/20.13 (11) ~ (all_52_11 = e2) % 136.14/20.13 (12) ~ (e2 = e0) % 136.14/20.13 (13) ~ (all_52_4 = all_52_12) % 136.14/20.13 (14) ~ (all_52_1 = all_52_2) % 136.14/20.13 (15) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.14/20.13 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.13 (16) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) % 136.14/20.13 | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = % 136.14/20.13 e3) % 136.14/20.13 (17) all_40_2 = all_6_2 % 136.14/20.13 (18) ( ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 & $i(all_22_0)) | ( ~ % 136.14/20.13 (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1)) % 136.14/20.13 (19) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 136.14/20.13 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 136.14/20.13 (20) ~ (all_52_7 = e3) % 136.14/20.13 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.13 (22) ~ (e2 = e1) % 136.14/20.13 (23) op(e2, e0) = all_26_0 % 136.14/20.13 (24) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 136.14/20.13 (25) ~ (all_52_1 = all_52_13) % 136.14/20.13 (26) ~ (all_52_2 = e1) % 136.14/20.13 (27) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) % 136.14/20.13 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = % 136.14/20.13 e2) % 136.14/20.13 (28) op(e2, e2) = e3 % 136.14/20.13 (29) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.14/20.13 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.14/20.13 (30) all_54_3 = all_52_12 % 136.14/20.13 (31) ~ (all_52_1 = all_52_9) % 136.14/20.13 (32) ~ (all_52_12 = e0) % 136.14/20.13 (33) ~ (all_52_11 = all_6_2) % 136.14/20.13 (34) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 136.14/20.13 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 136.14/20.13 (35) op(e0, e1) = all_52_11 % 136.14/20.13 (36) op(e0, e2) = all_52_7 % 136.14/20.13 (37) ~ (all_52_12 = all_10_2) % 136.14/20.13 (38) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 136.14/20.13 (39) ~ (all_10_2 = e0) % 136.14/20.13 (40) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 136.14/20.13 (41) ~ (all_6_2 = e2) % 136.14/20.13 (42) ~ (all_52_13 = e2) % 136.14/20.13 (43) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.14/20.13 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.14/20.13 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.14/20.13 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.14/20.13 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.14/20.13 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.13 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) % 136.14/20.13 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.14/20.13 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.13 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 136.14/20.13 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.14/20.13 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 136.14/20.13 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 136.14/20.13 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.14/20.13 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) % 136.14/20.13 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.14/20.13 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 136.14/20.13 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 136.14/20.13 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.14/20.13 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.14/20.13 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.13 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 136.14/20.13 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & % 136.14/20.13 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & % 136.14/20.13 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.13 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 136.14/20.13 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.14/20.13 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.13 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ % 136.14/20.13 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.14/20.13 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 136.14/20.13 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 136.14/20.13 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.14/20.13 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) % 136.14/20.13 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.14/20.13 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.14/20.13 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 % 136.14/20.13 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.14/20.13 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = % 136.14/20.13 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 136.14/20.13 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 136.14/20.13 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.14/20.13 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.14/20.13 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 136.14/20.13 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 136.14/20.13 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.14/20.13 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.14/20.13 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.14/20.13 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.14/20.13 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.14/20.13 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.14/20.13 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.14/20.13 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.14/20.13 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.14/20.13 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.14/20.13 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.14/20.13 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.14/20.13 $i(all_56_29)))) % 136.14/20.13 (44) ~ (all_26_0 = e1) % 136.14/20.13 (45) op(e2, e0) = e0 % 136.14/20.13 (46) op(e3, e3) = all_10_2 % 136.14/20.13 (47) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) | % 136.14/20.13 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.13 (48) ~ (all_52_9 = e3) % 136.14/20.13 (49) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.13 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 136.14/20.13 e1) % 136.14/20.13 (50) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.13 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.13 (51) op(e2, e1) = all_52_9 % 136.14/20.13 (52) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.14/20.13 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.14/20.13 (53) op(e1, e3) = all_52_2 % 136.14/20.13 (54) ~ (all_52_8 = all_52_12) % 136.14/20.13 (55) op(e3, e2) = all_52_4 % 136.14/20.13 (56) ~ (all_52_12 = e2) % 136.14/20.13 (57) ~ (all_52_13 = e3) % 136.14/20.13 (58) all_57_10 = e0 % 136.14/20.13 (59) ~ (all_52_1 = e3) % 136.14/20.13 (60) op(e0, e0) = e2 % 136.14/20.13 (61) ~ (all_10_2 = e2) % 136.14/20.13 (62) all_57_3 = e3 % 136.14/20.13 (63) op(e2, e3) = all_52_1 % 136.14/20.13 (64) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.13 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.14/20.13 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.13 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.13 (65) all_54_7 = all_52_13 % 136.14/20.13 (66) op(e3, e1) = all_52_8 % 136.14/20.13 (67) ~ (all_52_9 = all_52_11) % 136.14/20.13 (68) all_54_14 = all_52_11 % 136.14/20.13 (69) ~ (e1 = e0) % 136.14/20.13 (70) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.13 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.14/20.13 (71) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.13 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 136.14/20.13 (72) all_54_4 = all_52_1 % 136.14/20.13 (73) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.14/20.13 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.14/20.13 (74) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 136.14/20.13 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 136.14/20.13 (75) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) | % 136.14/20.13 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.13 (76) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | % 136.14/20.13 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 136.14/20.13 % 136.14/20.13 Begin of proof % 136.14/20.13 | % 136.14/20.13 | BETA: splitting (24) gives: % 136.14/20.13 | % 136.14/20.13 | Case 1: % 136.14/20.13 | | % 136.14/20.13 | | (77) all_54_3 = e3 % 136.14/20.13 | | % 136.14/20.13 | | COMBINE_EQS: (30), (77) imply: % 136.14/20.13 | | (78) all_52_12 = e3 % 136.14/20.13 | | % 136.14/20.13 | | REDUCE: (13), (78) imply: % 136.14/20.13 | | (79) ~ (all_52_4 = e3) % 136.14/20.13 | | % 136.14/20.13 | | REDUCE: (37), (78) imply: % 136.14/20.13 | | (80) ~ (all_10_2 = e3) % 136.14/20.13 | | % 136.14/20.13 | | SIMP: (80) implies: % 136.14/20.13 | | (81) ~ (all_10_2 = e3) % 136.14/20.13 | | % 136.14/20.13 | | REDUCE: (56), (78) imply: % 136.14/20.13 | | (82) ~ (e3 = e2) % 136.14/20.13 | | % 136.14/20.13 | | REDUCE: (1), (78) imply: % 136.14/20.13 | | (83) ~ (e3 = e1) % 136.14/20.13 | | % 136.14/20.13 | | REDUCE: (32), (78) imply: % 136.14/20.13 | | (84) ~ (e3 = e0) % 136.14/20.13 | | % 136.14/20.13 | | BETA: splitting (40) gives: % 136.14/20.13 | | % 136.14/20.13 | | Case 1: % 136.14/20.13 | | | % 136.14/20.13 | | | (85) all_54_0 = e3 % 136.14/20.13 | | | % 136.14/20.13 | | | COMBINE_EQS: (2), (85) imply: % 136.14/20.13 | | | (86) all_10_2 = e3 % 136.14/20.13 | | | % 136.14/20.13 | | | REDUCE: (81), (86) imply: % 136.14/20.13 | | | (87) $false % 136.14/20.13 | | | % 136.14/20.13 | | | CLOSE: (87) is inconsistent. % 136.14/20.13 | | | % 136.14/20.13 | | Case 2: % 136.14/20.13 | | | % 136.14/20.13 | | | (88) ~ (all_54_0 = e3) % 136.14/20.13 | | | (89) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 136.14/20.13 | | | % 136.14/20.13 | | | BETA: splitting (89) gives: % 136.14/20.13 | | | % 136.14/20.13 | | | Case 1: % 136.14/20.13 | | | | % 136.14/20.13 | | | | (90) all_54_0 = e2 % 136.14/20.13 | | | | % 136.14/20.13 | | | | COMBINE_EQS: (2), (90) imply: % 136.14/20.13 | | | | (91) all_10_2 = e2 % 136.14/20.13 | | | | % 136.14/20.13 | | | | REDUCE: (61), (91) imply: % 136.14/20.13 | | | | (92) $false % 136.14/20.13 | | | | % 136.14/20.13 | | | | CLOSE: (92) is inconsistent. % 136.14/20.13 | | | | % 136.14/20.13 | | | Case 2: % 136.14/20.13 | | | | % 136.14/20.13 | | | | (93) ~ (all_54_0 = e2) % 136.14/20.13 | | | | (94) all_54_0 = e1 | all_54_0 = e0 % 136.14/20.13 | | | | % 136.14/20.13 | | | | BETA: splitting (43) gives: % 136.14/20.13 | | | | % 136.14/20.13 | | | | Case 1: % 136.14/20.13 | | | | | % 136.14/20.14 | | | | | (95) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ % 136.14/20.14 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) % 136.14/20.14 | | | | | & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 % 136.14/20.14 | | | | | & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.14/20.14 | | | | | e0) = all_56_27 & $i(all_56_3) & $i(all_56_11) & % 136.14/20.14 | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & all_56_17 % 136.14/20.14 | | | | | = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.14 | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 136.14/20.14 | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.14/20.14 | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 % 136.14/20.14 | | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.14/20.14 | | | | | $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 136.14/20.14 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 136.14/20.14 | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & % 136.14/20.14 | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) % 136.14/20.14 | | | | | = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.14/20.14 | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = % 136.14/20.14 | | | | | e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.14/20.14 | | | | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, % 136.14/20.14 | | | | | e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.14/20.14 | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 136.14/20.14 | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.14 | | | | | $i(all_56_17) & $i(all_56_25)) % 136.14/20.14 | | | | | % 136.14/20.14 | | | | | BETA: splitting (95) gives: % 136.14/20.14 | | | | | % 136.14/20.14 | | | | | Case 1: % 136.14/20.14 | | | | | | % 136.14/20.14 | | | | | | (96) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ % 136.14/20.14 | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = % 136.14/20.14 | | | | | | e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = % 136.14/20.14 | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 136.14/20.14 | | | | | | & op(e2, e0) = all_56_27 & $i(all_56_3) & $i(all_56_11) & % 136.14/20.14 | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.14/20.14 | | | | | | all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) % 136.14/20.14 | | | | | | & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = % 136.14/20.14 | | | | | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) % 136.14/20.14 | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.14/20.14 | | | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.14/20.14 | | | | | | $i(all_56_29)) % 136.14/20.14 | | | | | | % 136.14/20.14 | | | | | | BETA: splitting (96) gives: % 136.14/20.14 | | | | | | % 136.14/20.14 | | | | | | Case 1: % 136.14/20.14 | | | | | | | % 136.14/20.14 | | | | | | | (97) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ % 136.14/20.14 | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = % 136.14/20.14 | | | | | | | e0) & op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = % 136.14/20.14 | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 136.14/20.14 | | | | | | | & op(e2, e0) = all_56_27 & $i(all_56_3) & $i(all_56_11) & % 136.14/20.14 | | | | | | | $i(all_56_19) & $i(all_56_27) % 136.14/20.14 | | | | | | | % 136.14/20.14 | | | | | | | ALPHA: (97) implies: % 136.14/20.14 | | | | | | | (98) op(e3, e3) = e2 % 136.14/20.14 | | | | | | | % 136.14/20.14 | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (12), (14), % 136.14/20.14 | | | | | | | (15), (16), (17), (19), (20), (21), (22), (23), (25), % 136.14/20.14 | | | | | | | (27), (28), (29), (31), (33), (34), (35), (36), (38), % 136.14/20.14 | | | | | | | (41), (42), (43), (44), (47), (48), (49), (50), (51), % 136.14/20.14 | | | | | | | (52), (53), (55), (57), (59), (60), (62), (63), (64), % 136.14/20.14 | | | | | | | (65), (67), (68), (69), (70), (71), (72), (73), (74), % 136.14/20.14 | | | | | | | (75), (76), (79), (82), (83), (84), (98) are % 136.14/20.14 | | | | | | | inconsistent by sub-proof #267. % 136.14/20.14 | | | | | | | % 136.14/20.14 | | | | | | Case 2: % 136.14/20.14 | | | | | | | % 136.14/20.14 | | | | | | | (99) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ % 136.14/20.14 | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = % 136.14/20.14 | | | | | | | e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = % 136.14/20.14 | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 % 136.14/20.14 | | | | | | | & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.14 | | | | | | | $i(all_56_21) & $i(all_56_29) % 136.14/20.14 | | | | | | | % 136.14/20.14 | | | | | | | ALPHA: (99) implies: % 136.14/20.14 | | | | | | | (100) op(e3, e1) = e3 % 136.14/20.14 | | | | | | | % 136.14/20.14 | | | | | | | REF_CLOSE: (1), (21), (24), (30), (32), (54), (56), (66), (100) % 136.14/20.14 | | | | | | | are inconsistent by sub-proof #319. % 136.14/20.14 | | | | | | | % 136.14/20.14 | | | | | | End of split % 136.14/20.14 | | | | | | % 136.14/20.14 | | | | | Case 2: % 136.14/20.14 | | | | | | % 136.14/20.14 | | | | | | (101) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ % 136.14/20.14 | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = % 136.14/20.14 | | | | | | e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 136.14/20.14 | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 136.14/20.14 | | | | | | all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.14/20.14 | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 136.14/20.14 | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ % 136.14/20.14 | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = % 136.14/20.14 | | | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 136.14/20.14 | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e2, % 136.14/20.14 | | | | | | e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & % 136.14/20.14 | | | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 136.14/20.14 | | | | | | % 136.14/20.14 | | | | | | BETA: splitting (101) gives: % 136.14/20.14 | | | | | | % 136.14/20.14 | | | | | | Case 1: % 136.14/20.14 | | | | | | | % 136.14/20.14 | | | | | | | (102) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ % 136.14/20.14 | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = % 136.14/20.14 | | | | | | | e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 136.14/20.14 | | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 136.14/20.14 | | | | | | | all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.14/20.14 | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.14/20.14 | | | | | | | % 136.14/20.14 | | | | | | | ALPHA: (102) implies: % 136.14/20.14 | | | | | | | (103) op(e3, e3) = e0 % 136.14/20.14 | | | | | | | % 136.14/20.14 | | | | | | | REF_CLOSE: (2), (21), (39), (46), (94), (103) are inconsistent by % 136.14/20.14 | | | | | | | sub-proof #263. % 136.14/20.14 | | | | | | | % 136.14/20.14 | | | | | | Case 2: % 136.14/20.14 | | | | | | | % 136.14/20.14 | | | | | | | (104) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ % 136.14/20.14 | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = % 136.14/20.14 | | | | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 136.14/20.14 | | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e2, % 136.14/20.14 | | | | | | | e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & % 136.14/20.14 | | | | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.14/20.14 | | | | | | | % 136.14/20.14 | | | | | | | ALPHA: (104) implies: % 136.14/20.14 | | | | | | | (105) op(e2, e3) = e2 % 136.14/20.14 | | | | | | | % 136.14/20.14 | | | | | | | BETA: splitting (94) gives: % 136.14/20.14 | | | | | | | % 136.14/20.14 | | | | | | | Case 1: % 136.14/20.14 | | | | | | | | % 136.14/20.14 | | | | | | | | (106) all_54_0 = e1 % 136.14/20.14 | | | | | | | | % 136.14/20.14 | | | | | | | | COMBINE_EQS: (2), (106) imply: % 136.14/20.14 | | | | | | | | (107) all_10_2 = e1 % 136.14/20.14 | | | | | | | | % 136.14/20.14 | | | | | | | | SIMP: (107) implies: % 136.14/20.14 | | | | | | | | (108) all_10_2 = e1 % 136.14/20.14 | | | | | | | | % 136.14/20.14 | | | | | | | | REDUCE: (81), (108) imply: % 136.14/20.14 | | | | | | | | (109) ~ (e3 = e1) % 136.14/20.14 | | | | | | | | % 136.14/20.14 | | | | | | | | REDUCE: (61), (108) imply: % 136.14/20.14 | | | | | | | | (110) ~ (e2 = e1) % 136.14/20.14 | | | | | | | | % 136.14/20.14 | | | | | | | | REDUCE: (46), (108) imply: % 136.14/20.14 | | | | | | | | (111) op(e3, e3) = e1 % 136.14/20.14 | | | | | | | | % 136.14/20.14 | | | | | | | | BETA: splitting (70) gives: % 136.14/20.14 | | | | | | | | % 136.14/20.14 | | | | | | | | Case 1: % 136.14/20.14 | | | | | | | | | % 136.14/20.14 | | | | | | | | | (112) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & % 136.14/20.14 | | | | | | | | | op(e2, e2) = e1) % 136.14/20.14 | | | | | | | | | % 136.14/20.14 | | | | | | | | | REF_CLOSE: (21), (22), (28), (83), (105), (112) are % 136.14/20.14 | | | | | | | | | inconsistent by sub-proof #292. % 136.14/20.14 | | | | | | | | | % 136.14/20.14 | | | | | | | | Case 2: % 136.14/20.14 | | | | | | | | | % 136.14/20.14 | | | | | | | | | (113) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & % 136.14/20.14 | | | | | | | | | op(e2, e0) = e1) % 136.14/20.14 | | | | | | | | | % 136.14/20.14 | | | | | | | | | BETA: splitting (113) gives: % 136.14/20.14 | | | | | | | | | % 136.14/20.14 | | | | | | | | | Case 1: % 136.14/20.14 | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | (114) all_57_5 = e1 & op(e2, e1) = e1 % 136.14/20.14 | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | ALPHA: (114) implies: % 136.14/20.14 | | | | | | | | | | (115) all_57_5 = e1 % 136.14/20.14 | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | BETA: splitting (76) gives: % 136.14/20.14 | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | Case 1: % 136.14/20.14 | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | (116) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 136.14/20.14 | | | | | | | | | | | & op(e2, e1) = e2) % 136.14/20.14 | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | BETA: splitting (116) gives: % 136.14/20.14 | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | Case 1: % 136.14/20.14 | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | (117) all_57_4 = e2 & op(e3, e1) = e2 % 136.14/20.14 | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | ALPHA: (117) implies: % 136.14/20.14 | | | | | | | | | | | | (118) all_57_4 = e2 % 136.14/20.14 | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | BETA: splitting (18) gives: % 136.14/20.14 | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | Case 1: % 136.14/20.14 | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | (119) ~ (all_22_0 = e0) & op(e3, e2) = all_22_0 & % 136.14/20.14 | | | | | | | | | | | | | $i(all_22_0) % 136.14/20.14 | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | ALPHA: (119) implies: % 136.14/20.14 | | | | | | | | | | | | | (120) ~ (all_22_0 = e0) % 136.14/20.14 | | | | | | | | | | | | | (121) op(e3, e2) = all_22_0 % 136.14/20.14 | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | BETA: splitting (15) gives: % 136.14/20.14 | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | Case 1: % 136.14/20.14 | | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | | (122) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 136.14/20.14 | | | | | | | | | | | | | | & op(e3, e2) = e0) % 136.14/20.14 | | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | | REF_CLOSE: (21), (69), (111), (120), (121), (122) are % 136.14/20.14 | | | | | | | | | | | | | | inconsistent by sub-proof #307. % 136.14/20.14 | | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | Case 2: % 136.14/20.14 | | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | | (123) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 136.14/20.14 | | | | | | | | | | | | | | & op(e3, e0) = e0) % 136.14/20.14 | | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | | BETA: splitting (123) gives: % 136.14/20.14 | | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | | Case 1: % 136.14/20.14 | | | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | | | (124) all_57_4 = e0 & op(e3, e1) = e0 % 136.14/20.14 | | | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | | | REF_CLOSE: (12), (118), (124) are inconsistent by sub-proof % 136.14/20.14 | | | | | | | | | | | | | | | #647. % 136.14/20.14 | | | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | | Case 2: % 136.14/20.14 | | | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | | | (125) all_57_9 = e0 & op(e3, e0) = e0 % 136.14/20.14 | | | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | | | ALPHA: (125) implies: % 136.14/20.14 | | | | | | | | | | | | | | | (126) all_57_9 = e0 % 136.14/20.14 | | | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | | | REF_CLOSE: (6), (21), (22), (47), (57), (58), (60), (69), % 136.14/20.14 | | | | | | | | | | | | | | | (75), (82), (83), (84), (126) are inconsistent by % 136.14/20.14 | | | | | | | | | | | | | | | sub-proof #294. % 136.14/20.14 | | | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | | End of split % 136.14/20.14 | | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | End of split % 136.14/20.14 | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | Case 2: % 136.14/20.14 | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | (127) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & % 136.14/20.14 | | | | | | | | | | | | | $i(all_22_1) % 136.14/20.14 | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | | REF_CLOSE: (21), (111), (127) are inconsistent by sub-proof % 136.14/20.14 | | | | | | | | | | | | | #305. % 136.14/20.14 | | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | End of split % 136.14/20.14 | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | Case 2: % 136.14/20.14 | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | (128) all_57_5 = e2 & op(e2, e1) = e2 % 136.14/20.14 | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | ALPHA: (128) implies: % 136.14/20.14 | | | | | | | | | | | | (129) all_57_5 = e2 % 136.14/20.14 | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | | REF_CLOSE: (22), (115), (129) are inconsistent by sub-proof % 136.14/20.14 | | | | | | | | | | | | #418. % 136.14/20.14 | | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | End of split % 136.14/20.14 | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | Case 2: % 136.14/20.14 | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | (130) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 136.14/20.14 | | | | | | | | | | | e2 & op(e0, e1) = e2) % 136.14/20.14 | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | | REF_CLOSE: (3), (12), (16), (20), (21), (22), (36), (41), % 136.14/20.14 | | | | | | | | | | | (49), (60), (64), (69), (82), (83), (84), (130) % 136.14/20.14 | | | | | | | | | | | are inconsistent by sub-proof #262. % 136.14/20.14 | | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | End of split % 136.14/20.14 | | | | | | | | | | % 136.14/20.14 | | | | | | | | | Case 2: % 136.14/20.14 | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | (131) all_57_10 = e1 & op(e2, e0) = e1 % 136.14/20.14 | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | ALPHA: (131) implies: % 136.14/20.14 | | | | | | | | | | (132) op(e2, e0) = e1 % 136.14/20.14 | | | | | | | | | | % 136.14/20.14 | | | | | | | | | | REF_CLOSE: (21), (45), (69), (132) are inconsistent by % 136.14/20.14 | | | | | | | | | | sub-proof #695. % 136.14/20.14 | | | | | | | | | | % 136.14/20.14 | | | | | | | | | End of split % 136.14/20.14 | | | | | | | | | % 136.14/20.14 | | | | | | | | End of split % 136.14/20.14 | | | | | | | | % 136.14/20.14 | | | | | | | Case 2: % 136.14/20.14 | | | | | | | | % 136.14/20.14 | | | | | | | | (133) all_54_0 = e0 % 136.14/20.14 | | | | | | | | % 136.14/20.14 | | | | | | | | REF_CLOSE: (2), (39), (133) are inconsistent by sub-proof #264. % 136.14/20.14 | | | | | | | | % 136.14/20.14 | | | | | | | End of split % 136.14/20.14 | | | | | | | % 136.14/20.14 | | | | | | End of split % 136.14/20.14 | | | | | | % 136.14/20.14 | | | | | End of split % 136.14/20.14 | | | | | % 136.14/20.14 | | | | Case 2: % 136.14/20.14 | | | | | % 136.14/20.14 | | | | | (134) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ % 136.14/20.14 | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) % 136.14/20.14 | | | | | & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 136.14/20.14 | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e1, e3) = % 136.14/20.14 | | | | | e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.14 | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & % 136.14/20.14 | | | | | all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & % 136.14/20.14 | | | | | ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 % 136.14/20.14 | | | | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.14/20.14 | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 % 136.14/20.14 | | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.14/20.14 | | | | | $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ % 136.14/20.14 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 136.14/20.14 | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & % 136.14/20.14 | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) % 136.14/20.14 | | | | | = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.14/20.14 | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_13 % 136.14/20.14 | | | | | = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.14/20.14 | | | | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.14/20.14 | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) % 136.14/20.14 | | | | | = all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 136.14/20.14 | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 136.14/20.14 | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 & % 136.14/20.14 | | | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 136.14/20.14 | | | | | (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 136.14/20.14 | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.14/20.14 | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.14/20.14 | | | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & % 136.14/20.14 | | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.14/20.14 | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 136.14/20.14 | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 136.14/20.14 | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.14/20.14 | | | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 136.14/20.14 | | | | | all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 136.14/20.14 | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.14/20.14 | | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 136.14/20.14 | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.14/20.14 | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & % 136.14/20.14 | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, % 136.14/20.14 | | | | | e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & % 136.14/20.14 | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~ % 136.14/20.14 | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 136.14/20.14 | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 136.14/20.14 | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & % 136.14/20.14 | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) % 136.14/20.14 | | | | | & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)))) % 136.14/20.14 | | | | | % 136.14/20.14 | | | | | BETA: splitting (134) gives: % 136.14/20.14 | | | | | % 136.14/20.14 | | | | | Case 1: % 136.14/20.14 | | | | | | % 136.14/20.14 | | | | | | (135) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ % 136.14/20.14 | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = % 136.14/20.14 | | | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 136.14/20.14 | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e1, % 136.14/20.14 | | | | | | e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & % 136.14/20.14 | | | | | | $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.14/20.14 | | | | | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 136.14/20.14 | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = % 136.14/20.14 | | | | | | e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = % 136.14/20.14 | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.14/20.14 | | | | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.14/20.14 | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 136.14/20.14 | | | | | | % 136.14/20.14 | | | | | | REF_CLOSE: (21), (26), (28), (53), (83), (135) are inconsistent by % 136.14/20.14 | | | | | | sub-proof #304. % 136.14/20.14 | | | | | | % 136.14/20.14 | | | | | Case 2: % 136.14/20.14 | | | | | | % 136.14/20.14 | | | | | | (136) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 136.14/20.14 | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = % 136.14/20.14 | | | | | | e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 136.14/20.14 | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 136.14/20.14 | | | | | | all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.14/20.14 | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 136.14/20.14 | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 136.14/20.14 | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = % 136.14/20.14 | | | | | | e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.14/20.14 | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e1, % 136.14/20.14 | | | | | | e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 136.14/20.14 | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, % 136.14/20.14 | | | | | | e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 136.14/20.14 | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.14/20.14 | | | | | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.14/20.14 | | | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 136.14/20.14 | | | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.14/20.14 | | | | | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.14 | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & % 136.14/20.14 | | | | | | all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.14/20.14 | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.14/20.14 | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.14/20.14 | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.14/20.14 | | | | | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 136.14/20.14 | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & % 136.14/20.14 | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.14/20.14 | | | | | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.14/20.14 | | | | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 136.14/20.14 | | | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 136.14/20.14 | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 136.14/20.14 | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & % 136.14/20.14 | | | | | | ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.14 | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 136.14/20.14 | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.14/20.14 | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 % 136.14/20.14 | | | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.14/20.14 | | | | | | $i(all_56_29)))) % 136.14/20.14 | | | | | | % 136.14/20.14 | | | | | | REF_CLOSE: (3), (7), (11), (17), (21), (22), (28), (33), (35), (38), % 136.14/20.14 | | | | | | (41), (45), (60), (68), (82), (84), (136) are % 136.14/20.14 | | | | | | inconsistent by sub-proof #265. % 136.14/20.14 | | | | | | % 136.14/20.14 | | | | | End of split % 136.14/20.14 | | | | | % 136.14/20.14 | | | | End of split % 136.14/20.14 | | | | % 136.14/20.14 | | | End of split % 136.14/20.14 | | | % 136.14/20.14 | | End of split % 136.14/20.14 | | % 136.14/20.14 | Case 2: % 136.14/20.14 | | % 136.14/20.14 | | (137) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 136.14/20.14 | | % 136.14/20.14 | | REF_CLOSE: (1), (30), (32), (56), (137) are inconsistent by sub-proof #320. % 136.14/20.14 | | % 136.14/20.14 | End of split % 136.14/20.14 | % 136.14/20.14 End of proof % 136.14/20.14 % 136.14/20.14 Sub-proof #262 shows that the following formulas are inconsistent: % 136.14/20.14 ---------------------------------------------------------------- % 136.14/20.14 (1) op(e1, e1) = all_6_2 % 136.14/20.14 (2) ~ (e2 = e0) % 136.14/20.14 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 136.14/20.14 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.14 (4) ~ (all_52_7 = e3) % 136.14/20.14 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.14 (6) ~ (e2 = e1) % 136.14/20.14 (7) ~ (e3 = e0) % 136.14/20.14 (8) ~ (e3 = e2) % 136.14/20.14 (9) op(e0, e2) = all_52_7 % 136.14/20.14 (10) ~ (all_6_2 = e2) % 136.14/20.14 (11) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.14 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 136.14/20.14 e1) % 136.14/20.14 (12) op(e0, e0) = e2 % 136.14/20.14 (13) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.14 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.14/20.14 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.14 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.14 (14) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 136.14/20.14 (15) ~ (e3 = e1) % 136.14/20.14 (16) ~ (e1 = e0) % 136.14/20.14 % 136.14/20.14 Begin of proof % 136.14/20.14 | % 136.14/20.14 | BETA: splitting (14) gives: % 136.14/20.14 | % 136.14/20.14 | Case 1: % 136.14/20.14 | | % 136.14/20.14 | | (17) all_57_8 = e2 & op(e1, e1) = e2 % 136.14/20.14 | | % 136.14/20.14 | | ALPHA: (17) implies: % 136.14/20.14 | | (18) op(e1, e1) = e2 % 136.14/20.14 | | % 136.14/20.14 | | REF_CLOSE: (1), (5), (10), (18) are inconsistent by sub-proof #767. % 136.14/20.14 | | % 136.14/20.14 | Case 2: % 136.14/20.14 | | % 136.14/20.14 | | (19) all_57_14 = e2 & op(e0, e1) = e2 % 136.14/20.14 | | % 136.14/20.14 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (15), % 136.14/20.14 | | (16), (19) are inconsistent by sub-proof #283. % 136.14/20.14 | | % 136.14/20.14 | End of split % 136.14/20.14 | % 136.14/20.14 End of proof % 136.14/20.14 % 136.14/20.14 Sub-proof #263 shows that the following formulas are inconsistent: % 136.14/20.14 ---------------------------------------------------------------- % 136.14/20.14 (1) all_54_0 = all_10_2 % 136.14/20.14 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.14 (3) ~ (all_10_2 = e0) % 136.14/20.14 (4) op(e3, e3) = all_10_2 % 136.14/20.14 (5) all_54_0 = e1 | all_54_0 = e0 % 136.14/20.14 (6) op(e3, e3) = e0 % 136.14/20.14 % 136.14/20.14 Begin of proof % 136.14/20.14 | % 136.14/20.14 | BETA: splitting (5) gives: % 136.14/20.14 | % 136.14/20.14 | Case 1: % 136.14/20.14 | | % 136.14/20.14 | | (7) all_54_0 = e1 % 136.14/20.14 | | % 136.14/20.14 | | COMBINE_EQS: (1), (7) imply: % 136.14/20.14 | | (8) all_10_2 = e1 % 136.14/20.14 | | % 136.14/20.14 | | SIMP: (8) implies: % 136.14/20.14 | | (9) all_10_2 = e1 % 136.14/20.14 | | % 136.14/20.14 | | REDUCE: (3), (9) imply: % 136.14/20.14 | | (10) ~ (e1 = e0) % 136.14/20.14 | | % 136.14/20.14 | | REDUCE: (4), (9) imply: % 136.14/20.14 | | (11) op(e3, e3) = e1 % 136.14/20.14 | | % 136.14/20.14 | | REF_CLOSE: (2), (6), (10), (11) are inconsistent by sub-proof #717. % 136.14/20.14 | | % 136.14/20.14 | Case 2: % 136.14/20.14 | | % 136.14/20.14 | | (12) all_54_0 = e0 % 136.14/20.14 | | % 136.14/20.14 | | REF_CLOSE: (1), (3), (12) are inconsistent by sub-proof #264. % 136.14/20.14 | | % 136.14/20.14 | End of split % 136.14/20.14 | % 136.14/20.14 End of proof % 136.14/20.14 % 136.14/20.14 Sub-proof #264 shows that the following formulas are inconsistent: % 136.14/20.14 ---------------------------------------------------------------- % 136.14/20.14 (1) all_54_0 = all_10_2 % 136.14/20.14 (2) all_54_0 = e0 % 136.14/20.14 (3) ~ (all_10_2 = e0) % 136.14/20.14 % 136.14/20.14 Begin of proof % 136.14/20.14 | % 136.14/20.14 | COMBINE_EQS: (1), (2) imply: % 136.14/20.14 | (4) all_10_2 = e0 % 136.14/20.14 | % 136.14/20.14 | SIMP: (4) implies: % 136.14/20.14 | (5) all_10_2 = e0 % 136.14/20.14 | % 136.14/20.14 | REDUCE: (3), (5) imply: % 136.14/20.14 | (6) $false % 136.14/20.14 | % 136.14/20.14 | CLOSE: (6) is inconsistent. % 136.14/20.14 | % 136.14/20.14 End of proof % 136.14/20.14 % 136.14/20.14 Sub-proof #265 shows that the following formulas are inconsistent: % 136.14/20.14 ---------------------------------------------------------------- % 136.14/20.14 (1) op(e1, e1) = all_6_2 % 136.14/20.14 (2) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & % 136.14/20.14 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & % 136.14/20.14 $i(all_40_1)) % 136.14/20.14 (3) ~ (all_52_11 = e2) % 136.14/20.14 (4) all_40_2 = all_6_2 % 136.14/20.14 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.14 (6) ~ (e2 = e1) % 136.14/20.14 (7) ~ (e3 = e0) % 136.14/20.14 (8) ~ (e3 = e2) % 136.14/20.14 (9) op(e2, e2) = e3 % 136.14/20.14 (10) ~ (all_52_11 = all_6_2) % 136.14/20.14 (11) op(e0, e1) = all_52_11 % 136.14/20.14 (12) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 136.14/20.14 (13) ~ (all_6_2 = e2) % 136.14/20.14 (14) op(e2, e0) = e0 % 136.14/20.14 (15) op(e0, e0) = e2 % 136.14/20.14 (16) all_54_14 = all_52_11 % 136.14/20.14 (17) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.14/20.14 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 136.14/20.14 op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.14/20.14 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.14/20.14 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 & % 136.14/20.14 all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ % 136.14/20.14 (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 136.14/20.14 op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 136.14/20.14 all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 136.14/20.14 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 136.14/20.14 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 136.14/20.14 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 136.14/20.14 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 136.14/20.14 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 % 136.14/20.14 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.14/20.14 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.14/20.14 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.14/20.14 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.14/20.14 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.14/20.14 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.14/20.14 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.14/20.14 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.14/20.14 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.14/20.14 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.14/20.14 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.14/20.14 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.14/20.14 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.14/20.14 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.14/20.14 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.14/20.14 $i(all_56_29)))) % 136.14/20.14 % 136.14/20.14 Begin of proof % 136.14/20.14 | % 136.14/20.14 | BETA: splitting (17) gives: % 136.14/20.14 | % 136.14/20.14 | Case 1: % 136.14/20.14 | | % 136.14/20.14 | | (18) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ (all_56_15 % 136.14/20.14 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e2, e2) = % 136.14/20.14 | | e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 136.14/20.14 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 136.14/20.14 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.14/20.14 | | % 136.14/20.14 | | ALPHA: (18) implies: % 136.14/20.14 | | (19) op(e2, e2) = e0 % 136.14/20.14 | | % 136.14/20.14 | | REF_CLOSE: (5), (7), (9), (19) are inconsistent by sub-proof #641. % 136.14/20.14 | | % 136.14/20.14 | Case 2: % 136.14/20.14 | | % 136.14/20.14 | | (20) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 136.14/20.14 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.14/20.14 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.14/20.14 | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) % 136.14/20.14 | | = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.14/20.14 | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 136.14/20.14 | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.14/20.14 | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.14/20.14 | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.14/20.14 | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.14/20.14 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.14/20.14 | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.14/20.14 | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.14/20.14 | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.14/20.14 | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.14/20.14 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 136.14/20.14 | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.14/20.14 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.14/20.14 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 136.14/20.14 | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) % 136.14/20.14 | | & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 136.14/20.14 | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.14 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 % 136.14/20.14 | | & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.14/20.14 | | = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.14 | | $i(all_56_21) & $i(all_56_29)))) % 136.14/20.14 | | % 136.14/20.14 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (12), (13), (14), % 136.14/20.14 | | (15), (16), (20) are inconsistent by sub-proof #266. % 136.14/20.14 | | % 136.14/20.14 | End of split % 136.14/20.14 | % 136.14/20.14 End of proof % 136.14/20.14 % 136.14/20.14 Sub-proof #266 shows that the following formulas are inconsistent: % 136.14/20.14 ---------------------------------------------------------------- % 136.14/20.14 (1) op(e1, e1) = all_6_2 % 136.14/20.14 (2) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & % 136.14/20.14 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & % 136.14/20.14 $i(all_40_1)) % 136.14/20.14 (3) ~ (all_52_11 = e2) % 136.14/20.14 (4) all_40_2 = all_6_2 % 136.14/20.14 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.14 (6) ~ (e2 = e1) % 136.14/20.14 (7) ~ (e3 = e2) % 136.14/20.14 (8) ~ (all_52_11 = all_6_2) % 136.14/20.14 (9) op(e0, e1) = all_52_11 % 136.14/20.14 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 136.14/20.14 (11) ~ (all_6_2 = e2) % 136.14/20.14 (12) op(e2, e0) = e0 % 136.14/20.14 (13) op(e0, e0) = e2 % 136.14/20.15 (14) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.14/20.15 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.14/20.15 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.14/20.15 e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 136.14/20.15 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 136.14/20.15 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 136.14/20.15 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 136.14/20.15 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 136.14/20.15 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 % 136.14/20.15 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.14/20.15 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.14/20.15 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.14/20.15 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.14/20.15 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.14/20.15 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.14/20.15 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.14/20.15 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.14/20.15 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.14/20.15 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.14/20.15 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.14/20.15 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.14/20.15 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.14/20.15 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.14/20.15 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.14/20.15 $i(all_56_29)))) % 136.14/20.15 (15) all_54_14 = all_52_11 % 136.14/20.15 % 136.14/20.15 Begin of proof % 136.14/20.15 | % 136.14/20.15 | BETA: splitting (14) gives: % 136.14/20.15 | % 136.14/20.15 | Case 1: % 136.14/20.15 | | % 136.14/20.15 | | (16) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.14/20.15 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.14/20.15 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.14/20.15 | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) % 136.14/20.15 | | & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.14/20.15 | | % 136.14/20.15 | | ALPHA: (16) implies: % 136.14/20.15 | | (17) op(e1, e1) = e2 % 136.14/20.15 | | % 136.14/20.15 | | REF_CLOSE: (1), (5), (11), (17) are inconsistent by sub-proof #767. % 136.14/20.15 | | % 136.14/20.15 | Case 2: % 136.14/20.15 | | % 136.14/20.15 | | (18) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 % 136.14/20.15 | | = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 136.14/20.15 | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) % 136.14/20.15 | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.14/20.15 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.14/20.15 | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 % 136.14/20.15 | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 136.14/20.15 | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.14/20.15 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.14/20.15 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.14/20.15 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 % 136.14/20.15 | | = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.14/20.15 | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, % 136.14/20.15 | | e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 136.14/20.15 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 136.14/20.15 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.14/20.15 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.14/20.15 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.14/20.15 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.14/20.15 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29))) % 136.14/20.15 | | % 136.14/20.15 | | ALPHA: (18) implies: % 136.14/20.15 | | (19) op(e0, e0) = all_56_31 % 136.14/20.15 | | (20) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.14/20.15 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.15 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.14/20.15 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 136.14/20.15 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 136.14/20.15 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 136.14/20.15 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.14/20.15 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.14/20.15 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.14/20.15 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 136.14/20.15 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 % 136.14/20.15 | | = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 136.14/20.15 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.14/20.15 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & % 136.14/20.15 | | all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.15 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 136.14/20.15 | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.14/20.15 | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.15 | | $i(all_56_21) & $i(all_56_29)) % 136.14/20.15 | | % 136.14/20.15 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), % 136.14/20.15 | | (15), (19), (20) are inconsistent by sub-proof #273. % 136.14/20.15 | | % 136.14/20.15 | End of split % 136.14/20.15 | % 136.14/20.15 End of proof % 136.14/20.15 % 136.14/20.15 Sub-proof #267 shows that the following formulas are inconsistent: % 136.14/20.15 ---------------------------------------------------------------- % 136.14/20.15 (1) op(e1, e1) = all_6_2 % 136.14/20.15 (2) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 136.14/20.15 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 136.14/20.15 (3) ~ (all_52_9 = all_6_2) % 136.14/20.15 (4) op(e2, e0) = all_52_13 % 136.14/20.15 (5) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & % 136.14/20.15 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & % 136.14/20.15 $i(all_40_1)) % 136.14/20.15 (6) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 136.14/20.15 (7) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 136.14/20.15 (8) op(e3, e3) = e2 % 136.14/20.15 (9) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.15 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 136.14/20.15 (10) ~ (e2 = e0) % 136.14/20.15 (11) ~ (all_52_1 = all_52_2) % 136.14/20.15 (12) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.14/20.15 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.15 (13) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) % 136.14/20.15 | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = % 136.14/20.15 e3) % 136.14/20.15 (14) all_40_2 = all_6_2 % 136.14/20.15 (15) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 136.14/20.15 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 136.14/20.15 (16) ~ (all_52_7 = e3) % 136.14/20.15 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.15 (18) ~ (e2 = e1) % 136.14/20.15 (19) ~ (e3 = e0) % 136.14/20.15 (20) op(e2, e0) = all_26_0 % 136.14/20.15 (21) ~ (all_52_1 = all_52_13) % 136.14/20.15 (22) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) % 136.14/20.15 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = % 136.14/20.15 e2) % 136.14/20.15 (23) ~ (e3 = e2) % 136.14/20.15 (24) op(e2, e2) = e3 % 136.14/20.15 (25) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.14/20.15 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.14/20.15 (26) ~ (all_52_1 = all_52_9) % 136.14/20.15 (27) ~ (all_52_11 = all_6_2) % 136.14/20.15 (28) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) | % 136.14/20.15 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 136.14/20.15 (29) op(e0, e1) = all_52_11 % 136.14/20.15 (30) op(e0, e2) = all_52_7 % 136.14/20.15 (31) ~ (all_52_4 = e3) % 136.14/20.15 (32) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 136.14/20.15 (33) ~ (all_6_2 = e2) % 136.14/20.15 (34) ~ (all_52_13 = e2) % 136.14/20.15 (35) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.14/20.15 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.14/20.15 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.14/20.15 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.14/20.15 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.14/20.15 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.15 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) % 136.14/20.15 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.14/20.15 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.15 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 136.14/20.15 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.14/20.15 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 136.14/20.15 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 136.14/20.15 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.14/20.15 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) % 136.14/20.15 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.14/20.15 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 136.14/20.15 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 136.14/20.15 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.14/20.15 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.14/20.15 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.15 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 136.14/20.15 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & % 136.14/20.15 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & % 136.14/20.15 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.15 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 136.14/20.15 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.14/20.15 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.15 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ % 136.14/20.15 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.14/20.15 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 136.14/20.15 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 136.14/20.15 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.14/20.15 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) % 136.14/20.15 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.14/20.15 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.14/20.15 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 % 136.14/20.15 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.14/20.15 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = % 136.14/20.15 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 136.14/20.15 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 136.14/20.15 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.14/20.15 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.14/20.15 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 136.14/20.15 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 136.14/20.15 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.14/20.15 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.14/20.15 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.14/20.15 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.14/20.15 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.14/20.15 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.14/20.15 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.14/20.15 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.14/20.15 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.14/20.15 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.14/20.15 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.14/20.15 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.14/20.15 $i(all_56_29)))) % 136.14/20.15 (36) ~ (all_26_0 = e1) % 136.14/20.15 (37) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) | % 136.14/20.15 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.15 (38) ~ (all_52_9 = e3) % 136.14/20.15 (39) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.15 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 136.14/20.15 e1) % 136.14/20.15 (40) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.15 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.15 (41) op(e2, e1) = all_52_9 % 136.14/20.15 (42) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.14/20.15 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.14/20.15 (43) op(e1, e3) = all_52_2 % 136.14/20.15 (44) op(e3, e2) = all_52_4 % 136.14/20.15 (45) ~ (all_52_13 = e3) % 136.14/20.15 (46) ~ (all_52_1 = e3) % 136.14/20.15 (47) op(e0, e0) = e2 % 136.14/20.15 (48) all_57_3 = e3 % 136.14/20.15 (49) op(e2, e3) = all_52_1 % 136.14/20.15 (50) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.15 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.14/20.15 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.15 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.15 (51) all_54_7 = all_52_13 % 136.14/20.15 (52) ~ (all_52_9 = all_52_11) % 136.14/20.15 (53) all_54_14 = all_52_11 % 136.14/20.15 (54) ~ (e3 = e1) % 136.14/20.15 (55) ~ (e1 = e0) % 136.14/20.15 (56) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.15 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.14/20.15 (57) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.15 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 136.14/20.15 (58) all_54_4 = all_52_1 % 136.14/20.15 (59) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.14/20.15 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.14/20.15 (60) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 136.14/20.15 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 136.14/20.15 (61) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) | % 136.14/20.15 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.15 (62) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | % 136.14/20.15 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 136.14/20.15 % 136.14/20.15 Begin of proof % 136.14/20.15 | % 136.14/20.15 | BETA: splitting (28) gives: % 136.14/20.15 | % 136.14/20.15 | Case 1: % 136.14/20.15 | | % 136.14/20.15 | | (63) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = % 136.14/20.15 | | e2) % 136.14/20.15 | | % 136.14/20.15 | | BETA: splitting (63) gives: % 136.14/20.15 | | % 136.14/20.15 | | Case 1: % 136.14/20.15 | | | % 136.14/20.15 | | | (64) all_57_6 = e2 & op(e1, e3) = e2 % 136.14/20.15 | | | % 136.14/20.15 | | | ALPHA: (64) implies: % 136.14/20.15 | | | (65) all_57_6 = e2 % 136.14/20.15 | | | % 136.14/20.15 | | | REF_CLOSE: (2), (8), (10), (15), (17), (18), (19), (23), (25), (42), (48), % 136.14/20.15 | | | (54), (55), (56), (57), (65) are inconsistent by sub-proof % 136.14/20.15 | | | #360. % 136.14/20.15 | | | % 136.14/20.15 | | Case 2: % 136.14/20.15 | | | % 136.14/20.15 | | | (66) all_57_7 = e2 & op(e1, e2) = e2 % 136.14/20.15 | | | % 136.14/20.15 | | | ALPHA: (66) implies: % 136.14/20.15 | | | (67) all_57_7 = e2 % 136.14/20.15 | | | % 136.14/20.15 | | | BETA: splitting (2) gives: % 136.14/20.15 | | | % 136.14/20.15 | | | Case 1: % 136.14/20.15 | | | | % 136.14/20.15 | | | | (68) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) % 136.14/20.15 | | | | = e2) % 136.14/20.15 | | | | % 136.14/20.15 | | | | BETA: splitting (68) gives: % 136.14/20.15 | | | | % 136.14/20.15 | | | | Case 1: % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | (69) all_57_2 = e2 & op(e2, e3) = e2 % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | ALPHA: (69) implies: % 136.14/20.15 | | | | | (70) all_57_2 = e2 % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | BETA: splitting (22) gives: % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | Case 1: % 136.14/20.15 | | | | | | % 136.14/20.15 | | | | | | (71) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & % 136.14/20.15 | | | | | | op(e0, e2) = e2) % 136.14/20.15 | | | | | | % 136.14/20.15 | | | | | | REF_CLOSE: (8), (9), (10), (15), (17), (18), (19), (23), (25), (40), % 136.14/20.15 | | | | | | (42), (48), (54), (55), (67), (71) are inconsistent by % 136.14/20.15 | | | | | | sub-proof #286. % 136.14/20.15 | | | | | | % 136.14/20.15 | | | | | Case 2: % 136.14/20.15 | | | | | | % 136.14/20.15 | | | | | | (72) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & % 136.14/20.15 | | | | | | op(e0, e0) = e2) % 136.14/20.15 | | | | | | % 136.14/20.15 | | | | | | BETA: splitting (72) gives: % 136.14/20.15 | | | | | | % 136.14/20.15 | | | | | | Case 1: % 136.14/20.15 | | | | | | | % 136.14/20.15 | | | | | | | (73) all_57_14 = e2 & op(e0, e1) = e2 % 136.14/20.15 | | | | | | | % 136.14/20.15 | | | | | | | REF_CLOSE: (10), (13), (16), (17), (18), (19), (23), (30), (39), % 136.14/20.15 | | | | | | | (47), (50), (54), (55), (73) are inconsistent by % 136.14/20.15 | | | | | | | sub-proof #283. % 136.14/20.15 | | | | | | | % 136.14/20.15 | | | | | | Case 2: % 136.14/20.15 | | | | | | | % 136.14/20.15 | | | | | | | (74) all_57_15 = e2 & op(e0, e0) = e2 % 136.14/20.15 | | | | | | | % 136.14/20.15 | | | | | | | ALPHA: (74) implies: % 136.14/20.15 | | | | | | | (75) all_57_15 = e2 % 136.14/20.15 | | | | | | | % 136.14/20.15 | | | | | | | BETA: splitting (62) gives: % 136.14/20.15 | | | | | | | % 136.14/20.15 | | | | | | | Case 1: % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | (76) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & % 136.14/20.15 | | | | | | | | op(e2, e1) = e2) % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | BETA: splitting (76) gives: % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | Case 1: % 136.14/20.15 | | | | | | | | | % 136.14/20.15 | | | | | | | | | (77) all_57_4 = e2 & op(e3, e1) = e2 % 136.14/20.15 | | | | | | | | | % 136.14/20.15 | | | | | | | | | ALPHA: (77) implies: % 136.14/20.15 | | | | | | | | | (78) all_57_4 = e2 % 136.14/20.15 | | | | | | | | | % 136.14/20.15 | | | | | | | | | REF_CLOSE: (8), (10), (12), (17), (18), (19), (23), (31), % 136.14/20.15 | | | | | | | | | (44), (54), (55), (59), (60), (78) are inconsistent % 136.14/20.15 | | | | | | | | | by sub-proof #278. % 136.14/20.15 | | | | | | | | | % 136.14/20.15 | | | | | | | | Case 2: % 136.14/20.15 | | | | | | | | | % 136.14/20.15 | | | | | | | | | (79) all_57_5 = e2 & op(e2, e1) = e2 % 136.14/20.15 | | | | | | | | | % 136.14/20.15 | | | | | | | | | ALPHA: (79) implies: % 136.14/20.15 | | | | | | | | | (80) all_57_5 = e2 % 136.14/20.15 | | | | | | | | | % 136.14/20.15 | | | | | | | | | BETA: splitting (56) gives: % 136.14/20.15 | | | | | | | | | % 136.14/20.15 | | | | | | | | | Case 1: % 136.14/20.15 | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | (81) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & % 136.14/20.15 | | | | | | | | | | op(e2, e2) = e1) % 136.14/20.15 | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | BETA: splitting (81) gives: % 136.14/20.15 | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | Case 1: % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | (82) all_57_2 = e1 & op(e2, e3) = e1 % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | REF_CLOSE: (18), (70), (82) are inconsistent by sub-proof % 136.14/20.15 | | | | | | | | | | | #497. % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | Case 2: % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | (83) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | REF_CLOSE: (48), (54), (83) are inconsistent by sub-proof % 136.14/20.15 | | | | | | | | | | | #303. % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | End of split % 136.14/20.15 | | | | | | | | | | % 136.14/20.15 | | | | | | | | | Case 2: % 136.14/20.15 | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | (84) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 % 136.14/20.15 | | | | | | | | | | & op(e2, e0) = e1) % 136.14/20.15 | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | BETA: splitting (84) gives: % 136.14/20.15 | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | Case 1: % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | (85) all_57_5 = e1 & op(e2, e1) = e1 % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | REF_CLOSE: (18), (80), (85) are inconsistent by sub-proof % 136.14/20.15 | | | | | | | | | | | #500. % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | Case 2: % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | (86) all_57_10 = e1 & op(e2, e0) = e1 % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | ALPHA: (86) implies: % 136.14/20.15 | | | | | | | | | | | (87) all_57_10 = e1 % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | BETA: splitting (57) gives: % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | Case 1: % 136.14/20.15 | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | (88) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 % 136.14/20.15 | | | | | | | | | | | | & op(e2, e2) = e0) % 136.14/20.15 | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | BETA: splitting (88) gives: % 136.14/20.15 | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | Case 1: % 136.14/20.15 | | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | | (89) all_57_2 = e0 & op(e2, e3) = e0 % 136.14/20.15 | | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | | REF_CLOSE: (10), (70), (89) are inconsistent by sub-proof % 136.14/20.15 | | | | | | | | | | | | | #494. % 136.14/20.15 | | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | Case 2: % 136.14/20.15 | | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | | (90) all_57_3 = e0 & op(e2, e2) = e0 % 136.14/20.15 | | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | | REF_CLOSE: (19), (48), (90) are inconsistent by sub-proof % 136.14/20.15 | | | | | | | | | | | | | #302. % 136.14/20.15 | | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | End of split % 136.14/20.15 | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | Case 2: % 136.14/20.15 | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | (91) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = % 136.14/20.15 | | | | | | | | | | | | e0 & op(e2, e0) = e0) % 136.14/20.15 | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | BETA: splitting (91) gives: % 136.14/20.15 | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | Case 1: % 136.14/20.15 | | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | | (92) all_57_5 = e0 & op(e2, e1) = e0 % 136.14/20.15 | | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | | REF_CLOSE: (10), (80), (92) are inconsistent by sub-proof % 136.14/20.15 | | | | | | | | | | | | | #277. % 136.14/20.15 | | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | Case 2: % 136.14/20.15 | | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | | (93) all_57_10 = e0 & op(e2, e0) = e0 % 136.14/20.15 | | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | | ALPHA: (93) implies: % 136.14/20.15 | | | | | | | | | | | | | (94) all_57_10 = e0 % 136.14/20.15 | | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | | REF_CLOSE: (55), (87), (94) are inconsistent by sub-proof % 136.14/20.15 | | | | | | | | | | | | | #639. % 136.14/20.15 | | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | | End of split % 136.14/20.15 | | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | End of split % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | End of split % 136.14/20.15 | | | | | | | | | | % 136.14/20.15 | | | | | | | | | End of split % 136.14/20.15 | | | | | | | | | % 136.14/20.15 | | | | | | | | End of split % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | Case 2: % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | (95) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & % 136.14/20.15 | | | | | | | | op(e0, e1) = e2) % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | REF_CLOSE: (1), (10), (13), (16), (17), (18), (19), (23), (30), % 136.14/20.15 | | | | | | | | (33), (39), (50), (54), (55), (75), (95) are % 136.14/20.15 | | | | | | | | inconsistent by sub-proof #276. % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | End of split % 136.14/20.15 | | | | | | | % 136.14/20.15 | | | | | | End of split % 136.14/20.15 | | | | | | % 136.14/20.15 | | | | | End of split % 136.14/20.15 | | | | | % 136.14/20.15 | | | | Case 2: % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | (96) all_57_3 = e2 & op(e2, e2) = e2 % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | REF_CLOSE: (23), (48), (96) are inconsistent by sub-proof #375. % 136.14/20.15 | | | | | % 136.14/20.15 | | | | End of split % 136.14/20.15 | | | | % 136.14/20.15 | | | Case 2: % 136.14/20.15 | | | | % 136.14/20.15 | | | | (97) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) % 136.14/20.15 | | | | = e2) % 136.14/20.15 | | | | % 136.14/20.15 | | | | BETA: splitting (97) gives: % 136.14/20.15 | | | | % 136.14/20.15 | | | | Case 1: % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | (98) all_57_5 = e2 & op(e2, e1) = e2 % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | ALPHA: (98) implies: % 136.14/20.15 | | | | | (99) op(e2, e1) = e2 % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | GROUND_INST: instantiating (17) with all_52_13, all_26_0, e0, e2, % 136.14/20.15 | | | | | simplifying with (4), (20) gives: % 136.14/20.15 | | | | | (100) all_52_13 = all_26_0 % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | GROUND_INST: instantiating (17) with all_52_9, e2, e1, e2, simplifying % 136.14/20.15 | | | | | with (41), (99) gives: % 136.14/20.15 | | | | | (101) all_52_9 = e2 % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | COMBINE_EQS: (51), (100) imply: % 136.14/20.15 | | | | | (102) all_54_7 = all_26_0 % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | REDUCE: (26), (101) imply: % 136.14/20.15 | | | | | (103) ~ (all_52_1 = e2) % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | REDUCE: (21), (100) imply: % 136.14/20.15 | | | | | (104) ~ (all_52_1 = all_26_0) % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | REDUCE: (52), (101) imply: % 136.14/20.15 | | | | | (105) ~ (all_52_11 = e2) % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | SIMP: (105) implies: % 136.14/20.15 | | | | | (106) ~ (all_52_11 = e2) % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | REDUCE: (3), (101) imply: % 136.14/20.15 | | | | | (107) ~ (all_6_2 = e2) % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | REDUCE: (38), (101) imply: % 136.14/20.15 | | | | | (108) ~ (e3 = e2) % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | REDUCE: (45), (100) imply: % 136.14/20.15 | | | | | (109) ~ (all_26_0 = e3) % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | REDUCE: (34), (100) imply: % 136.14/20.15 | | | | | (110) ~ (all_26_0 = e2) % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | BETA: splitting (7) gives: % 136.14/20.15 | | | | | % 136.14/20.15 | | | | | Case 1: % 136.14/20.15 | | | | | | % 136.14/20.15 | | | | | | (111) all_54_7 = e3 % 136.14/20.15 | | | | | | % 136.14/20.15 | | | | | | COMBINE_EQS: (102), (111) imply: % 136.14/20.15 | | | | | | (112) all_26_0 = e3 % 136.14/20.15 | | | | | | % 136.14/20.15 | | | | | | SIMP: (112) implies: % 136.14/20.15 | | | | | | (113) all_26_0 = e3 % 136.14/20.15 | | | | | | % 136.14/20.15 | | | | | | REDUCE: (109), (113) imply: % 136.14/20.15 | | | | | | (114) $false % 136.14/20.15 | | | | | | % 136.14/20.15 | | | | | | CLOSE: (114) is inconsistent. % 136.14/20.15 | | | | | | % 136.14/20.15 | | | | | Case 2: % 136.14/20.15 | | | | | | % 136.14/20.15 | | | | | | (115) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 136.14/20.15 | | | | | | % 136.14/20.15 | | | | | | BETA: splitting (115) gives: % 136.14/20.15 | | | | | | % 136.14/20.15 | | | | | | Case 1: % 136.14/20.15 | | | | | | | % 136.14/20.15 | | | | | | | (116) all_54_7 = e2 % 136.14/20.15 | | | | | | | % 136.14/20.15 | | | | | | | COMBINE_EQS: (102), (116) imply: % 136.14/20.15 | | | | | | | (117) all_26_0 = e2 % 136.14/20.15 | | | | | | | % 136.14/20.15 | | | | | | | SIMP: (117) implies: % 136.14/20.15 | | | | | | | (118) all_26_0 = e2 % 136.14/20.15 | | | | | | | % 136.14/20.15 | | | | | | | REDUCE: (110), (118) imply: % 136.14/20.15 | | | | | | | (119) $false % 136.14/20.15 | | | | | | | % 136.14/20.15 | | | | | | | CLOSE: (119) is inconsistent. % 136.14/20.15 | | | | | | | % 136.14/20.15 | | | | | | Case 2: % 136.14/20.15 | | | | | | | % 136.14/20.15 | | | | | | | (120) ~ (all_54_7 = e2) % 136.14/20.15 | | | | | | | (121) all_54_7 = e1 | all_54_7 = e0 % 136.14/20.15 | | | | | | | % 136.14/20.15 | | | | | | | BETA: splitting (121) gives: % 136.14/20.15 | | | | | | | % 136.14/20.15 | | | | | | | Case 1: % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | (122) all_54_7 = e1 % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | COMBINE_EQS: (102), (122) imply: % 136.14/20.15 | | | | | | | | (123) all_26_0 = e1 % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | SIMP: (123) implies: % 136.14/20.15 | | | | | | | | (124) all_26_0 = e1 % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | REDUCE: (36), (124) imply: % 136.14/20.15 | | | | | | | | (125) $false % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | CLOSE: (125) is inconsistent. % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | Case 2: % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | (126) all_54_7 = e0 % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | COMBINE_EQS: (102), (126) imply: % 136.14/20.15 | | | | | | | | (127) all_26_0 = e0 % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | SIMP: (127) implies: % 136.14/20.15 | | | | | | | | (128) all_26_0 = e0 % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | REDUCE: (104), (128) imply: % 136.14/20.15 | | | | | | | | (129) ~ (all_52_1 = e0) % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | REDUCE: (110), (128) imply: % 136.14/20.15 | | | | | | | | (130) ~ (e2 = e0) % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | REDUCE: (20), (128) imply: % 136.14/20.15 | | | | | | | | (131) op(e2, e0) = e0 % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | BETA: splitting (6) gives: % 136.14/20.15 | | | | | | | | % 136.14/20.15 | | | | | | | | Case 1: % 136.14/20.15 | | | | | | | | | % 136.14/20.15 | | | | | | | | | (132) all_54_4 = e3 % 136.14/20.15 | | | | | | | | | % 136.14/20.15 | | | | | | | | | REF_CLOSE: (46), (58), (132) are inconsistent by sub-proof % 136.14/20.15 | | | | | | | | | #481. % 136.14/20.15 | | | | | | | | | % 136.14/20.15 | | | | | | | | Case 2: % 136.14/20.15 | | | | | | | | | % 136.14/20.15 | | | | | | | | | (133) ~ (all_54_4 = e3) % 136.14/20.15 | | | | | | | | | (134) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 136.14/20.15 | | | | | | | | | % 136.14/20.15 | | | | | | | | | BETA: splitting (134) gives: % 136.14/20.15 | | | | | | | | | % 136.14/20.15 | | | | | | | | | Case 1: % 136.14/20.15 | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | (135) all_54_4 = e2 % 136.14/20.15 | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | COMBINE_EQS: (58), (135) imply: % 136.14/20.15 | | | | | | | | | | (136) all_52_1 = e2 % 136.14/20.15 | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | SIMP: (136) implies: % 136.14/20.15 | | | | | | | | | | (137) all_52_1 = e2 % 136.14/20.15 | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | REDUCE: (103), (137) imply: % 136.14/20.15 | | | | | | | | | | (138) $false % 136.14/20.15 | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | CLOSE: (138) is inconsistent. % 136.14/20.15 | | | | | | | | | | % 136.14/20.15 | | | | | | | | | Case 2: % 136.14/20.15 | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | (139) ~ (all_54_4 = e2) % 136.14/20.15 | | | | | | | | | | (140) all_54_4 = e1 | all_54_4 = e0 % 136.14/20.15 | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | BETA: splitting (140) gives: % 136.14/20.15 | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | Case 1: % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | (141) all_54_4 = e1 % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | COMBINE_EQS: (58), (141) imply: % 136.14/20.15 | | | | | | | | | | | (142) all_52_1 = e1 % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | SIMP: (142) implies: % 136.14/20.15 | | | | | | | | | | | (143) all_52_1 = e1 % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | REDUCE: (11), (143) imply: % 136.14/20.15 | | | | | | | | | | | (144) ~ (all_52_2 = e1) % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | SIMP: (144) implies: % 136.14/20.15 | | | | | | | | | | | (145) ~ (all_52_2 = e1) % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | REDUCE: (46), (143) imply: % 136.14/20.15 | | | | | | | | | | | (146) ~ (e3 = e1) % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | REDUCE: (103), (143) imply: % 136.14/20.15 | | | | | | | | | | | (147) ~ (e2 = e1) % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | REDUCE: (49), (143) imply: % 136.14/20.15 | | | | | | | | | | | (148) op(e2, e3) = e1 % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | BETA: splitting (35) gives: % 136.14/20.15 | | | | | | | | | | | % 136.14/20.15 | | | | | | | | | | | Case 1: % 136.14/20.15 | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | (149) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 136.14/20.16 | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 136.14/20.16 | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.14/20.16 | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 136.14/20.16 | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 136.14/20.16 | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.14/20.16 | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.14/20.16 | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 136.14/20.16 | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 136.14/20.16 | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 136.14/20.16 | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 136.14/20.16 | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 136.14/20.16 | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.14/20.16 | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 136.14/20.16 | | | | | | | | | | | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 136.14/20.16 | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 136.14/20.16 | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.14/20.16 | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 136.14/20.16 | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.14/20.16 | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.14/20.16 | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 136.14/20.16 | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 136.14/20.16 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 136.14/20.16 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.14/20.16 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 136.14/20.16 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 136.14/20.16 | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.16 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 136.14/20.16 | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | BETA: splitting (149) gives: % 136.14/20.16 | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | Case 1: % 136.14/20.16 | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | (150) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = % 136.14/20.16 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 136.14/20.16 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.14/20.16 | | | | | | | | | | | | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, % 136.14/20.16 | | | | | | | | | | | | | e2) = all_56_11 & op(e2, e1) = all_56_19 & % 136.14/20.16 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.14/20.16 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.14/20.16 | | | | | | | | | | | | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = % 136.14/20.16 | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 136.14/20.16 | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 136.14/20.16 | | | | | | | | | | | | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, % 136.14/20.16 | | | | | | | | | | | | | e2) = all_56_13 & op(e1, e1) = all_56_21 & % 136.14/20.16 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.14/20.16 | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 136.14/20.16 | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | REF_CLOSE: (8), (17), (18), (131), (150) are inconsistent by % 136.14/20.16 | | | | | | | | | | | | | sub-proof #274. % 136.14/20.16 | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | Case 2: % 136.14/20.16 | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | (151) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 136.14/20.16 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 136.14/20.16 | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.14/20.16 | | | | | | | | | | | | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, % 136.14/20.16 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.14/20.16 | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.14/20.16 | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 136.14/20.16 | | | | | | | | | | | | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 136.14/20.16 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 136.14/20.16 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.14/20.16 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 136.14/20.16 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & % 136.14/20.16 | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.16 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) % 136.14/20.16 | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | BETA: splitting (151) gives: % 136.14/20.16 | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | Case 1: % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | (152) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = % 136.14/20.16 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 136.14/20.16 | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, % 136.14/20.16 | | | | | | | | | | | | | | e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 136.14/20.16 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 136.14/20.16 | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | ALPHA: (152) implies: % 136.14/20.16 | | | | | | | | | | | | | | (153) op(e3, e3) = e0 % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (17), (153) are inconsistent by % 136.14/20.16 | | | | | | | | | | | | | | sub-proof #495. % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | Case 2: % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | (154) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = % 136.14/20.16 | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & % 136.14/20.16 | | | | | | | | | | | | | | ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.14/20.16 | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 136.14/20.16 | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, % 136.14/20.16 | | | | | | | | | | | | | | e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25) % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | ALPHA: (154) implies: % 136.14/20.16 | | | | | | | | | | | | | | (155) op(e2, e3) = e2 % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with e1, e2, e3, e2, % 136.14/20.16 | | | | | | | | | | | | | | simplifying with (148), (155) gives: % 136.14/20.16 | | | | | | | | | | | | | | (156) e2 = e1 % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | REDUCE: (18), (156) imply: % 136.14/20.16 | | | | | | | | | | | | | | (157) $false % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | CLOSE: (157) is inconsistent. % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | End of split % 136.14/20.16 | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | End of split % 136.14/20.16 | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | Case 2: % 136.14/20.16 | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | (158) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 136.14/20.16 | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 136.14/20.16 | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.14/20.16 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 136.14/20.16 | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 136.14/20.16 | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.16 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 136.14/20.16 | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 136.14/20.16 | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 136.14/20.16 | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 136.14/20.16 | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.14/20.16 | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.14/20.16 | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.16 | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 % 136.14/20.16 | | | | | | | | | | | | & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 136.14/20.16 | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.14/20.16 | | | | | | | | | | | | (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) % 136.14/20.16 | | | | | | | | | | | | = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 136.14/20.16 | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) % 136.14/20.16 | | | | | | | | | | | | = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 136.14/20.16 | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 % 136.14/20.16 | | | | | | | | | | | | & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 136.14/20.16 | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 136.14/20.16 | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 136.14/20.16 | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 136.14/20.16 | | | | | | | | | | | | & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & % 136.14/20.16 | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 136.14/20.16 | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 136.14/20.16 | | | | | | | | | | | | all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 136.14/20.16 | | | | | | | | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.14/20.16 | | | | | | | | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 136.14/20.16 | | | | | | | | | | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.14/20.16 | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = % 136.14/20.16 | | | | | | | | | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 136.14/20.16 | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.16 | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 % 136.14/20.16 | | | | | | | | | | | | = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & % 136.14/20.16 | | | | | | | | | | | | ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 136.14/20.16 | | | | | | | | | | | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 136.14/20.16 | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 136.14/20.16 | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 136.14/20.16 | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 136.14/20.16 | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 136.14/20.16 | | | | | | | | | | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & % 136.14/20.16 | | | | | | | | | | | | ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 136.14/20.16 | | | | | | | | | | | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 136.14/20.16 | | | | | | | | | | | | op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 136.14/20.16 | | | | | | | | | | | | op(e0, e2) = all_56_15 & op(e0, e1) = % 136.14/20.16 | | | | | | | | | | | | all_56_23 & $i(all_56_7) & $i(all_56_15) & % 136.14/20.16 | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 136.14/20.16 | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.14/20.16 | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 136.14/20.16 | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 136.14/20.16 | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 136.14/20.16 | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.14/20.16 | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 136.14/20.16 | | | | | | | | | | | | & $i(all_56_29)))) % 136.14/20.16 | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | BETA: splitting (158) gives: % 136.14/20.16 | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | Case 1: % 136.14/20.16 | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | (159) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = % 136.14/20.16 | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 136.14/20.16 | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.14/20.16 | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 136.14/20.16 | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e1, e3) = e1 & % 136.14/20.16 | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.16 | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 % 136.14/20.16 | | | | | | | | | | | | | & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 136.14/20.16 | | | | | | | | | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 136.14/20.16 | | | | | | | | | | | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 136.14/20.16 | | | | | | | | | | | | | = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.14/20.16 | | | | | | | | | | | | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.14/20.16 | | | | | | | | | | | | | = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.16 | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 136.14/20.16 | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | REF_CLOSE: (17), (24), (43), (54), (145), (159) are % 136.14/20.16 | | | | | | | | | | | | | inconsistent by sub-proof #304. % 136.14/20.16 | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | Case 2: % 136.14/20.16 | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | (160) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 136.14/20.16 | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 136.14/20.16 | | | | | | | | | | | | | e1) & ~ (all_56_31 = e0) & op(e2, e2) = e0 & % 136.14/20.16 | | | | | | | | | | | | | op(e2, e0) = e2 & op(e0, e3) = all_56_7 & op(e0, % 136.14/20.16 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.14/20.16 | | | | | | | | | | | | | op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.14/20.16 | | | | | | | | | | | | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 136.14/20.16 | | | | | | | | | | | | | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 136.14/20.16 | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 136.14/20.16 | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.14/20.16 | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.14/20.16 | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 136.14/20.16 | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 136.14/20.16 | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.14/20.16 | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 136.14/20.16 | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 136.14/20.16 | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 136.14/20.16 | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.16 | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 136.14/20.16 | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.14/20.16 | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 136.14/20.16 | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 136.14/20.16 | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 136.14/20.16 | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.14/20.16 | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 136.14/20.16 | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 136.14/20.16 | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 136.14/20.16 | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.14/20.16 | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 136.14/20.16 | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 136.14/20.16 | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.14/20.16 | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.14/20.16 | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 136.14/20.16 | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.14/20.16 | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.14/20.16 | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 136.14/20.16 | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 136.14/20.16 | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.14/20.16 | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 136.14/20.16 | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 136.14/20.16 | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 136.14/20.16 | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.14/20.16 | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 136.14/20.16 | | | | | | | | | | | | | & $i(all_56_29)))) % 136.14/20.16 | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | BETA: splitting (160) gives: % 136.14/20.16 | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | Case 1: % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | (161) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 136.14/20.16 | | | | | | | | | | | | | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 136.14/20.16 | | | | | | | | | | | | | | & ~ (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, % 136.14/20.16 | | | | | | | | | | | | | | e0) = e2 & op(e0, e3) = all_56_7 & op(e0, e2) = % 136.14/20.16 | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 136.14/20.16 | | | | | | | | | | | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & % 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_23) & $i(all_56_31) % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | ALPHA: (161) implies: % 136.14/20.16 | | | | | | | | | | | | | | (162) op(e2, e0) = e2 % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with e0, e2, e0, e2, % 136.14/20.16 | | | | | | | | | | | | | | simplifying with (131), (162) gives: % 136.14/20.16 | | | | | | | | | | | | | | (163) e2 = e0 % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | REDUCE: (10), (163) imply: % 136.14/20.16 | | | | | | | | | | | | | | (164) $false % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | CLOSE: (164) is inconsistent. % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | Case 2: % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | (165) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 136.14/20.16 | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 136.14/20.16 | | | | | | | | | | | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.14/20.16 | | | | | | | | | | | | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.14/20.16 | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) % 136.14/20.16 | | | | | | | | | | | | | | = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.14/20.16 | | | | | | | | | | | | | | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 136.14/20.16 | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 136.14/20.16 | | | | | | | | | | | | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 % 136.14/20.16 | | | | | | | | | | | | | | = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.16 | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, % 136.14/20.16 | | | | | | | | | | | | | | e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.14/20.16 | | | | | | | | | | | | | | op(e0, e3) = e0 & $i(all_56_1) & % 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_9) & $i(all_56_17) & % 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 136.14/20.16 | | | | | | | | | | | | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.14/20.16 | | | | | | | | | | | | | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 136.14/20.16 | | | | | | | | | | | | | | = e0) & op(e2, e3) = all_56_3 & op(e2, e2) % 136.14/20.16 | | | | | | | | | | | | | | = all_56_11 & op(e2, e1) = all_56_19 & % 136.14/20.16 | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 136.14/20.16 | | | | | | | | | | | | | | & $i(all_56_27)) | (all_56_21 = e0 & % 136.14/20.16 | | | | | | | | | | | | | | all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.14/20.16 | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.14/20.16 | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 136.14/20.16 | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.14/20.16 | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & % 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 % 136.14/20.16 | | | | | | | | | | | | | | = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.14/20.16 | | | | | | | | | | | | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 % 136.14/20.16 | | | | | | | | | | | | | | = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 136.14/20.16 | | | | | | | | | | | | | | = all_56_13 & op(e1, e1) = all_56_21 & % 136.14/20.16 | | | | | | | | | | | | | | op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.14/20.16 | | | | | | | | | | | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 136.14/20.16 | | | | | | | | | | | | | | & $i(all_56_29)))) % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | BETA: splitting (165) gives: % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | Case 1: % 136.14/20.16 | | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | | (166) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = % 136.14/20.16 | | | | | | | | | | | | | | | e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) % 136.14/20.16 | | | | | | | | | | | | | | | & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 136.14/20.16 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 136.14/20.16 | | | | | | | | | | | | | | | op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 136.14/20.16 | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27) % 136.14/20.16 | | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | | ALPHA: (166) implies: % 136.14/20.16 | | | | | | | | | | | | | | | (167) op(e1, e1) = e2 % 136.14/20.16 | | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | | REF_CLOSE: (1), (17), (33), (167) are inconsistent by % 136.14/20.16 | | | | | | | | | | | | | | | sub-proof #767. % 136.14/20.16 | | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | Case 2: % 136.14/20.16 | | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | | (168) op(e0, e0) = all_56_31 & $i(all_56_31) & % 136.14/20.16 | | | | | | | | | | | | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 136.14/20.16 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 136.14/20.16 | | | | | | | | | | | | | | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.16 | | | | | | | | | | | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 136.14/20.16 | | | | | | | | | | | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 136.14/20.16 | | | | | | | | | | | | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = % 136.14/20.16 | | | | | | | | | | | | | | | e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.14/20.16 | | | | | | | | | | | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 136.14/20.16 | | | | | | | | | | | | | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 136.14/20.16 | | | | | | | | | | | | | | | op(e2, e2) = all_56_11 & op(e2, e1) = % 136.14/20.16 | | | | | | | | | | | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 136.14/20.16 | | | | | | | | | | | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 136.14/20.16 | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.14/20.16 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.14/20.16 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, % 136.14/20.16 | | | | | | | | | | | | | | | e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.14/20.16 | | | | | | | | | | | | | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 136.14/20.16 | | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ % 136.14/20.16 | | | | | | | | | | | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.16 | | | | | | | | | | | | | | | (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.14/20.16 | | | | | | | | | | | | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 % 136.14/20.16 | | | | | | | | | | | | | | | & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.14/20.16 | | | | | | | | | | | | | | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_13) & $i(all_56_21) & % 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_29))) % 136.14/20.16 | | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | | ALPHA: (168) implies: % 136.14/20.16 | | | | | | | | | | | | | | | (169) op(e0, e0) = all_56_31 % 136.14/20.16 | | | | | | | | | | | | | | | (170) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 136.14/20.16 | | | | | | | | | | | | | | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 136.14/20.16 | | | | | | | | | | | | | | | & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.14/20.16 | | | | | | | | | | | | | | | op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & % 136.14/20.16 | | | | | | | | | | | | | | | op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 136.14/20.16 | | | | | | | | | | | | | | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & % 136.14/20.16 | | | | | | | | | | | | | | | ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.14/20.16 | | | | | | | | | | | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.14/20.16 | | | | | | | | | | | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 % 136.14/20.16 | | | | | | | | | | | | | | | & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 136.14/20.16 | | | | | | | | | | | | | | | & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = % 136.14/20.16 | | | | | | | | | | | | | | | e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.14/20.16 | | | | | | | | | | | | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.14/20.16 | | | | | | | | | | | | | | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 136.14/20.16 | | | | | | | | | | | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 136.14/20.16 | | | | | | | | | | | | | | | all_56_15 & op(e0, e1) = all_56_23 & % 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 136.14/20.16 | | | | | | | | | | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = % 136.14/20.16 | | | | | | | | | | | | | | | e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 136.14/20.16 | | | | | | | | | | | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 136.14/20.16 | | | | | | | | | | | | | | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.14/20.16 | | | | | | | | | | | | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) % 136.14/20.16 | | | | | | | | | | | | | | | = e0 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.16 | | | | | | | | | | | | | | | $i(all_56_21) & $i(all_56_29)) % 136.14/20.16 | | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (14), (17), (18), (23), (27), (29), % 136.14/20.16 | | | | | | | | | | | | | | | (32), (47), (53), (106), (131), (169), (170) are % 136.14/20.16 | | | | | | | | | | | | | | | inconsistent by sub-proof #273. % 136.14/20.16 | | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | | End of split % 136.14/20.16 | | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | | End of split % 136.14/20.16 | | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | | End of split % 136.14/20.16 | | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | End of split % 136.14/20.16 | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | Case 2: % 136.14/20.16 | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | (171) all_54_4 = e0 % 136.14/20.16 | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | COMBINE_EQS: (58), (171) imply: % 136.14/20.16 | | | | | | | | | | | (172) all_52_1 = e0 % 136.14/20.16 | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | SIMP: (172) implies: % 136.14/20.16 | | | | | | | | | | | (173) all_52_1 = e0 % 136.14/20.16 | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | REDUCE: (129), (173) imply: % 136.14/20.16 | | | | | | | | | | | (174) $false % 136.14/20.16 | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | | CLOSE: (174) is inconsistent. % 136.14/20.16 | | | | | | | | | | | % 136.14/20.16 | | | | | | | | | | End of split % 136.14/20.16 | | | | | | | | | | % 136.14/20.16 | | | | | | | | | End of split % 136.14/20.16 | | | | | | | | | % 136.14/20.16 | | | | | | | | End of split % 136.14/20.16 | | | | | | | | % 136.14/20.16 | | | | | | | End of split % 136.14/20.16 | | | | | | | % 136.14/20.16 | | | | | | End of split % 136.14/20.16 | | | | | | % 136.14/20.16 | | | | | End of split % 136.14/20.16 | | | | | % 136.14/20.16 | | | | Case 2: % 136.14/20.16 | | | | | % 136.14/20.16 | | | | | (175) all_57_10 = e2 & op(e2, e0) = e2 % 136.14/20.16 | | | | | % 136.14/20.16 | | | | | ALPHA: (175) implies: % 136.14/20.16 | | | | | (176) all_57_10 = e2 % 136.14/20.16 | | | | | % 136.14/20.16 | | | | | REF_CLOSE: (1), (8), (9), (10), (12), (13), (15), (16), (17), (18), % 136.14/20.16 | | | | | (19), (22), (23), (25), (30), (31), (33), (39), (40), (42), % 136.14/20.16 | | | | | (44), (47), (48), (50), (54), (55), (56), (57), (59), (60), % 136.14/20.16 | | | | | (62), (67), (176) are inconsistent by sub-proof #269. % 136.14/20.16 | | | | | % 136.14/20.16 | | | | End of split % 136.14/20.16 | | | | % 136.14/20.16 | | | End of split % 136.14/20.16 | | | % 136.14/20.16 | | End of split % 136.14/20.16 | | % 136.14/20.16 | Case 2: % 136.14/20.16 | | % 136.14/20.16 | | (177) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = % 136.14/20.16 | | e2) % 136.14/20.16 | | % 136.14/20.16 | | REF_CLOSE: (1), (4), (10), (17), (18), (19), (23), (33), (37), (45), (47), % 136.14/20.16 | | (50), (54), (55), (61), (177) are inconsistent by sub-proof #268. % 136.14/20.16 | | % 136.14/20.16 | End of split % 136.14/20.16 | % 136.14/20.16 End of proof % 136.14/20.16 % 136.14/20.16 Sub-proof #268 shows that the following formulas are inconsistent: % 136.14/20.16 ---------------------------------------------------------------- % 136.14/20.16 (1) op(e1, e1) = all_6_2 % 136.14/20.16 (2) op(e2, e0) = all_52_13 % 136.14/20.16 (3) ~ (e2 = e0) % 136.14/20.16 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.16 (5) ~ (e2 = e1) % 136.14/20.16 (6) ~ (e3 = e0) % 136.14/20.16 (7) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 136.14/20.16 (8) ~ (e3 = e2) % 136.14/20.16 (9) ~ (all_6_2 = e2) % 136.14/20.16 (10) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) | % 136.14/20.16 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.16 (11) ~ (all_52_13 = e3) % 136.14/20.16 (12) op(e0, e0) = e2 % 136.14/20.16 (13) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.16 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.14/20.16 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.16 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.16 (14) ~ (e3 = e1) % 136.14/20.16 (15) ~ (e1 = e0) % 136.14/20.16 (16) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) | % 136.14/20.16 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.16 % 136.14/20.16 Begin of proof % 136.14/20.16 | % 136.14/20.16 | BETA: splitting (7) gives: % 136.14/20.16 | % 136.14/20.16 | Case 1: % 136.14/20.16 | | % 136.14/20.16 | | (17) all_57_8 = e2 & op(e1, e1) = e2 % 136.14/20.16 | | % 136.14/20.16 | | ALPHA: (17) implies: % 136.14/20.16 | | (18) op(e1, e1) = e2 % 136.14/20.16 | | % 136.14/20.16 | | REF_CLOSE: (1), (4), (9), (18) are inconsistent by sub-proof #767. % 136.14/20.16 | | % 136.14/20.16 | Case 2: % 136.14/20.16 | | % 136.14/20.16 | | (19) all_57_11 = e2 & op(e1, e0) = e2 % 136.14/20.16 | | % 136.14/20.16 | | ALPHA: (19) implies: % 136.14/20.16 | | (20) all_57_11 = e2 % 136.14/20.16 | | % 136.14/20.16 | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (10), (11), (12), (13), (14), (15), % 136.14/20.16 | | (16), (20) are inconsistent by sub-proof #633. % 136.14/20.16 | | % 136.14/20.16 | End of split % 136.14/20.16 | % 136.14/20.16 End of proof % 136.14/20.16 % 136.14/20.16 Sub-proof #269 shows that the following formulas are inconsistent: % 136.14/20.16 ---------------------------------------------------------------- % 136.14/20.16 (1) op(e1, e1) = all_6_2 % 136.14/20.16 (2) op(e3, e3) = e2 % 136.14/20.16 (3) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.16 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 136.14/20.16 (4) ~ (e2 = e0) % 136.14/20.16 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.14/20.16 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.16 (6) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 136.14/20.16 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.16 (7) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 136.14/20.16 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 136.14/20.16 (8) ~ (all_52_7 = e3) % 136.14/20.16 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.16 (10) ~ (e2 = e1) % 136.14/20.16 (11) ~ (e3 = e0) % 136.14/20.16 (12) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) % 136.14/20.16 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = % 136.14/20.16 e2) % 136.14/20.16 (13) ~ (e3 = e2) % 136.14/20.16 (14) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.14/20.16 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.14/20.16 (15) op(e0, e2) = all_52_7 % 136.14/20.16 (16) ~ (all_52_4 = e3) % 136.14/20.16 (17) ~ (all_6_2 = e2) % 136.14/20.16 (18) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.16 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 136.14/20.16 e1) % 136.14/20.16 (19) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.16 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.16 (20) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.14/20.16 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.14/20.16 (21) op(e3, e2) = all_52_4 % 136.14/20.16 (22) op(e0, e0) = e2 % 136.14/20.16 (23) all_57_3 = e3 % 136.14/20.16 (24) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.16 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.14/20.16 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.16 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.16 (25) ~ (e3 = e1) % 136.14/20.16 (26) ~ (e1 = e0) % 136.14/20.16 (27) all_57_7 = e2 % 136.14/20.16 (28) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.16 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.14/20.16 (29) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.16 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 136.14/20.16 (30) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.14/20.16 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.14/20.16 (31) all_57_10 = e2 % 136.14/20.16 (32) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 136.14/20.16 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 136.14/20.16 (33) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | % 136.14/20.16 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 136.14/20.16 % 136.14/20.16 Begin of proof % 136.14/20.16 | % 136.14/20.16 | BETA: splitting (12) gives: % 136.14/20.16 | % 136.14/20.16 | Case 1: % 136.14/20.16 | | % 136.14/20.16 | | (34) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = % 136.14/20.16 | | e2) % 136.14/20.16 | | % 136.14/20.16 | | REF_CLOSE: (2), (3), (4), (7), (9), (10), (11), (13), (14), (19), (20), % 136.14/20.16 | | (23), (25), (26), (27), (34) are inconsistent by sub-proof #286. % 136.14/20.16 | | % 136.14/20.16 | Case 2: % 136.14/20.16 | | % 136.14/20.16 | | (35) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = % 136.14/20.16 | | e2) % 136.14/20.16 | | % 136.14/20.16 | | BETA: splitting (35) gives: % 136.14/20.16 | | % 136.14/20.16 | | Case 1: % 136.14/20.16 | | | % 136.14/20.16 | | | (36) all_57_14 = e2 & op(e0, e1) = e2 % 136.14/20.16 | | | % 136.14/20.16 | | | REF_CLOSE: (4), (6), (8), (9), (10), (11), (13), (15), (18), (22), (24), % 136.14/20.16 | | | (25), (26), (36) are inconsistent by sub-proof #283. % 136.14/20.16 | | | % 136.14/20.16 | | Case 2: % 136.14/20.16 | | | % 136.14/20.16 | | | (37) all_57_15 = e2 & op(e0, e0) = e2 % 136.14/20.16 | | | % 136.14/20.16 | | | ALPHA: (37) implies: % 136.14/20.16 | | | (38) all_57_15 = e2 % 136.14/20.16 | | | % 136.14/20.16 | | | BETA: splitting (33) gives: % 136.14/20.16 | | | % 136.14/20.16 | | | Case 1: % 136.14/20.16 | | | | % 136.14/20.16 | | | | (39) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) % 136.14/20.16 | | | | = e2) % 136.14/20.16 | | | | % 136.14/20.16 | | | | BETA: splitting (39) gives: % 136.14/20.16 | | | | % 136.14/20.16 | | | | Case 1: % 136.14/20.16 | | | | | % 136.14/20.16 | | | | | (40) all_57_4 = e2 & op(e3, e1) = e2 % 136.14/20.16 | | | | | % 136.14/20.16 | | | | | ALPHA: (40) implies: % 136.14/20.16 | | | | | (41) all_57_4 = e2 % 136.14/20.16 | | | | | % 136.14/20.16 | | | | | REF_CLOSE: (2), (4), (5), (9), (10), (11), (13), (16), (21), (25), % 136.14/20.16 | | | | | (26), (30), (32), (41) are inconsistent by sub-proof #278. % 136.14/20.16 | | | | | % 136.14/20.16 | | | | Case 2: % 136.14/20.16 | | | | | % 136.14/20.16 | | | | | (42) all_57_5 = e2 & op(e2, e1) = e2 % 136.14/20.16 | | | | | % 136.14/20.16 | | | | | ALPHA: (42) implies: % 136.14/20.16 | | | | | (43) all_57_5 = e2 % 136.14/20.16 | | | | | % 136.14/20.16 | | | | | BETA: splitting (28) gives: % 136.14/20.16 | | | | | % 136.14/20.16 | | | | | Case 1: % 136.14/20.16 | | | | | | % 136.14/20.16 | | | | | | (44) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, % 136.14/20.16 | | | | | | e2) = e1) % 136.14/20.16 | | | | | | % 136.14/20.16 | | | | | | BETA: splitting (44) gives: % 136.14/20.16 | | | | | | % 136.14/20.16 | | | | | | Case 1: % 136.14/20.16 | | | | | | | % 136.14/20.16 | | | | | | | (45) all_57_2 = e1 & op(e2, e3) = e1 % 136.14/20.16 | | | | | | | % 136.14/20.16 | | | | | | | ALPHA: (45) implies: % 136.14/20.16 | | | | | | | (46) all_57_2 = e1 % 136.14/20.16 | | | | | | | % 136.14/20.16 | | | | | | | REF_CLOSE: (4), (11), (23), (26), (29), (31), (43), (46) are % 136.14/20.16 | | | | | | | inconsistent by sub-proof #271. % 136.14/20.16 | | | | | | | % 136.14/20.16 | | | | | | Case 2: % 136.14/20.16 | | | | | | | % 136.14/20.17 | | | | | | | (47) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.17 | | | | | | | % 136.14/20.17 | | | | | | | REF_CLOSE: (23), (25), (47) are inconsistent by sub-proof #370. % 136.14/20.17 | | | | | | | % 136.14/20.17 | | | | | | End of split % 136.14/20.17 | | | | | | % 136.14/20.17 | | | | | Case 2: % 136.14/20.17 | | | | | | % 136.14/20.17 | | | | | | (48) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, % 136.14/20.17 | | | | | | e0) = e1) % 136.14/20.17 | | | | | | % 136.14/20.17 | | | | | | BETA: splitting (48) gives: % 136.14/20.17 | | | | | | % 136.14/20.17 | | | | | | Case 1: % 136.14/20.17 | | | | | | | % 136.14/20.17 | | | | | | | (49) all_57_5 = e1 & op(e2, e1) = e1 % 136.14/20.17 | | | | | | | % 136.14/20.17 | | | | | | | REF_CLOSE: (10), (43), (49) are inconsistent by sub-proof #500. % 136.14/20.17 | | | | | | | % 136.14/20.17 | | | | | | Case 2: % 136.14/20.17 | | | | | | | % 136.14/20.17 | | | | | | | (50) all_57_10 = e1 & op(e2, e0) = e1 % 136.14/20.17 | | | | | | | % 136.14/20.17 | | | | | | | REF_CLOSE: (10), (31), (50) are inconsistent by sub-proof #270. % 136.14/20.17 | | | | | | | % 136.14/20.17 | | | | | | End of split % 136.14/20.17 | | | | | | % 136.14/20.17 | | | | | End of split % 136.14/20.17 | | | | | % 136.14/20.17 | | | | End of split % 136.14/20.17 | | | | % 136.14/20.17 | | | Case 2: % 136.14/20.17 | | | | % 136.14/20.17 | | | | (51) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) % 136.14/20.17 | | | | = e2) % 136.14/20.17 | | | | % 136.14/20.17 | | | | REF_CLOSE: (1), (4), (6), (8), (9), (10), (11), (13), (15), (17), (18), % 136.14/20.17 | | | | (24), (25), (26), (38), (51) are inconsistent by sub-proof % 136.14/20.17 | | | | #276. % 136.14/20.17 | | | | % 136.14/20.17 | | | End of split % 136.14/20.17 | | | % 136.14/20.17 | | End of split % 136.14/20.17 | | % 136.14/20.17 | End of split % 136.14/20.17 | % 136.14/20.17 End of proof % 136.14/20.17 % 136.14/20.17 Sub-proof #270 shows that the following formulas are inconsistent: % 136.14/20.17 ---------------------------------------------------------------- % 136.14/20.17 (1) all_57_10 = e1 & op(e2, e0) = e1 % 136.14/20.17 (2) all_57_10 = e2 % 136.14/20.17 (3) ~ (e2 = e1) % 136.14/20.17 % 136.14/20.17 Begin of proof % 136.14/20.17 | % 136.14/20.17 | ALPHA: (1) implies: % 136.14/20.17 | (4) all_57_10 = e1 % 136.14/20.17 | % 136.14/20.17 | COMBINE_EQS: (2), (4) imply: % 136.14/20.17 | (5) e2 = e1 % 136.14/20.17 | % 136.14/20.17 | REDUCE: (3), (5) imply: % 136.14/20.17 | (6) $false % 136.14/20.17 | % 136.14/20.17 | CLOSE: (6) is inconsistent. % 136.14/20.17 | % 136.14/20.17 End of proof % 136.14/20.17 % 136.14/20.17 Sub-proof #271 shows that the following formulas are inconsistent: % 136.14/20.17 ---------------------------------------------------------------- % 136.14/20.17 (1) all_57_2 = e1 % 136.14/20.17 (2) ~ (e2 = e0) % 136.14/20.17 (3) all_57_5 = e2 % 136.14/20.17 (4) ~ (e3 = e0) % 136.14/20.17 (5) all_57_3 = e3 % 136.14/20.17 (6) ~ (e1 = e0) % 136.14/20.17 (7) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.17 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 136.14/20.17 (8) all_57_10 = e2 % 136.14/20.17 % 136.14/20.17 Begin of proof % 136.14/20.17 | % 136.14/20.17 | BETA: splitting (7) gives: % 136.14/20.17 | % 136.14/20.17 | Case 1: % 136.14/20.17 | | % 136.14/20.17 | | (9) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) % 136.14/20.17 | | % 136.14/20.17 | | BETA: splitting (9) gives: % 136.14/20.17 | | % 136.14/20.17 | | Case 1: % 136.14/20.17 | | | % 136.14/20.17 | | | (10) all_57_2 = e0 & op(e2, e3) = e0 % 136.14/20.17 | | | % 136.14/20.17 | | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #272. % 136.14/20.17 | | | % 136.14/20.17 | | Case 2: % 136.14/20.17 | | | % 136.14/20.17 | | | (11) all_57_3 = e0 & op(e2, e2) = e0 % 136.14/20.17 | | | % 136.14/20.17 | | | REF_CLOSE: (4), (5), (11) are inconsistent by sub-proof #302. % 136.14/20.17 | | | % 136.14/20.17 | | End of split % 136.14/20.17 | | % 136.14/20.17 | Case 2: % 136.14/20.17 | | % 136.14/20.17 | | (12) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = % 136.14/20.17 | | e0) % 136.14/20.17 | | % 136.14/20.17 | | BETA: splitting (12) gives: % 136.14/20.17 | | % 136.14/20.17 | | Case 1: % 136.14/20.17 | | | % 136.14/20.17 | | | (13) all_57_5 = e0 & op(e2, e1) = e0 % 136.14/20.17 | | | % 136.14/20.17 | | | REF_CLOSE: (2), (3), (13) are inconsistent by sub-proof #277. % 136.14/20.17 | | | % 136.14/20.17 | | Case 2: % 136.14/20.17 | | | % 136.14/20.17 | | | (14) all_57_10 = e0 & op(e2, e0) = e0 % 136.14/20.17 | | | % 136.14/20.17 | | | REF_CLOSE: (2), (8), (14) are inconsistent by sub-proof #363. % 136.14/20.17 | | | % 136.14/20.17 | | End of split % 136.14/20.17 | | % 136.14/20.17 | End of split % 136.14/20.17 | % 136.14/20.17 End of proof % 136.14/20.17 % 136.14/20.17 Sub-proof #272 shows that the following formulas are inconsistent: % 136.14/20.17 ---------------------------------------------------------------- % 136.14/20.17 (1) all_57_2 = e0 & op(e2, e3) = e0 % 136.14/20.17 (2) all_57_2 = e1 % 136.14/20.17 (3) ~ (e1 = e0) % 136.14/20.17 % 136.14/20.17 Begin of proof % 136.14/20.17 | % 136.14/20.17 | ALPHA: (1) implies: % 136.14/20.17 | (4) all_57_2 = e0 % 136.14/20.17 | % 136.14/20.17 | COMBINE_EQS: (2), (4) imply: % 136.14/20.17 | (5) e1 = e0 % 136.14/20.17 | % 136.14/20.17 | REDUCE: (3), (5) imply: % 136.14/20.17 | (6) $false % 136.14/20.17 | % 136.14/20.17 | CLOSE: (6) is inconsistent. % 136.14/20.17 | % 136.14/20.17 End of proof % 136.14/20.17 % 136.14/20.17 Sub-proof #273 shows that the following formulas are inconsistent: % 136.14/20.17 ---------------------------------------------------------------- % 136.14/20.17 (1) op(e1, e1) = all_6_2 % 136.14/20.17 (2) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & % 136.14/20.17 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & % 136.14/20.17 $i(all_40_1)) % 136.14/20.17 (3) ~ (all_52_11 = e2) % 136.14/20.17 (4) all_40_2 = all_6_2 % 136.14/20.17 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.17 (6) ~ (e2 = e1) % 136.14/20.17 (7) ~ (e3 = e2) % 136.14/20.17 (8) ~ (all_52_11 = all_6_2) % 136.14/20.17 (9) op(e0, e1) = all_52_11 % 136.14/20.17 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 136.14/20.17 (11) op(e2, e0) = e0 % 136.14/20.17 (12) op(e0, e0) = e2 % 136.14/20.17 (13) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.14/20.17 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.17 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 136.14/20.17 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.17 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 136.14/20.17 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 136.14/20.17 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.14/20.17 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.14/20.17 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.14/20.17 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.14/20.17 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 136.14/20.17 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.14/20.17 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 136.14/20.17 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.14/20.17 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 136.14/20.17 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 136.14/20.17 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.17 $i(all_56_21) & $i(all_56_29)) % 136.14/20.17 (14) all_54_14 = all_52_11 % 136.14/20.17 (15) op(e0, e0) = all_56_31 % 136.14/20.17 % 136.14/20.17 Begin of proof % 136.14/20.17 | % 136.14/20.17 | GROUND_INST: instantiating (5) with e2, all_56_31, e0, e0, simplifying with % 136.14/20.17 | (12), (15) gives: % 136.14/20.17 | (16) all_56_31 = e2 % 136.14/20.17 | % 136.14/20.17 | BETA: splitting (13) gives: % 136.14/20.17 | % 136.14/20.17 | Case 1: % 136.14/20.17 | | % 136.14/20.17 | | (17) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.14/20.17 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.17 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.14/20.17 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 136.14/20.17 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 136.14/20.17 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 136.14/20.17 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.14/20.17 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.14/20.17 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.14/20.17 | | $i(all_56_27)) % 136.14/20.17 | | % 136.14/20.17 | | BETA: splitting (17) gives: % 136.14/20.17 | | % 136.14/20.17 | | Case 1: % 136.14/20.17 | | | % 136.14/20.17 | | | (18) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.14/20.17 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.17 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.14/20.17 | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 136.14/20.17 | | | & $i(all_56_17) & $i(all_56_25) % 136.14/20.17 | | | % 136.14/20.17 | | | ALPHA: (18) implies: % 136.14/20.17 | | | (19) all_56_31 = e3 % 136.14/20.17 | | | % 136.14/20.17 | | | REF_CLOSE: (7), (16), (19) are inconsistent by sub-proof #532. % 136.14/20.17 | | | % 136.14/20.17 | | Case 2: % 136.14/20.17 | | | % 136.14/20.17 | | | (20) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.14/20.17 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.14/20.17 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.14/20.17 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.14/20.17 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.14/20.17 | | | % 136.14/20.17 | | | ALPHA: (20) implies: % 136.14/20.17 | | | (21) ~ (all_56_27 = e0) % 136.14/20.17 | | | (22) op(e2, e0) = all_56_27 % 136.14/20.17 | | | % 136.14/20.17 | | | GROUND_INST: instantiating (5) with e0, all_56_27, e0, e2, simplifying % 136.14/20.17 | | | with (11), (22) gives: % 136.14/20.17 | | | (23) all_56_27 = e0 % 136.14/20.17 | | | % 136.14/20.17 | | | REDUCE: (21), (23) imply: % 136.14/20.17 | | | (24) $false % 136.14/20.17 | | | % 136.14/20.17 | | | CLOSE: (24) is inconsistent. % 136.14/20.17 | | | % 136.14/20.17 | | End of split % 136.14/20.17 | | % 136.14/20.17 | Case 2: % 136.14/20.17 | | % 136.14/20.17 | | (25) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.14/20.17 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.14/20.17 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.14/20.17 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.14/20.17 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.14/20.17 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.14/20.17 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.14/20.17 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.14/20.17 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.14/20.17 | | $i(all_56_29)) % 136.14/20.17 | | % 136.14/20.17 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12), (14), (16), % 136.14/20.17 | | (25) are inconsistent by sub-proof #524. % 136.14/20.17 | | % 136.14/20.17 | End of split % 136.14/20.17 | % 136.14/20.17 End of proof % 136.14/20.17 % 136.14/20.17 Sub-proof #274 shows that the following formulas are inconsistent: % 136.14/20.17 ---------------------------------------------------------------- % 136.14/20.17 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 136.14/20.17 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 136.14/20.17 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.14/20.17 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.14/20.17 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.14/20.17 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.17 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 136.14/20.17 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.14/20.17 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.17 $i(all_56_21) & $i(all_56_29)) % 136.14/20.17 (2) op(e3, e3) = e2 % 136.14/20.17 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.17 (4) ~ (e2 = e1) % 136.14/20.17 (5) op(e2, e0) = e0 % 136.14/20.17 % 136.14/20.17 Begin of proof % 136.14/20.17 | % 136.14/20.17 | BETA: splitting (1) gives: % 136.14/20.17 | % 136.14/20.17 | Case 1: % 136.14/20.17 | | % 136.14/20.17 | | (6) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.14/20.17 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.14/20.17 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.14/20.17 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.14/20.17 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.14/20.17 | | % 136.14/20.17 | | ALPHA: (6) implies: % 136.14/20.17 | | (7) ~ (all_56_27 = e0) % 136.14/20.17 | | (8) op(e2, e0) = all_56_27 % 136.14/20.17 | | % 136.14/20.17 | | REF_CLOSE: (3), (5), (7), (8) are inconsistent by sub-proof #275. % 136.14/20.17 | | % 136.14/20.17 | Case 2: % 136.14/20.17 | | % 136.14/20.17 | | (9) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.14/20.17 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 136.14/20.17 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.14/20.17 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.14/20.17 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.14/20.17 | | % 136.14/20.17 | | ALPHA: (9) implies: % 136.14/20.17 | | (10) op(e3, e3) = e1 % 136.14/20.17 | | % 136.14/20.17 | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #743. % 136.14/20.17 | | % 136.14/20.17 | End of split % 136.14/20.17 | % 136.14/20.17 End of proof % 136.14/20.17 % 136.14/20.17 Sub-proof #275 shows that the following formulas are inconsistent: % 136.14/20.17 ---------------------------------------------------------------- % 136.14/20.17 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.17 (2) op(e2, e0) = all_56_27 % 136.14/20.17 (3) op(e2, e0) = e0 % 136.14/20.17 (4) ~ (all_56_27 = e0) % 136.14/20.17 % 136.14/20.17 Begin of proof % 136.14/20.17 | % 136.14/20.17 | GROUND_INST: instantiating (1) with e0, all_56_27, e0, e2, simplifying with % 136.14/20.17 | (2), (3) gives: % 136.14/20.17 | (5) all_56_27 = e0 % 136.14/20.17 | % 136.14/20.17 | REDUCE: (4), (5) imply: % 136.14/20.17 | (6) $false % 136.14/20.17 | % 136.14/20.17 | CLOSE: (6) is inconsistent. % 136.14/20.17 | % 136.14/20.17 End of proof % 136.14/20.17 % 136.14/20.17 Sub-proof #276 shows that the following formulas are inconsistent: % 136.14/20.17 ---------------------------------------------------------------- % 136.14/20.17 (1) op(e1, e1) = all_6_2 % 136.14/20.17 (2) ~ (e2 = e0) % 136.14/20.17 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 136.14/20.17 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.17 (4) ~ (all_52_7 = e3) % 136.14/20.17 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.17 (6) ~ (e2 = e1) % 136.14/20.17 (7) ~ (e3 = e0) % 136.14/20.17 (8) ~ (e3 = e2) % 136.14/20.17 (9) op(e0, e2) = all_52_7 % 136.14/20.17 (10) ~ (all_6_2 = e2) % 136.14/20.17 (11) all_57_15 = e2 % 136.14/20.17 (12) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.17 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 136.14/20.17 e1) % 136.14/20.17 (13) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.17 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.14/20.17 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.17 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.17 (14) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 136.14/20.17 (15) ~ (e3 = e1) % 136.14/20.17 (16) ~ (e1 = e0) % 136.14/20.17 % 136.14/20.17 Begin of proof % 136.14/20.17 | % 136.14/20.17 | BETA: splitting (14) gives: % 136.14/20.17 | % 136.14/20.17 | Case 1: % 136.14/20.17 | | % 136.14/20.17 | | (17) all_57_8 = e2 & op(e1, e1) = e2 % 136.14/20.17 | | % 136.14/20.17 | | ALPHA: (17) implies: % 136.14/20.17 | | (18) op(e1, e1) = e2 % 136.14/20.17 | | % 136.14/20.17 | | REF_CLOSE: (1), (5), (10), (18) are inconsistent by sub-proof #767. % 136.14/20.17 | | % 136.14/20.17 | Case 2: % 136.14/20.17 | | % 136.14/20.17 | | (19) all_57_14 = e2 & op(e0, e1) = e2 % 136.14/20.17 | | % 136.14/20.17 | | ALPHA: (19) implies: % 136.14/20.17 | | (20) all_57_14 = e2 % 136.14/20.17 | | % 136.14/20.17 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (15), % 136.14/20.17 | | (16), (20) are inconsistent by sub-proof #433. % 136.14/20.17 | | % 136.14/20.17 | End of split % 136.14/20.17 | % 136.14/20.17 End of proof % 136.14/20.17 % 136.14/20.17 Sub-proof #277 shows that the following formulas are inconsistent: % 136.14/20.17 ---------------------------------------------------------------- % 136.14/20.17 (1) all_57_5 = e0 & op(e2, e1) = e0 % 136.14/20.17 (2) all_57_5 = e2 % 136.14/20.17 (3) ~ (e2 = e0) % 136.14/20.17 % 136.14/20.17 Begin of proof % 136.14/20.17 | % 136.14/20.17 | ALPHA: (1) implies: % 136.14/20.17 | (4) all_57_5 = e0 % 136.14/20.17 | % 136.14/20.17 | COMBINE_EQS: (2), (4) imply: % 136.14/20.17 | (5) e2 = e0 % 136.14/20.17 | % 136.14/20.17 | REDUCE: (3), (5) imply: % 136.14/20.17 | (6) $false % 136.14/20.17 | % 136.14/20.17 | CLOSE: (6) is inconsistent. % 136.14/20.17 | % 136.14/20.17 End of proof % 136.14/20.17 % 136.14/20.17 Sub-proof #278 shows that the following formulas are inconsistent: % 136.14/20.17 ---------------------------------------------------------------- % 136.14/20.17 (1) op(e3, e3) = e2 % 136.14/20.17 (2) ~ (e2 = e0) % 136.14/20.17 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.14/20.17 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.17 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.17 (5) ~ (e2 = e1) % 136.14/20.17 (6) ~ (e3 = e0) % 136.14/20.17 (7) ~ (e3 = e2) % 136.14/20.17 (8) ~ (all_52_4 = e3) % 136.14/20.17 (9) all_57_4 = e2 % 136.14/20.17 (10) op(e3, e2) = all_52_4 % 136.14/20.17 (11) ~ (e3 = e1) % 136.14/20.17 (12) ~ (e1 = e0) % 136.14/20.17 (13) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.14/20.17 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.14/20.17 (14) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 136.14/20.17 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 136.14/20.17 % 136.14/20.17 Begin of proof % 136.14/20.17 | % 136.14/20.17 | BETA: splitting (13) gives: % 136.14/20.17 | % 136.14/20.17 | Case 1: % 136.14/20.17 | | % 136.14/20.17 | | (15) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = % 136.14/20.17 | | e3) % 136.14/20.17 | | % 136.14/20.17 | | REF_CLOSE: (1), (4), (7), (8), (10), (15) are inconsistent by sub-proof % 136.14/20.17 | | #282. % 136.14/20.17 | | % 136.14/20.17 | Case 2: % 136.14/20.17 | | % 136.14/20.17 | | (16) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = % 136.14/20.17 | | e3) % 136.14/20.17 | | % 136.14/20.17 | | BETA: splitting (16) gives: % 136.14/20.17 | | % 136.14/20.17 | | Case 1: % 136.14/20.17 | | | % 136.14/20.17 | | | (17) all_57_4 = e3 & op(e3, e1) = e3 % 136.14/20.17 | | | % 136.14/20.17 | | | REF_CLOSE: (7), (9), (17) are inconsistent by sub-proof #734. % 136.14/20.17 | | | % 136.14/20.17 | | Case 2: % 136.14/20.17 | | | % 136.14/20.17 | | | (18) all_57_9 = e3 & op(e3, e0) = e3 % 136.14/20.17 | | | % 136.14/20.17 | | | ALPHA: (18) implies: % 136.14/20.17 | | | (19) all_57_9 = e3 % 136.14/20.17 | | | % 136.14/20.17 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (11), (12), (14), (19) are % 136.14/20.17 | | | inconsistent by sub-proof #279. % 136.14/20.17 | | | % 136.14/20.17 | | End of split % 136.14/20.17 | | % 136.14/20.17 | End of split % 136.14/20.17 | % 136.14/20.17 End of proof % 136.14/20.17 % 136.14/20.17 Sub-proof #279 shows that the following formulas are inconsistent: % 136.14/20.17 ---------------------------------------------------------------- % 136.14/20.17 (1) op(e3, e3) = e2 % 136.14/20.17 (2) ~ (e2 = e0) % 136.14/20.17 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.14/20.17 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.17 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.17 (5) ~ (e2 = e1) % 136.14/20.17 (6) ~ (e3 = e0) % 136.14/20.17 (7) all_57_9 = e3 % 136.14/20.17 (8) all_57_4 = e2 % 136.14/20.17 (9) ~ (e3 = e1) % 136.14/20.17 (10) ~ (e1 = e0) % 136.14/20.17 (11) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 136.14/20.17 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 136.14/20.17 % 136.14/20.17 Begin of proof % 136.14/20.17 | % 136.14/20.17 | BETA: splitting (3) gives: % 136.14/20.17 | % 136.14/20.17 | Case 1: % 136.14/20.17 | | % 136.14/20.17 | | (12) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = % 136.14/20.17 | | e0) % 136.14/20.17 | | % 136.14/20.17 | | BETA: splitting (12) gives: % 136.14/20.17 | | % 136.14/20.17 | | Case 1: % 136.14/20.17 | | | % 136.14/20.17 | | | (13) all_57_0 = e0 & op(e3, e3) = e0 % 136.14/20.17 | | | % 136.14/20.17 | | | ALPHA: (13) implies: % 136.14/20.17 | | | (14) op(e3, e3) = e0 % 136.14/20.17 | | | % 136.14/20.17 | | | REF_CLOSE: (1), (2), (4), (14) are inconsistent by sub-proof #495. % 136.14/20.17 | | | % 136.14/20.17 | | Case 2: % 136.14/20.17 | | | % 136.14/20.17 | | | (15) all_57_1 = e0 & op(e3, e2) = e0 % 136.14/20.17 | | | % 136.14/20.17 | | | ALPHA: (15) implies: % 136.14/20.17 | | | (16) all_57_1 = e0 % 136.14/20.17 | | | % 136.14/20.17 | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (11), (16) are inconsistent % 136.14/20.17 | | | by sub-proof #280. % 136.14/20.17 | | | % 136.14/20.17 | | End of split % 136.14/20.17 | | % 136.14/20.17 | Case 2: % 136.14/20.17 | | % 136.14/20.17 | | (17) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = % 136.14/20.17 | | e0) % 136.14/20.17 | | % 136.14/20.17 | | BETA: splitting (17) gives: % 136.14/20.17 | | % 136.14/20.17 | | Case 1: % 136.14/20.17 | | | % 136.14/20.17 | | | (18) all_57_4 = e0 & op(e3, e1) = e0 % 136.14/20.17 | | | % 136.14/20.17 | | | REF_CLOSE: (2), (8), (18) are inconsistent by sub-proof #647. % 136.14/20.17 | | | % 136.14/20.17 | | Case 2: % 136.14/20.17 | | | % 136.14/20.17 | | | (19) all_57_9 = e0 & op(e3, e0) = e0 % 136.14/20.17 | | | % 136.14/20.17 | | | ALPHA: (19) implies: % 136.14/20.17 | | | (20) all_57_9 = e0 % 136.14/20.17 | | | % 136.14/20.17 | | | REF_CLOSE: (6), (7), (20) are inconsistent by sub-proof #670. % 136.14/20.17 | | | % 136.14/20.17 | | End of split % 136.14/20.17 | | % 136.14/20.17 | End of split % 136.14/20.17 | % 136.14/20.17 End of proof % 136.14/20.17 % 136.14/20.17 Sub-proof #280 shows that the following formulas are inconsistent: % 136.14/20.17 ---------------------------------------------------------------- % 136.14/20.17 (1) op(e3, e3) = e2 % 136.14/20.17 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.17 (3) ~ (e2 = e1) % 136.14/20.17 (4) all_57_9 = e3 % 136.14/20.17 (5) all_57_4 = e2 % 136.14/20.17 (6) all_57_1 = e0 % 136.14/20.17 (7) ~ (e3 = e1) % 136.14/20.17 (8) ~ (e1 = e0) % 136.14/20.17 (9) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 136.14/20.17 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 136.14/20.17 % 136.14/20.17 Begin of proof % 136.14/20.17 | % 136.14/20.17 | BETA: splitting (9) gives: % 136.14/20.17 | % 136.14/20.17 | Case 1: % 136.14/20.17 | | % 136.14/20.17 | | (10) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = % 136.14/20.17 | | e1) % 136.14/20.17 | | % 136.14/20.17 | | REF_CLOSE: (1), (2), (3), (6), (8), (10) are inconsistent by sub-proof #281. % 136.14/20.17 | | % 136.14/20.17 | Case 2: % 136.14/20.17 | | % 136.14/20.17 | | (11) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = % 136.14/20.17 | | e1) % 136.14/20.17 | | % 136.14/20.17 | | BETA: splitting (11) gives: % 136.14/20.17 | | % 136.14/20.17 | | Case 1: % 136.14/20.17 | | | % 136.14/20.17 | | | (12) all_57_4 = e1 & op(e3, e1) = e1 % 136.14/20.17 | | | % 136.14/20.17 | | | ALPHA: (12) implies: % 136.14/20.17 | | | (13) all_57_4 = e1 % 136.14/20.17 | | | % 136.14/20.17 | | | REF_CLOSE: (3), (5), (13) are inconsistent by sub-proof #669. % 136.14/20.17 | | | % 136.14/20.17 | | Case 2: % 136.14/20.17 | | | % 136.14/20.17 | | | (14) all_57_9 = e1 & op(e3, e0) = e1 % 136.14/20.17 | | | % 136.14/20.17 | | | REF_CLOSE: (4), (7), (14) are inconsistent by sub-proof #640. % 136.14/20.17 | | | % 136.14/20.17 | | End of split % 136.14/20.17 | | % 136.14/20.17 | End of split % 136.14/20.17 | % 136.14/20.17 End of proof % 136.14/20.17 % 136.14/20.17 Sub-proof #281 shows that the following formulas are inconsistent: % 136.14/20.17 ---------------------------------------------------------------- % 136.14/20.17 (1) op(e3, e3) = e2 % 136.14/20.17 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.17 (3) ~ (e2 = e1) % 136.14/20.17 (4) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) % 136.14/20.17 (5) all_57_1 = e0 % 136.14/20.17 (6) ~ (e1 = e0) % 136.14/20.17 % 136.14/20.17 Begin of proof % 136.14/20.17 | % 136.14/20.17 | BETA: splitting (4) gives: % 136.14/20.17 | % 136.14/20.17 | Case 1: % 136.14/20.17 | | % 136.14/20.17 | | (7) all_57_0 = e1 & op(e3, e3) = e1 % 136.14/20.17 | | % 136.14/20.17 | | ALPHA: (7) implies: % 136.14/20.17 | | (8) op(e3, e3) = e1 % 136.14/20.17 | | % 136.14/20.17 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #743. % 136.14/20.17 | | % 136.14/20.17 | Case 2: % 136.14/20.17 | | % 136.14/20.17 | | (9) all_57_1 = e1 & op(e3, e2) = e1 % 136.14/20.17 | | % 136.14/20.17 | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #289. % 136.14/20.17 | | % 136.14/20.17 | End of split % 136.14/20.17 | % 136.14/20.17 End of proof % 136.14/20.17 % 136.14/20.17 Sub-proof #282 shows that the following formulas are inconsistent: % 136.14/20.17 ---------------------------------------------------------------- % 136.14/20.17 (1) op(e3, e3) = e2 % 136.14/20.17 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.17 (3) ~ (e3 = e2) % 136.14/20.17 (4) ~ (all_52_4 = e3) % 136.14/20.17 (5) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) % 136.14/20.17 (6) op(e3, e2) = all_52_4 % 136.14/20.17 % 136.14/20.17 Begin of proof % 136.14/20.17 | % 136.14/20.17 | BETA: splitting (5) gives: % 136.14/20.17 | % 136.14/20.17 | Case 1: % 136.14/20.17 | | % 136.14/20.17 | | (7) all_57_0 = e3 & op(e3, e3) = e3 % 136.14/20.17 | | % 136.14/20.17 | | ALPHA: (7) implies: % 136.14/20.17 | | (8) op(e3, e3) = e3 % 136.14/20.17 | | % 136.14/20.17 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #778. % 136.14/20.17 | | % 136.14/20.17 | Case 2: % 136.14/20.17 | | % 136.14/20.17 | | (9) all_57_1 = e3 & op(e3, e2) = e3 % 136.14/20.17 | | % 136.14/20.17 | | ALPHA: (9) implies: % 136.14/20.17 | | (10) op(e3, e2) = e3 % 136.14/20.17 | | % 136.14/20.17 | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #738. % 136.14/20.17 | | % 136.14/20.17 | End of split % 136.14/20.17 | % 136.14/20.17 End of proof % 136.14/20.17 % 136.14/20.17 Sub-proof #283 shows that the following formulas are inconsistent: % 136.14/20.17 ---------------------------------------------------------------- % 136.14/20.17 (1) all_57_14 = e2 & op(e0, e1) = e2 % 136.14/20.17 (2) ~ (e2 = e0) % 136.14/20.17 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 136.14/20.17 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.17 (4) ~ (all_52_7 = e3) % 136.14/20.17 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.17 (6) ~ (e2 = e1) % 136.14/20.17 (7) ~ (e3 = e0) % 136.14/20.17 (8) ~ (e3 = e2) % 136.14/20.17 (9) op(e0, e2) = all_52_7 % 136.14/20.17 (10) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.17 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 136.14/20.17 e1) % 136.14/20.17 (11) op(e0, e0) = e2 % 136.14/20.17 (12) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.17 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.14/20.17 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.17 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.17 (13) ~ (e3 = e1) % 136.14/20.17 (14) ~ (e1 = e0) % 136.14/20.17 % 136.14/20.17 Begin of proof % 136.14/20.17 | % 136.14/20.17 | ALPHA: (1) implies: % 136.14/20.17 | (15) all_57_14 = e2 % 136.14/20.17 | % 136.14/20.17 | BETA: splitting (3) gives: % 136.14/20.17 | % 136.14/20.17 | Case 1: % 136.14/20.17 | | % 136.14/20.17 | | (16) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = % 136.14/20.17 | | e3) % 136.14/20.17 | | % 136.14/20.17 | | BETA: splitting (16) gives: % 136.14/20.17 | | % 136.14/20.17 | | Case 1: % 136.14/20.17 | | | % 136.14/20.17 | | | (17) all_57_12 = e3 & op(e0, e3) = e3 % 136.14/20.17 | | | % 136.14/20.17 | | | ALPHA: (17) implies: % 136.14/20.17 | | | (18) all_57_12 = e3 % 136.14/20.17 | | | % 136.14/20.17 | | | BETA: splitting (12) gives: % 136.14/20.17 | | | % 136.14/20.17 | | | Case 1: % 136.14/20.17 | | | | % 136.14/20.17 | | | | (19) all_57_15 = e0 & op(e0, e0) = e0 % 136.14/20.17 | | | | % 136.14/20.17 | | | | ALPHA: (19) implies: % 136.14/20.17 | | | | (20) op(e0, e0) = e0 % 136.14/20.17 | | | | % 136.14/20.17 | | | | REF_CLOSE: (2), (5), (11), (20) are inconsistent by sub-proof #714. % 136.14/20.17 | | | | % 136.14/20.17 | | | Case 2: % 136.14/20.17 | | | | % 136.14/20.17 | | | | (21) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, % 136.14/20.17 | | | | e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & % 136.14/20.17 | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, % 136.14/20.17 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 136.14/20.17 | | | | % 136.14/20.17 | | | | ALPHA: (21) implies: % 136.14/20.17 | | | | (22) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, % 136.14/20.18 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 136.14/20.18 | | | | % 136.14/20.18 | | | | REF_CLOSE: (2), (5), (6), (7), (10), (11), (13), (14), (15), (18), (22) % 136.14/20.18 | | | | are inconsistent by sub-proof #284. % 136.14/20.18 | | | | % 136.14/20.18 | | | End of split % 136.14/20.18 | | | % 136.14/20.18 | | Case 2: % 136.14/20.18 | | | % 136.14/20.18 | | | (23) all_57_13 = e3 & op(e0, e2) = e3 % 136.14/20.18 | | | % 136.14/20.18 | | | REF_CLOSE: (4), (5), (9), (23) are inconsistent by sub-proof #556. % 136.14/20.18 | | | % 136.14/20.18 | | End of split % 136.14/20.18 | | % 136.14/20.18 | Case 2: % 136.14/20.18 | | % 136.14/20.18 | | (24) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = % 136.14/20.18 | | e3) % 136.14/20.18 | | % 136.14/20.18 | | BETA: splitting (24) gives: % 136.14/20.18 | | % 136.14/20.18 | | Case 1: % 136.14/20.18 | | | % 136.14/20.18 | | | (25) all_57_14 = e3 & op(e0, e1) = e3 % 136.14/20.18 | | | % 136.14/20.18 | | | ALPHA: (25) implies: % 136.14/20.18 | | | (26) all_57_14 = e3 % 136.14/20.18 | | | % 136.14/20.18 | | | REF_CLOSE: (8), (15), (26) are inconsistent by sub-proof #407. % 136.14/20.18 | | | % 136.14/20.18 | | Case 2: % 136.14/20.18 | | | % 136.14/20.18 | | | (27) all_57_15 = e3 & op(e0, e0) = e3 % 136.14/20.18 | | | % 136.14/20.18 | | | ALPHA: (27) implies: % 136.14/20.18 | | | (28) op(e0, e0) = e3 % 136.14/20.18 | | | % 136.14/20.18 | | | REF_CLOSE: (5), (8), (11), (28) are inconsistent by sub-proof #634. % 136.14/20.18 | | | % 136.14/20.18 | | End of split % 136.14/20.18 | | % 136.14/20.18 | End of split % 136.14/20.18 | % 136.14/20.18 End of proof % 136.14/20.18 % 136.14/20.18 Sub-proof #284 shows that the following formulas are inconsistent: % 136.14/20.18 ---------------------------------------------------------------- % 136.14/20.18 (1) ~ (e2 = e0) % 136.14/20.18 (2) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) | % 136.14/20.18 (all_57_14 = e0 & op(e0, e1) = e0) % 136.14/20.18 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.18 (4) ~ (e2 = e1) % 136.14/20.18 (5) ~ (e3 = e0) % 136.14/20.18 (6) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) | % 136.14/20.18 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.18 (7) all_57_12 = e3 % 136.14/20.18 (8) all_57_14 = e2 % 136.14/20.18 (9) op(e0, e0) = e2 % 136.14/20.18 (10) ~ (e3 = e1) % 136.14/20.18 (11) ~ (e1 = e0) % 136.14/20.18 % 136.14/20.18 Begin of proof % 136.14/20.18 | % 136.14/20.18 | BETA: splitting (6) gives: % 136.14/20.18 | % 136.14/20.18 | Case 1: % 136.14/20.18 | | % 136.14/20.18 | | (12) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = % 136.14/20.18 | | e1) % 136.14/20.18 | | % 136.14/20.18 | | BETA: splitting (12) gives: % 136.14/20.18 | | % 136.14/20.18 | | Case 1: % 136.14/20.18 | | | % 136.14/20.18 | | | (13) all_57_12 = e1 & op(e0, e3) = e1 % 136.14/20.18 | | | % 136.14/20.18 | | | ALPHA: (13) implies: % 136.14/20.18 | | | (14) all_57_12 = e1 % 136.14/20.18 | | | % 136.14/20.18 | | | REF_CLOSE: (7), (10), (14) are inconsistent by sub-proof #591. % 136.14/20.18 | | | % 136.14/20.18 | | Case 2: % 136.14/20.18 | | | % 136.14/20.18 | | | (15) all_57_13 = e1 & op(e0, e2) = e1 % 136.14/20.18 | | | % 136.14/20.18 | | | ALPHA: (15) implies: % 136.14/20.18 | | | (16) all_57_13 = e1 % 136.14/20.18 | | | % 136.14/20.18 | | | REF_CLOSE: (1), (2), (5), (7), (8), (11), (16) are inconsistent by % 136.14/20.18 | | | sub-proof #285. % 136.14/20.18 | | | % 136.14/20.18 | | End of split % 136.14/20.18 | | % 136.14/20.18 | Case 2: % 136.14/20.18 | | % 136.14/20.18 | | (17) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 136.14/20.18 | | e1) % 136.14/20.18 | | % 136.14/20.18 | | BETA: splitting (17) gives: % 136.14/20.18 | | % 136.14/20.18 | | Case 1: % 136.14/20.18 | | | % 136.14/20.18 | | | (18) all_57_14 = e1 & op(e0, e1) = e1 % 136.14/20.18 | | | % 136.14/20.18 | | | ALPHA: (18) implies: % 136.14/20.18 | | | (19) all_57_14 = e1 % 136.14/20.18 | | | % 136.14/20.18 | | | REF_CLOSE: (4), (8), (19) are inconsistent by sub-proof #560. % 136.14/20.18 | | | % 136.14/20.18 | | Case 2: % 136.14/20.18 | | | % 136.14/20.18 | | | (20) all_57_15 = e1 & op(e0, e0) = e1 % 136.14/20.18 | | | % 136.14/20.18 | | | ALPHA: (20) implies: % 136.14/20.18 | | | (21) op(e0, e0) = e1 % 136.14/20.18 | | | % 136.14/20.18 | | | REF_CLOSE: (3), (4), (9), (21) are inconsistent by sub-proof #636. % 136.14/20.18 | | | % 136.14/20.18 | | End of split % 136.14/20.18 | | % 136.14/20.18 | End of split % 136.14/20.18 | % 136.14/20.18 End of proof % 136.14/20.18 % 136.14/20.18 Sub-proof #285 shows that the following formulas are inconsistent: % 136.14/20.18 ---------------------------------------------------------------- % 136.14/20.18 (1) ~ (e2 = e0) % 136.14/20.18 (2) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) | % 136.14/20.18 (all_57_14 = e0 & op(e0, e1) = e0) % 136.14/20.18 (3) ~ (e3 = e0) % 136.14/20.18 (4) all_57_13 = e1 % 136.14/20.18 (5) all_57_12 = e3 % 136.14/20.18 (6) all_57_14 = e2 % 136.14/20.18 (7) ~ (e1 = e0) % 136.14/20.18 % 136.14/20.18 Begin of proof % 136.14/20.18 | % 136.14/20.18 | BETA: splitting (2) gives: % 136.14/20.18 | % 136.14/20.18 | Case 1: % 136.14/20.18 | | % 136.14/20.18 | | (8) all_57_12 = e0 & op(e0, e3) = e0 % 136.14/20.18 | | % 136.14/20.18 | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #436. % 136.14/20.18 | | % 136.14/20.18 | Case 2: % 136.14/20.18 | | % 136.14/20.18 | | (9) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = % 136.14/20.18 | | e0) % 136.14/20.18 | | % 136.14/20.18 | | REF_CLOSE: (1), (4), (6), (7), (9) are inconsistent by sub-proof #579. % 136.14/20.18 | | % 136.14/20.18 | End of split % 136.14/20.18 | % 136.14/20.18 End of proof % 136.14/20.18 % 136.14/20.18 Sub-proof #286 shows that the following formulas are inconsistent: % 136.14/20.18 ---------------------------------------------------------------- % 136.14/20.18 (1) op(e3, e3) = e2 % 136.14/20.18 (2) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.18 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 136.14/20.18 (3) ~ (e2 = e0) % 136.14/20.18 (4) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 136.14/20.18 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 136.14/20.18 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.18 (6) ~ (e2 = e1) % 136.14/20.18 (7) ~ (e3 = e0) % 136.14/20.18 (8) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) % 136.14/20.18 (9) ~ (e3 = e2) % 136.14/20.18 (10) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.14/20.18 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.14/20.18 (11) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.18 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.18 (12) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.14/20.18 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.14/20.18 (13) all_57_3 = e3 % 136.14/20.18 (14) ~ (e3 = e1) % 136.14/20.18 (15) ~ (e1 = e0) % 136.14/20.18 (16) all_57_7 = e2 % 136.14/20.18 % 136.14/20.18 Begin of proof % 136.14/20.18 | % 136.14/20.18 | BETA: splitting (8) gives: % 136.14/20.18 | % 136.14/20.18 | Case 1: % 136.14/20.18 | | % 136.14/20.18 | | (17) all_57_12 = e2 & op(e0, e3) = e2 % 136.14/20.18 | | % 136.14/20.18 | | ALPHA: (17) implies: % 136.14/20.18 | | (18) all_57_12 = e2 % 136.14/20.18 | | % 136.14/20.18 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (12), (14), (15), (18) % 136.14/20.18 | | are inconsistent by sub-proof #290. % 136.14/20.18 | | % 136.14/20.18 | Case 2: % 136.14/20.18 | | % 136.14/20.18 | | (19) all_57_13 = e2 & op(e0, e2) = e2 % 136.14/20.18 | | % 136.14/20.18 | | ALPHA: (19) implies: % 136.14/20.18 | | (20) all_57_13 = e2 % 136.14/20.18 | | % 136.14/20.18 | | REF_CLOSE: (2), (3), (6), (7), (11), (13), (14), (15), (16), (20) are % 136.14/20.18 | | inconsistent by sub-proof #287. % 136.14/20.18 | | % 136.14/20.18 | End of split % 136.14/20.18 | % 136.14/20.18 End of proof % 136.14/20.18 % 136.14/20.18 Sub-proof #287 shows that the following formulas are inconsistent: % 136.14/20.18 ---------------------------------------------------------------- % 136.14/20.18 (1) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.18 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 136.14/20.18 (2) ~ (e2 = e0) % 136.14/20.18 (3) ~ (e2 = e1) % 136.14/20.18 (4) ~ (e3 = e0) % 136.14/20.18 (5) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.18 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.18 (6) all_57_13 = e2 % 136.14/20.18 (7) all_57_3 = e3 % 136.14/20.18 (8) ~ (e3 = e1) % 136.14/20.18 (9) ~ (e1 = e0) % 136.14/20.18 (10) all_57_7 = e2 % 136.14/20.18 % 136.14/20.18 Begin of proof % 136.14/20.18 | % 136.14/20.18 | BETA: splitting (1) gives: % 136.14/20.18 | % 136.14/20.18 | Case 1: % 136.14/20.18 | | % 136.14/20.18 | | (11) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = % 136.14/20.18 | | e0) % 136.14/20.18 | | % 136.14/20.18 | | BETA: splitting (11) gives: % 136.14/20.18 | | % 136.14/20.18 | | Case 1: % 136.14/20.18 | | | % 136.14/20.18 | | | (12) all_57_1 = e0 & op(e3, e2) = e0 % 136.14/20.18 | | | % 136.14/20.18 | | | ALPHA: (12) implies: % 136.14/20.18 | | | (13) all_57_1 = e0 % 136.14/20.18 | | | % 136.14/20.18 | | | BETA: splitting (5) gives: % 136.14/20.18 | | | % 136.14/20.18 | | | Case 1: % 136.14/20.18 | | | | % 136.14/20.18 | | | | (14) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) % 136.14/20.18 | | | | = e1) % 136.14/20.18 | | | | % 136.14/20.18 | | | | BETA: splitting (14) gives: % 136.14/20.18 | | | | % 136.14/20.18 | | | | Case 1: % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | (15) all_57_1 = e1 & op(e3, e2) = e1 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | REF_CLOSE: (9), (13), (15) are inconsistent by sub-proof #289. % 136.14/20.18 | | | | | % 136.14/20.18 | | | | Case 2: % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | (16) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | REF_CLOSE: (7), (8), (16) are inconsistent by sub-proof #370. % 136.14/20.18 | | | | | % 136.14/20.18 | | | | End of split % 136.14/20.18 | | | | % 136.14/20.18 | | | Case 2: % 136.14/20.18 | | | | % 136.14/20.18 | | | | (17) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) % 136.14/20.18 | | | | = e1) % 136.14/20.18 | | | | % 136.14/20.18 | | | | BETA: splitting (17) gives: % 136.14/20.18 | | | | % 136.14/20.18 | | | | Case 1: % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | (18) all_57_7 = e1 & op(e1, e2) = e1 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | ALPHA: (18) implies: % 136.14/20.18 | | | | | (19) all_57_7 = e1 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | REF_CLOSE: (3), (10), (19) are inconsistent by sub-proof #288. % 136.14/20.18 | | | | | % 136.14/20.18 | | | | Case 2: % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | (20) all_57_13 = e1 & op(e0, e2) = e1 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | ALPHA: (20) implies: % 136.14/20.18 | | | | | (21) all_57_13 = e1 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | REF_CLOSE: (3), (6), (21) are inconsistent by sub-proof #567. % 136.14/20.18 | | | | | % 136.14/20.18 | | | | End of split % 136.14/20.18 | | | | % 136.14/20.18 | | | End of split % 136.14/20.18 | | | % 136.14/20.18 | | Case 2: % 136.14/20.18 | | | % 136.14/20.18 | | | (22) all_57_3 = e0 & op(e2, e2) = e0 % 136.14/20.18 | | | % 136.14/20.18 | | | REF_CLOSE: (4), (7), (22) are inconsistent by sub-proof #374. % 136.14/20.18 | | | % 136.14/20.18 | | End of split % 136.14/20.18 | | % 136.14/20.18 | Case 2: % 136.14/20.18 | | % 136.14/20.18 | | (23) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = % 136.14/20.18 | | e0) % 136.14/20.18 | | % 136.14/20.18 | | BETA: splitting (23) gives: % 136.14/20.18 | | % 136.14/20.18 | | Case 1: % 136.14/20.18 | | | % 136.14/20.18 | | | (24) all_57_7 = e0 & op(e1, e2) = e0 % 136.14/20.18 | | | % 136.14/20.18 | | | REF_CLOSE: (2), (10), (24) are inconsistent by sub-proof #664. % 136.14/20.18 | | | % 136.14/20.18 | | Case 2: % 136.14/20.18 | | | % 136.14/20.18 | | | (25) all_57_13 = e0 & op(e0, e2) = e0 % 136.14/20.18 | | | % 136.14/20.18 | | | REF_CLOSE: (2), (6), (25) are inconsistent by sub-proof #411. % 136.14/20.18 | | | % 136.14/20.18 | | End of split % 136.14/20.18 | | % 136.14/20.18 | End of split % 136.14/20.18 | % 136.14/20.18 End of proof % 136.14/20.18 % 136.14/20.18 Sub-proof #288 shows that the following formulas are inconsistent: % 136.14/20.18 ---------------------------------------------------------------- % 136.14/20.18 (1) all_57_7 = e2 % 136.14/20.18 (2) all_57_7 = e1 % 136.14/20.18 (3) ~ (e2 = e1) % 136.14/20.18 % 136.14/20.18 Begin of proof % 136.14/20.18 | % 136.14/20.18 | COMBINE_EQS: (1), (2) imply: % 136.14/20.18 | (4) e2 = e1 % 136.14/20.18 | % 136.14/20.18 | SIMP: (4) implies: % 136.14/20.18 | (5) e2 = e1 % 136.14/20.18 | % 136.14/20.18 | REDUCE: (3), (5) imply: % 136.14/20.18 | (6) $false % 136.14/20.18 | % 136.14/20.18 | CLOSE: (6) is inconsistent. % 136.14/20.18 | % 136.14/20.18 End of proof % 136.14/20.18 % 136.14/20.18 Sub-proof #289 shows that the following formulas are inconsistent: % 136.14/20.18 ---------------------------------------------------------------- % 136.14/20.18 (1) all_57_1 = e1 & op(e3, e2) = e1 % 136.14/20.18 (2) all_57_1 = e0 % 136.14/20.18 (3) ~ (e1 = e0) % 136.14/20.18 % 136.14/20.18 Begin of proof % 136.14/20.18 | % 136.14/20.18 | ALPHA: (1) implies: % 136.14/20.18 | (4) all_57_1 = e1 % 136.14/20.18 | % 136.14/20.18 | COMBINE_EQS: (2), (4) imply: % 136.14/20.18 | (5) e1 = e0 % 136.14/20.18 | % 136.14/20.18 | SIMP: (5) implies: % 136.14/20.18 | (6) e1 = e0 % 136.14/20.18 | % 136.14/20.18 | REDUCE: (3), (6) imply: % 136.14/20.18 | (7) $false % 136.14/20.18 | % 136.14/20.18 | CLOSE: (7) is inconsistent. % 136.14/20.18 | % 136.14/20.18 End of proof % 136.14/20.18 % 136.14/20.18 Sub-proof #290 shows that the following formulas are inconsistent: % 136.14/20.18 ---------------------------------------------------------------- % 136.14/20.18 (1) op(e3, e3) = e2 % 136.14/20.18 (2) ~ (e2 = e0) % 136.14/20.18 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 136.14/20.18 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 136.14/20.18 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.18 (5) ~ (e2 = e1) % 136.14/20.18 (6) ~ (e3 = e0) % 136.14/20.18 (7) ~ (e3 = e2) % 136.14/20.18 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.14/20.18 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.14/20.18 (9) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.14/20.18 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.14/20.18 (10) ~ (e3 = e1) % 136.14/20.18 (11) ~ (e1 = e0) % 136.14/20.18 (12) all_57_12 = e2 % 136.14/20.18 % 136.14/20.18 Begin of proof % 136.14/20.18 | % 136.14/20.18 | BETA: splitting (8) gives: % 136.14/20.18 | % 136.14/20.18 | Case 1: % 136.14/20.18 | | % 136.14/20.18 | | (13) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = % 136.14/20.18 | | e3) % 136.14/20.18 | | % 136.14/20.18 | | BETA: splitting (13) gives: % 136.14/20.18 | | % 136.14/20.18 | | Case 1: % 136.14/20.18 | | | % 136.14/20.18 | | | (14) all_57_0 = e3 & op(e3, e3) = e3 % 136.14/20.18 | | | % 136.14/20.18 | | | ALPHA: (14) implies: % 136.14/20.18 | | | (15) op(e3, e3) = e3 % 136.14/20.18 | | | % 136.14/20.18 | | | REF_CLOSE: (1), (4), (7), (15) are inconsistent by sub-proof #778. % 136.14/20.18 | | | % 136.14/20.18 | | Case 2: % 136.14/20.18 | | | % 136.14/20.18 | | | (16) all_57_2 = e3 & op(e2, e3) = e3 % 136.14/20.18 | | | % 136.14/20.18 | | | ALPHA: (16) implies: % 136.14/20.18 | | | (17) all_57_2 = e3 % 136.14/20.18 | | | % 136.14/20.18 | | | BETA: splitting (9) gives: % 136.14/20.18 | | | % 136.14/20.18 | | | Case 1: % 136.14/20.18 | | | | % 136.14/20.18 | | | | (18) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) % 136.14/20.18 | | | | = e0) % 136.14/20.18 | | | | % 136.14/20.18 | | | | REF_CLOSE: (1), (2), (4), (6), (17), (18) are inconsistent by sub-proof % 136.14/20.18 | | | | #426. % 136.14/20.18 | | | | % 136.14/20.18 | | | Case 2: % 136.14/20.18 | | | | % 136.14/20.18 | | | | (19) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) % 136.14/20.18 | | | | = e0) % 136.14/20.18 | | | | % 136.14/20.18 | | | | BETA: splitting (19) gives: % 136.14/20.18 | | | | % 136.14/20.18 | | | | Case 1: % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | (20) all_57_6 = e0 & op(e1, e3) = e0 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | ALPHA: (20) implies: % 136.14/20.18 | | | | | (21) all_57_6 = e0 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | BETA: splitting (3) gives: % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | Case 1: % 136.14/20.18 | | | | | | % 136.14/20.18 | | | | | | (22) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, % 136.14/20.18 | | | | | | e3) = e1) % 136.14/20.18 | | | | | | % 136.14/20.18 | | | | | | REF_CLOSE: (1), (4), (5), (10), (17), (22) are inconsistent by % 136.14/20.18 | | | | | | sub-proof #356. % 136.14/20.18 | | | | | | % 136.14/20.18 | | | | | Case 2: % 136.14/20.18 | | | | | | % 136.14/20.18 | | | | | | (23) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, % 136.14/20.18 | | | | | | e3) = e1) % 136.14/20.18 | | | | | | % 136.14/20.18 | | | | | | REF_CLOSE: (5), (11), (12), (21), (23) are inconsistent by sub-proof % 136.14/20.18 | | | | | | #417. % 136.14/20.18 | | | | | | % 136.14/20.18 | | | | | End of split % 136.14/20.18 | | | | | % 136.14/20.18 | | | | Case 2: % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | (24) all_57_12 = e0 & op(e0, e3) = e0 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | REF_CLOSE: (2), (12), (24) are inconsistent by sub-proof #578. % 136.14/20.18 | | | | | % 136.14/20.18 | | | | End of split % 136.14/20.18 | | | | % 136.14/20.18 | | | End of split % 136.14/20.18 | | | % 136.14/20.18 | | End of split % 136.14/20.18 | | % 136.14/20.18 | Case 2: % 136.14/20.18 | | % 136.14/20.18 | | (25) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = % 136.14/20.18 | | e3) % 136.14/20.18 | | % 136.14/20.18 | | BETA: splitting (25) gives: % 136.14/20.18 | | % 136.14/20.18 | | Case 1: % 136.14/20.18 | | | % 136.14/20.18 | | | (26) all_57_6 = e3 & op(e1, e3) = e3 % 136.14/20.18 | | | % 136.14/20.18 | | | ALPHA: (26) implies: % 136.14/20.18 | | | (27) all_57_6 = e3 % 136.14/20.18 | | | % 136.14/20.18 | | | BETA: splitting (9) gives: % 136.14/20.18 | | | % 136.14/20.18 | | | Case 1: % 136.14/20.18 | | | | % 136.14/20.18 | | | | (28) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) % 136.14/20.18 | | | | = e0) % 136.14/20.18 | | | | % 136.14/20.18 | | | | BETA: splitting (28) gives: % 136.14/20.18 | | | | % 136.14/20.18 | | | | Case 1: % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | (29) all_57_0 = e0 & op(e3, e3) = e0 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | ALPHA: (29) implies: % 136.14/20.18 | | | | | (30) op(e3, e3) = e0 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | REF_CLOSE: (1), (2), (4), (30) are inconsistent by sub-proof #495. % 136.14/20.18 | | | | | % 136.14/20.18 | | | | Case 2: % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | (31) all_57_2 = e0 & op(e2, e3) = e0 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | ALPHA: (31) implies: % 136.14/20.18 | | | | | (32) all_57_2 = e0 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | REF_CLOSE: (1), (3), (4), (5), (10), (11), (12), (27), (32) are % 136.14/20.18 | | | | | inconsistent by sub-proof #643. % 136.14/20.18 | | | | | % 136.14/20.18 | | | | End of split % 136.14/20.18 | | | | % 136.14/20.18 | | | Case 2: % 136.14/20.18 | | | | % 136.14/20.18 | | | | (33) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) % 136.14/20.18 | | | | = e0) % 136.14/20.18 | | | | % 136.14/20.18 | | | | REF_CLOSE: (2), (6), (12), (27), (33) are inconsistent by sub-proof % 136.14/20.18 | | | | #577. % 136.14/20.18 | | | | % 136.14/20.18 | | | End of split % 136.14/20.18 | | | % 136.14/20.18 | | Case 2: % 136.14/20.18 | | | % 136.14/20.18 | | | (34) all_57_12 = e3 & op(e0, e3) = e3 % 136.14/20.18 | | | % 136.14/20.18 | | | ALPHA: (34) implies: % 136.14/20.18 | | | (35) all_57_12 = e3 % 136.14/20.18 | | | % 136.14/20.18 | | | REF_CLOSE: (7), (12), (35) are inconsistent by sub-proof #518. % 136.14/20.18 | | | % 136.14/20.18 | | End of split % 136.14/20.18 | | % 136.14/20.18 | End of split % 136.14/20.18 | % 136.14/20.18 End of proof % 136.14/20.18 % 136.14/20.18 Sub-proof #291 shows that the following formulas are inconsistent: % 136.14/20.18 ---------------------------------------------------------------- % 136.14/20.18 (1) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 136.14/20.18 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 136.14/20.18 (2) op(e2, e0) = all_52_13 % 136.14/20.18 (3) ~ (e2 = e0) % 136.14/20.18 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.18 (5) ~ (e2 = e1) % 136.14/20.18 (6) ~ (e3 = e0) % 136.14/20.18 (7) ~ (e3 = e2) % 136.14/20.18 (8) op(e2, e2) = e3 % 136.14/20.18 (9) op(e2, e0) = e0 % 136.14/20.18 (10) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) | % 136.14/20.18 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.18 (11) ~ (all_52_13 = e3) % 136.14/20.18 (12) op(e0, e0) = e2 % 136.14/20.18 (13) all_57_3 = e3 % 136.14/20.18 (14) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.18 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.14/20.18 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.18 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.18 (15) ~ (e3 = e1) % 136.14/20.18 (16) ~ (e1 = e0) % 136.14/20.18 (17) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.18 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.14/20.18 (18) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.18 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 136.14/20.18 (19) all_57_9 = e0 % 136.14/20.18 (20) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) | % 136.14/20.18 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.18 % 136.14/20.18 Begin of proof % 136.14/20.18 | % 136.14/20.18 | BETA: splitting (18) gives: % 136.14/20.18 | % 136.14/20.18 | Case 1: % 136.14/20.18 | | % 136.14/20.18 | | (21) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = % 136.14/20.18 | | e0) % 136.14/20.18 | | % 136.14/20.18 | | BETA: splitting (21) gives: % 136.14/20.18 | | % 136.14/20.18 | | Case 1: % 136.14/20.18 | | | % 136.14/20.18 | | | (22) all_57_2 = e0 & op(e2, e3) = e0 % 136.14/20.18 | | | % 136.14/20.18 | | | ALPHA: (22) implies: % 136.14/20.18 | | | (23) all_57_2 = e0 % 136.14/20.18 | | | % 136.14/20.18 | | | BETA: splitting (10) gives: % 136.14/20.18 | | | % 136.14/20.18 | | | Case 1: % 136.14/20.18 | | | | % 136.14/20.18 | | | | (24) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) % 136.14/20.18 | | | | = e3) % 136.14/20.18 | | | | % 136.14/20.18 | | | | BETA: splitting (24) gives: % 136.14/20.18 | | | | % 136.14/20.18 | | | | Case 1: % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | (25) all_57_9 = e3 & op(e3, e0) = e3 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | REF_CLOSE: (6), (19), (25) are inconsistent by sub-proof #614. % 136.14/20.18 | | | | | % 136.14/20.18 | | | | Case 2: % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | (26) all_57_10 = e3 & op(e2, e0) = e3 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | REF_CLOSE: (2), (4), (11), (26) are inconsistent by sub-proof #749. % 136.14/20.18 | | | | | % 136.14/20.18 | | | | End of split % 136.14/20.18 | | | | % 136.14/20.18 | | | Case 2: % 136.14/20.18 | | | | % 136.14/20.18 | | | | (27) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, % 136.14/20.18 | | | | e0) = e3) % 136.14/20.18 | | | | % 136.14/20.18 | | | | BETA: splitting (27) gives: % 136.14/20.18 | | | | % 136.14/20.18 | | | | Case 1: % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | (28) all_57_11 = e3 & op(e1, e0) = e3 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | ALPHA: (28) implies: % 136.14/20.18 | | | | | (29) all_57_11 = e3 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | BETA: splitting (20) gives: % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | Case 1: % 136.14/20.18 | | | | | | % 136.14/20.18 | | | | | | (30) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, % 136.14/20.18 | | | | | | e0) = e1) % 136.14/20.18 | | | | | | % 136.14/20.18 | | | | | | BETA: splitting (30) gives: % 136.14/20.18 | | | | | | % 136.14/20.18 | | | | | | Case 1: % 136.14/20.18 | | | | | | | % 136.14/20.18 | | | | | | | (31) all_57_9 = e1 & op(e3, e0) = e1 % 136.14/20.18 | | | | | | | % 136.14/20.18 | | | | | | | REF_CLOSE: (16), (19), (31) are inconsistent by sub-proof #298. % 136.14/20.18 | | | | | | | % 136.14/20.18 | | | | | | Case 2: % 136.14/20.18 | | | | | | | % 136.14/20.18 | | | | | | | (32) all_57_10 = e1 & op(e2, e0) = e1 % 136.14/20.18 | | | | | | | % 136.14/20.18 | | | | | | | ALPHA: (32) implies: % 136.14/20.18 | | | | | | | (33) all_57_10 = e1 % 136.14/20.18 | | | | | | | % 136.14/20.18 | | | | | | | BETA: splitting (1) gives: % 136.14/20.18 | | | | | | | % 136.14/20.18 | | | | | | | Case 1: % 136.14/20.18 | | | | | | | | % 136.14/20.18 | | | | | | | | (34) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & % 136.14/20.18 | | | | | | | | op(e2, e2) = e2) % 136.14/20.18 | | | | | | | | % 136.14/20.18 | | | | | | | | BETA: splitting (34) gives: % 136.14/20.18 | | | | | | | | % 136.14/20.18 | | | | | | | | Case 1: % 136.14/20.18 | | | | | | | | | % 136.14/20.18 | | | | | | | | | (35) all_57_2 = e2 & op(e2, e3) = e2 % 136.14/20.18 | | | | | | | | | % 136.14/20.18 | | | | | | | | | REF_CLOSE: (3), (23), (35) are inconsistent by sub-proof #680. % 136.14/20.18 | | | | | | | | | % 136.14/20.18 | | | | | | | | Case 2: % 136.14/20.18 | | | | | | | | | % 136.14/20.18 | | | | | | | | | (36) all_57_3 = e2 & op(e2, e2) = e2 % 136.14/20.18 | | | | | | | | | % 136.14/20.18 | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (11), (12), % 136.14/20.18 | | | | | | | | | (13), (14), (15), (16), (20), (29), (36) are % 136.14/20.18 | | | | | | | | | inconsistent by sub-proof #297. % 136.14/20.18 | | | | | | | | | % 136.14/20.18 | | | | | | | | End of split % 136.14/20.18 | | | | | | | | % 136.14/20.18 | | | | | | | Case 2: % 136.14/20.18 | | | | | | | | % 136.14/20.18 | | | | | | | | (37) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & % 136.14/20.18 | | | | | | | | op(e2, e0) = e2) % 136.14/20.18 | | | | | | | | % 136.14/20.18 | | | | | | | | BETA: splitting (37) gives: % 136.14/20.18 | | | | | | | | % 136.14/20.18 | | | | | | | | Case 1: % 136.14/20.18 | | | | | | | | | % 136.14/20.18 | | | | | | | | | (38) all_57_5 = e2 & op(e2, e1) = e2 % 136.14/20.18 | | | | | | | | | % 136.14/20.18 | | | | | | | | | ALPHA: (38) implies: % 136.14/20.18 | | | | | | | | | (39) all_57_5 = e2 % 136.14/20.18 | | | | | | | | | % 136.14/20.18 | | | | | | | | | BETA: splitting (17) gives: % 136.14/20.18 | | | | | | | | | % 136.14/20.18 | | | | | | | | | Case 1: % 136.14/20.18 | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | (40) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & % 136.14/20.18 | | | | | | | | | | op(e2, e2) = e1) % 136.14/20.18 | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | BETA: splitting (40) gives: % 136.14/20.18 | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | Case 1: % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | | (41) all_57_2 = e1 & op(e2, e3) = e1 % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | | ALPHA: (41) implies: % 136.14/20.18 | | | | | | | | | | | (42) all_57_2 = e1 % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | | COMBINE_EQS: (23), (42) imply: % 136.14/20.18 | | | | | | | | | | | (43) e1 = e0 % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | | SIMP: (43) implies: % 136.14/20.18 | | | | | | | | | | | (44) e1 = e0 % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | | COMBINE_EQS: (33), (44) imply: % 136.14/20.18 | | | | | | | | | | | (45) all_57_10 = e0 % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (10), (11), (12), (15), % 136.14/20.18 | | | | | | | | | | | (16), (19), (20), (45) are inconsistent by % 136.14/20.18 | | | | | | | | | | | sub-proof #294. % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | Case 2: % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | | (46) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | | ALPHA: (46) implies: % 136.14/20.18 | | | | | | | | | | | (47) op(e2, e2) = e1 % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | | REF_CLOSE: (4), (8), (15), (47) are inconsistent by sub-proof % 136.14/20.18 | | | | | | | | | | | #325. % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | End of split % 136.14/20.18 | | | | | | | | | | % 136.14/20.18 | | | | | | | | | Case 2: % 136.14/20.18 | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | (48) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 % 136.14/20.18 | | | | | | | | | | & op(e2, e0) = e1) % 136.14/20.18 | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | BETA: splitting (48) gives: % 136.14/20.18 | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | Case 1: % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | | (49) all_57_5 = e1 & op(e2, e1) = e1 % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | | ALPHA: (49) implies: % 136.14/20.18 | | | | | | | | | | | (50) all_57_5 = e1 % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | | REF_CLOSE: (5), (39), (50) are inconsistent by sub-proof % 136.14/20.18 | | | | | | | | | | | #418. % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | Case 2: % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (10), (11), (12), % 136.14/20.18 | | | | | | | | | | | (15), (16), (19), (20), (32) are inconsistent by % 136.14/20.18 | | | | | | | | | | | sub-proof #293. % 136.14/20.18 | | | | | | | | | | | % 136.14/20.18 | | | | | | | | | | End of split % 136.14/20.18 | | | | | | | | | | % 136.14/20.18 | | | | | | | | | End of split % 136.14/20.18 | | | | | | | | | % 136.14/20.18 | | | | | | | | Case 2: % 136.14/20.18 | | | | | | | | | % 136.14/20.18 | | | | | | | | | (51) all_57_10 = e2 & op(e2, e0) = e2 % 136.14/20.18 | | | | | | | | | % 136.14/20.18 | | | | | | | | | ALPHA: (51) implies: % 136.14/20.18 | | | | | | | | | (52) op(e2, e0) = e2 % 136.14/20.18 | | | | | | | | | % 136.14/20.18 | | | | | | | | | REF_CLOSE: (3), (4), (9), (52) are inconsistent by sub-proof % 136.14/20.18 | | | | | | | | | #451. % 136.14/20.18 | | | | | | | | | % 136.14/20.18 | | | | | | | | End of split % 136.14/20.18 | | | | | | | | % 136.14/20.18 | | | | | | | End of split % 136.14/20.18 | | | | | | | % 136.14/20.18 | | | | | | End of split % 136.14/20.18 | | | | | | % 136.14/20.18 | | | | | Case 2: % 136.14/20.18 | | | | | | % 136.14/20.18 | | | | | | (53) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & % 136.14/20.18 | | | | | | op(e0, e0) = e1) % 136.14/20.18 | | | | | | % 136.14/20.18 | | | | | | REF_CLOSE: (4), (5), (12), (15), (29), (53) are inconsistent by % 136.14/20.18 | | | | | | sub-proof #295. % 136.14/20.18 | | | | | | % 136.14/20.18 | | | | | End of split % 136.14/20.18 | | | | | % 136.14/20.18 | | | | Case 2: % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | (54) all_57_15 = e3 & op(e0, e0) = e3 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | ALPHA: (54) implies: % 136.14/20.18 | | | | | (55) op(e0, e0) = e3 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | REF_CLOSE: (4), (7), (12), (55) are inconsistent by sub-proof #634. % 136.14/20.18 | | | | | % 136.14/20.18 | | | | End of split % 136.14/20.18 | | | | % 136.14/20.18 | | | End of split % 136.14/20.18 | | | % 136.14/20.18 | | Case 2: % 136.14/20.18 | | | % 136.14/20.18 | | | (56) all_57_3 = e0 & op(e2, e2) = e0 % 136.14/20.18 | | | % 136.14/20.18 | | | ALPHA: (56) implies: % 136.14/20.18 | | | (57) op(e2, e2) = e0 % 136.14/20.18 | | | % 136.14/20.18 | | | REF_CLOSE: (4), (6), (8), (57) are inconsistent by sub-proof #641. % 136.14/20.18 | | | % 136.14/20.18 | | End of split % 136.14/20.18 | | % 136.14/20.18 | Case 2: % 136.14/20.18 | | % 136.14/20.18 | | (58) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = % 136.14/20.18 | | e0) % 136.14/20.18 | | % 136.14/20.18 | | BETA: splitting (58) gives: % 136.14/20.18 | | % 136.14/20.18 | | Case 1: % 136.14/20.18 | | | % 136.14/20.18 | | | (59) all_57_5 = e0 & op(e2, e1) = e0 % 136.14/20.18 | | | % 136.14/20.18 | | | ALPHA: (59) implies: % 136.14/20.18 | | | (60) all_57_5 = e0 % 136.14/20.18 | | | % 136.14/20.18 | | | BETA: splitting (10) gives: % 136.14/20.18 | | | % 136.14/20.18 | | | Case 1: % 136.14/20.18 | | | | % 136.14/20.18 | | | | (61) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) % 136.14/20.18 | | | | = e3) % 136.14/20.18 | | | | % 136.14/20.18 | | | | BETA: splitting (61) gives: % 136.14/20.18 | | | | % 136.14/20.18 | | | | Case 1: % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | (62) all_57_9 = e3 & op(e3, e0) = e3 % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | REF_CLOSE: (6), (19), (62) are inconsistent by sub-proof #614. % 136.14/20.18 | | | | | % 136.14/20.18 | | | | Case 2: % 136.14/20.18 | | | | | % 136.14/20.18 | | | | | (63) all_57_10 = e3 & op(e2, e0) = e3 % 136.14/20.18 | | | | | % 136.14/20.19 | | | | | REF_CLOSE: (2), (4), (11), (63) are inconsistent by sub-proof #749. % 136.14/20.19 | | | | | % 136.14/20.19 | | | | End of split % 136.14/20.19 | | | | % 136.14/20.19 | | | Case 2: % 136.14/20.19 | | | | % 136.14/20.19 | | | | (64) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, % 136.14/20.19 | | | | e0) = e3) % 136.14/20.19 | | | | % 136.14/20.19 | | | | BETA: splitting (64) gives: % 136.14/20.19 | | | | % 136.14/20.19 | | | | Case 1: % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | (65) all_57_11 = e3 & op(e1, e0) = e3 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | ALPHA: (65) implies: % 136.14/20.19 | | | | | (66) all_57_11 = e3 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | BETA: splitting (20) gives: % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | Case 1: % 136.14/20.19 | | | | | | % 136.14/20.19 | | | | | | (67) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, % 136.14/20.19 | | | | | | e0) = e1) % 136.14/20.19 | | | | | | % 136.14/20.19 | | | | | | BETA: splitting (67) gives: % 136.14/20.19 | | | | | | % 136.14/20.19 | | | | | | Case 1: % 136.14/20.19 | | | | | | | % 136.14/20.19 | | | | | | | (68) all_57_9 = e1 & op(e3, e0) = e1 % 136.14/20.19 | | | | | | | % 136.14/20.19 | | | | | | | REF_CLOSE: (16), (19), (68) are inconsistent by sub-proof #298. % 136.14/20.19 | | | | | | | % 136.14/20.19 | | | | | | Case 2: % 136.14/20.19 | | | | | | | % 136.14/20.19 | | | | | | | (69) all_57_10 = e1 & op(e2, e0) = e1 % 136.14/20.19 | | | | | | | % 136.14/20.19 | | | | | | | ALPHA: (69) implies: % 136.14/20.19 | | | | | | | (70) all_57_10 = e1 % 136.14/20.19 | | | | | | | % 136.14/20.19 | | | | | | | BETA: splitting (1) gives: % 136.14/20.19 | | | | | | | % 136.14/20.19 | | | | | | | Case 1: % 136.14/20.19 | | | | | | | | % 136.14/20.19 | | | | | | | | (71) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & % 136.14/20.19 | | | | | | | | op(e2, e2) = e2) % 136.14/20.19 | | | | | | | | % 136.14/20.19 | | | | | | | | BETA: splitting (71) gives: % 136.14/20.19 | | | | | | | | % 136.14/20.19 | | | | | | | | Case 1: % 136.14/20.19 | | | | | | | | | % 136.14/20.19 | | | | | | | | | (72) all_57_2 = e2 & op(e2, e3) = e2 % 136.14/20.19 | | | | | | | | | % 136.14/20.19 | | | | | | | | | ALPHA: (72) implies: % 136.14/20.19 | | | | | | | | | (73) op(e2, e3) = e2 % 136.14/20.19 | | | | | | | | | % 136.14/20.19 | | | | | | | | | BETA: splitting (17) gives: % 136.14/20.19 | | | | | | | | | % 136.14/20.19 | | | | | | | | | Case 1: % 136.14/20.19 | | | | | | | | | | % 136.14/20.19 | | | | | | | | | | (74) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & % 136.14/20.19 | | | | | | | | | | op(e2, e2) = e1) % 136.14/20.19 | | | | | | | | | | % 136.14/20.19 | | | | | | | | | | REF_CLOSE: (4), (5), (8), (15), (73), (74) are inconsistent % 136.14/20.19 | | | | | | | | | | by sub-proof #292. % 136.14/20.19 | | | | | | | | | | % 136.14/20.19 | | | | | | | | | Case 2: % 136.14/20.19 | | | | | | | | | | % 136.14/20.19 | | | | | | | | | | (75) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 % 136.14/20.19 | | | | | | | | | | & op(e2, e0) = e1) % 136.14/20.19 | | | | | | | | | | % 136.14/20.19 | | | | | | | | | | BETA: splitting (75) gives: % 136.14/20.19 | | | | | | | | | | % 136.14/20.19 | | | | | | | | | | Case 1: % 136.14/20.19 | | | | | | | | | | | % 136.14/20.19 | | | | | | | | | | | (76) all_57_5 = e1 & op(e2, e1) = e1 % 136.14/20.19 | | | | | | | | | | | % 136.14/20.19 | | | | | | | | | | | ALPHA: (76) implies: % 136.14/20.19 | | | | | | | | | | | (77) all_57_5 = e1 % 136.14/20.19 | | | | | | | | | | | % 136.14/20.19 | | | | | | | | | | | COMBINE_EQS: (60), (77) imply: % 136.14/20.19 | | | | | | | | | | | (78) e1 = e0 % 136.14/20.19 | | | | | | | | | | | % 136.14/20.19 | | | | | | | | | | | COMBINE_EQS: (70), (78) imply: % 136.14/20.19 | | | | | | | | | | | (79) all_57_10 = e0 % 136.14/20.19 | | | | | | | | | | | % 136.14/20.19 | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (10), (11), (12), (15), % 136.14/20.19 | | | | | | | | | | | (16), (19), (20), (79) are inconsistent by % 136.14/20.19 | | | | | | | | | | | sub-proof #294. % 136.14/20.19 | | | | | | | | | | | % 136.14/20.19 | | | | | | | | | | Case 2: % 136.14/20.19 | | | | | | | | | | | % 136.14/20.19 | | | | | | | | | | | % 136.14/20.19 | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (10), (11), (12), % 136.14/20.19 | | | | | | | | | | | (15), (16), (19), (20), (69) are inconsistent by % 136.14/20.19 | | | | | | | | | | | sub-proof #293. % 136.14/20.19 | | | | | | | | | | | % 136.14/20.19 | | | | | | | | | | End of split % 136.14/20.19 | | | | | | | | | | % 136.14/20.19 | | | | | | | | | End of split % 136.14/20.19 | | | | | | | | | % 136.14/20.19 | | | | | | | | Case 2: % 136.14/20.19 | | | | | | | | | % 136.14/20.19 | | | | | | | | | (80) all_57_3 = e2 & op(e2, e2) = e2 % 136.14/20.19 | | | | | | | | | % 136.14/20.19 | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (11), (12), % 136.14/20.19 | | | | | | | | | (13), (14), (15), (16), (20), (66), (80) are % 136.14/20.19 | | | | | | | | | inconsistent by sub-proof #297. % 136.14/20.19 | | | | | | | | | % 136.14/20.19 | | | | | | | | End of split % 136.14/20.19 | | | | | | | | % 136.14/20.19 | | | | | | | Case 2: % 136.14/20.19 | | | | | | | | % 136.14/20.19 | | | | | | | | (81) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & % 136.14/20.19 | | | | | | | | op(e2, e0) = e2) % 136.14/20.19 | | | | | | | | % 136.14/20.19 | | | | | | | | BETA: splitting (81) gives: % 136.14/20.19 | | | | | | | | % 136.14/20.19 | | | | | | | | Case 1: % 136.14/20.19 | | | | | | | | | % 136.14/20.19 | | | | | | | | | (82) all_57_5 = e2 & op(e2, e1) = e2 % 136.14/20.19 | | | | | | | | | % 136.14/20.19 | | | | | | | | | ALPHA: (82) implies: % 136.14/20.19 | | | | | | | | | (83) all_57_5 = e2 % 136.14/20.19 | | | | | | | | | % 136.14/20.19 | | | | | | | | | REF_CLOSE: (3), (60), (83) are inconsistent by sub-proof #372. % 136.14/20.19 | | | | | | | | | % 136.14/20.19 | | | | | | | | Case 2: % 136.14/20.19 | | | | | | | | | % 136.14/20.19 | | | | | | | | | (84) all_57_10 = e2 & op(e2, e0) = e2 % 136.14/20.19 | | | | | | | | | % 136.14/20.19 | | | | | | | | | ALPHA: (84) implies: % 136.14/20.19 | | | | | | | | | (85) op(e2, e0) = e2 % 136.14/20.19 | | | | | | | | | % 136.14/20.19 | | | | | | | | | REF_CLOSE: (3), (4), (9), (85) are inconsistent by sub-proof % 136.14/20.19 | | | | | | | | | #451. % 136.14/20.19 | | | | | | | | | % 136.14/20.19 | | | | | | | | End of split % 136.14/20.19 | | | | | | | | % 136.14/20.19 | | | | | | | End of split % 136.14/20.19 | | | | | | | % 136.14/20.19 | | | | | | End of split % 136.14/20.19 | | | | | | % 136.14/20.19 | | | | | Case 2: % 136.14/20.19 | | | | | | % 136.14/20.19 | | | | | | (86) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & % 136.14/20.19 | | | | | | op(e0, e0) = e1) % 136.14/20.19 | | | | | | % 136.14/20.19 | | | | | | REF_CLOSE: (4), (5), (12), (15), (66), (86) are inconsistent by % 136.14/20.19 | | | | | | sub-proof #295. % 136.14/20.19 | | | | | | % 136.14/20.19 | | | | | End of split % 136.14/20.19 | | | | | % 136.14/20.19 | | | | Case 2: % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | (87) all_57_15 = e3 & op(e0, e0) = e3 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | ALPHA: (87) implies: % 136.14/20.19 | | | | | (88) op(e0, e0) = e3 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | REF_CLOSE: (4), (7), (12), (88) are inconsistent by sub-proof #634. % 136.14/20.19 | | | | | % 136.14/20.19 | | | | End of split % 136.14/20.19 | | | | % 136.14/20.19 | | | End of split % 136.14/20.19 | | | % 136.14/20.19 | | Case 2: % 136.14/20.19 | | | % 136.14/20.19 | | | (89) all_57_10 = e0 & op(e2, e0) = e0 % 136.14/20.19 | | | % 136.14/20.19 | | | ALPHA: (89) implies: % 136.14/20.19 | | | (90) all_57_10 = e0 % 136.14/20.19 | | | % 136.14/20.19 | | | REF_CLOSE: (2), (4), (5), (6), (7), (10), (11), (12), (15), (16), (19), % 136.14/20.19 | | | (20), (90) are inconsistent by sub-proof #294. % 136.14/20.19 | | | % 136.14/20.19 | | End of split % 136.14/20.19 | | % 136.14/20.19 | End of split % 136.14/20.19 | % 136.14/20.19 End of proof % 136.14/20.19 % 136.14/20.19 Sub-proof #292 shows that the following formulas are inconsistent: % 136.14/20.19 ---------------------------------------------------------------- % 136.14/20.19 (1) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) % 136.14/20.19 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.19 (3) ~ (e2 = e1) % 136.14/20.19 (4) op(e2, e2) = e3 % 136.14/20.19 (5) ~ (e3 = e1) % 136.14/20.19 (6) op(e2, e3) = e2 % 136.14/20.19 % 136.14/20.19 Begin of proof % 136.14/20.19 | % 136.14/20.19 | BETA: splitting (1) gives: % 136.14/20.19 | % 136.14/20.19 | Case 1: % 136.14/20.19 | | % 136.14/20.19 | | (7) all_57_2 = e1 & op(e2, e3) = e1 % 136.14/20.19 | | % 136.14/20.19 | | ALPHA: (7) implies: % 136.14/20.19 | | (8) op(e2, e3) = e1 % 136.14/20.19 | | % 136.14/20.19 | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #450. % 136.14/20.19 | | % 136.14/20.19 | Case 2: % 136.14/20.19 | | % 136.14/20.19 | | (9) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.19 | | % 136.14/20.19 | | ALPHA: (9) implies: % 136.14/20.19 | | (10) op(e2, e2) = e1 % 136.14/20.19 | | % 136.14/20.19 | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #325. % 136.14/20.19 | | % 136.14/20.19 | End of split % 136.14/20.19 | % 136.14/20.19 End of proof % 136.14/20.19 % 136.14/20.19 Sub-proof #293 shows that the following formulas are inconsistent: % 136.14/20.19 ---------------------------------------------------------------- % 136.14/20.19 (1) op(e2, e0) = all_52_13 % 136.14/20.19 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.19 (3) ~ (e2 = e1) % 136.14/20.19 (4) ~ (e3 = e0) % 136.14/20.19 (5) ~ (e3 = e2) % 136.14/20.19 (6) op(e2, e0) = e0 % 136.14/20.19 (7) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) | % 136.14/20.19 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.19 (8) all_57_10 = e1 & op(e2, e0) = e1 % 136.14/20.19 (9) ~ (all_52_13 = e3) % 136.14/20.19 (10) op(e0, e0) = e2 % 136.14/20.19 (11) ~ (e3 = e1) % 136.14/20.19 (12) ~ (e1 = e0) % 136.14/20.19 (13) all_57_9 = e0 % 136.14/20.19 (14) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) | % 136.14/20.19 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.19 % 136.14/20.19 Begin of proof % 136.14/20.19 | % 136.14/20.19 | ALPHA: (8) implies: % 136.14/20.19 | (15) all_57_10 = e1 % 136.14/20.19 | (16) op(e2, e0) = e1 % 136.14/20.19 | % 136.14/20.19 | GROUND_INST: instantiating (2) with e0, e1, e0, e2, simplifying with (6), (16) % 136.14/20.19 | gives: % 136.14/20.19 | (17) e1 = e0 % 136.14/20.19 | % 136.14/20.19 | COMBINE_EQS: (15), (17) imply: % 136.14/20.19 | (18) all_57_10 = e0 % 136.14/20.19 | % 136.14/20.19 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (12), (13), (14), % 136.14/20.19 | (18) are inconsistent by sub-proof #294. % 136.14/20.19 | % 136.14/20.19 End of proof % 136.14/20.19 % 136.14/20.19 Sub-proof #294 shows that the following formulas are inconsistent: % 136.14/20.19 ---------------------------------------------------------------- % 136.14/20.19 (1) op(e2, e0) = all_52_13 % 136.14/20.19 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.19 (3) ~ (e2 = e1) % 136.14/20.19 (4) ~ (e3 = e0) % 136.14/20.19 (5) ~ (e3 = e2) % 136.14/20.19 (6) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) | % 136.14/20.19 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.19 (7) ~ (all_52_13 = e3) % 136.14/20.19 (8) all_57_10 = e0 % 136.14/20.19 (9) op(e0, e0) = e2 % 136.14/20.19 (10) ~ (e3 = e1) % 136.14/20.19 (11) ~ (e1 = e0) % 136.14/20.19 (12) all_57_9 = e0 % 136.14/20.19 (13) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) | % 136.14/20.19 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.19 % 136.14/20.19 Begin of proof % 136.14/20.19 | % 136.14/20.19 | BETA: splitting (6) gives: % 136.14/20.19 | % 136.14/20.19 | Case 1: % 136.14/20.19 | | % 136.14/20.19 | | (14) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = % 136.14/20.19 | | e3) % 136.14/20.19 | | % 136.14/20.19 | | BETA: splitting (14) gives: % 136.14/20.19 | | % 136.14/20.19 | | Case 1: % 136.14/20.19 | | | % 136.14/20.19 | | | (15) all_57_9 = e3 & op(e3, e0) = e3 % 136.14/20.19 | | | % 136.14/20.19 | | | REF_CLOSE: (4), (12), (15) are inconsistent by sub-proof #614. % 136.14/20.19 | | | % 136.14/20.19 | | Case 2: % 136.14/20.19 | | | % 136.14/20.19 | | | (16) all_57_10 = e3 & op(e2, e0) = e3 % 136.14/20.19 | | | % 136.14/20.19 | | | REF_CLOSE: (1), (2), (7), (16) are inconsistent by sub-proof #749. % 136.14/20.19 | | | % 136.14/20.19 | | End of split % 136.14/20.19 | | % 136.14/20.19 | Case 2: % 136.14/20.19 | | % 136.14/20.19 | | (17) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = % 136.14/20.19 | | e3) % 136.14/20.19 | | % 136.14/20.19 | | BETA: splitting (17) gives: % 136.14/20.19 | | % 136.14/20.19 | | Case 1: % 136.14/20.19 | | | % 136.14/20.19 | | | (18) all_57_11 = e3 & op(e1, e0) = e3 % 136.14/20.19 | | | % 136.14/20.19 | | | ALPHA: (18) implies: % 136.14/20.19 | | | (19) all_57_11 = e3 % 136.14/20.19 | | | % 136.14/20.19 | | | BETA: splitting (13) gives: % 136.14/20.19 | | | % 136.14/20.19 | | | Case 1: % 136.14/20.19 | | | | % 136.14/20.19 | | | | (20) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) % 136.14/20.19 | | | | = e1) % 136.14/20.19 | | | | % 136.14/20.19 | | | | BETA: splitting (20) gives: % 136.14/20.19 | | | | % 136.14/20.19 | | | | Case 1: % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | (21) all_57_9 = e1 & op(e3, e0) = e1 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | REF_CLOSE: (11), (12), (21) are inconsistent by sub-proof #298. % 136.14/20.19 | | | | | % 136.14/20.19 | | | | Case 2: % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | (22) all_57_10 = e1 & op(e2, e0) = e1 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | ALPHA: (22) implies: % 136.14/20.19 | | | | | (23) all_57_10 = e1 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | REF_CLOSE: (8), (11), (23) are inconsistent by sub-proof #639. % 136.14/20.19 | | | | | % 136.14/20.19 | | | | End of split % 136.14/20.19 | | | | % 136.14/20.19 | | | Case 2: % 136.14/20.19 | | | | % 136.14/20.19 | | | | (24) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, % 136.14/20.19 | | | | e0) = e1) % 136.14/20.19 | | | | % 136.14/20.19 | | | | REF_CLOSE: (2), (3), (9), (10), (19), (24) are inconsistent by sub-proof % 136.14/20.19 | | | | #295. % 136.14/20.19 | | | | % 136.14/20.19 | | | End of split % 136.14/20.19 | | | % 136.14/20.19 | | Case 2: % 136.14/20.19 | | | % 136.14/20.19 | | | (25) all_57_15 = e3 & op(e0, e0) = e3 % 136.14/20.19 | | | % 136.14/20.19 | | | ALPHA: (25) implies: % 136.14/20.19 | | | (26) op(e0, e0) = e3 % 136.14/20.19 | | | % 136.14/20.19 | | | REF_CLOSE: (2), (5), (9), (26) are inconsistent by sub-proof #634. % 136.14/20.19 | | | % 136.14/20.19 | | End of split % 136.14/20.19 | | % 136.14/20.19 | End of split % 136.14/20.19 | % 136.14/20.19 End of proof % 136.14/20.19 % 136.14/20.19 Sub-proof #295 shows that the following formulas are inconsistent: % 136.14/20.19 ---------------------------------------------------------------- % 136.14/20.19 (1) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.19 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.19 (3) ~ (e2 = e1) % 136.14/20.19 (4) all_57_11 = e3 % 136.14/20.19 (5) op(e0, e0) = e2 % 136.14/20.19 (6) ~ (e3 = e1) % 136.14/20.19 % 136.14/20.19 Begin of proof % 136.14/20.19 | % 136.14/20.19 | BETA: splitting (1) gives: % 136.14/20.19 | % 136.14/20.19 | Case 1: % 136.14/20.19 | | % 136.14/20.19 | | (7) all_57_11 = e1 & op(e1, e0) = e1 % 136.14/20.19 | | % 136.14/20.19 | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #296. % 136.14/20.19 | | % 136.14/20.19 | Case 2: % 136.14/20.19 | | % 136.14/20.19 | | (8) all_57_15 = e1 & op(e0, e0) = e1 % 136.14/20.19 | | % 136.14/20.19 | | ALPHA: (8) implies: % 136.14/20.19 | | (9) op(e0, e0) = e1 % 136.14/20.19 | | % 136.14/20.19 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #636. % 136.14/20.19 | | % 136.14/20.19 | End of split % 136.14/20.19 | % 136.14/20.19 End of proof % 136.14/20.19 % 136.14/20.19 Sub-proof #296 shows that the following formulas are inconsistent: % 136.14/20.19 ---------------------------------------------------------------- % 136.14/20.19 (1) all_57_11 = e1 & op(e1, e0) = e1 % 136.14/20.19 (2) all_57_11 = e3 % 136.14/20.19 (3) ~ (e3 = e1) % 136.14/20.19 % 136.14/20.19 Begin of proof % 136.14/20.19 | % 136.14/20.19 | ALPHA: (1) implies: % 136.14/20.19 | (4) all_57_11 = e1 % 136.14/20.19 | % 136.14/20.19 | COMBINE_EQS: (2), (4) imply: % 136.14/20.19 | (5) e3 = e1 % 136.14/20.19 | % 136.14/20.19 | REDUCE: (3), (5) imply: % 136.14/20.19 | (6) $false % 136.14/20.19 | % 136.14/20.19 | CLOSE: (6) is inconsistent. % 136.14/20.19 | % 136.14/20.19 End of proof % 136.14/20.19 % 136.14/20.19 Sub-proof #297 shows that the following formulas are inconsistent: % 136.14/20.19 ---------------------------------------------------------------- % 136.14/20.19 (1) op(e2, e0) = all_52_13 % 136.14/20.19 (2) ~ (e2 = e0) % 136.14/20.19 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.19 (4) ~ (e2 = e1) % 136.14/20.19 (5) ~ (e3 = e0) % 136.14/20.19 (6) ~ (e3 = e2) % 136.14/20.19 (7) all_57_3 = e2 & op(e2, e2) = e2 % 136.14/20.19 (8) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) | % 136.14/20.19 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.19 (9) all_57_11 = e3 % 136.14/20.19 (10) ~ (all_52_13 = e3) % 136.14/20.19 (11) op(e0, e0) = e2 % 136.14/20.19 (12) all_57_3 = e3 % 136.14/20.19 (13) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.19 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.14/20.19 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.19 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.19 (14) ~ (e3 = e1) % 136.14/20.19 (15) ~ (e1 = e0) % 136.14/20.19 (16) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) | % 136.14/20.19 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.19 % 136.14/20.19 Begin of proof % 136.14/20.19 | % 136.14/20.19 | ALPHA: (7) implies: % 136.14/20.19 | (17) all_57_3 = e2 % 136.14/20.19 | % 136.14/20.19 | COMBINE_EQS: (12), (17) imply: % 136.14/20.19 | (18) e3 = e2 % 136.14/20.19 | % 136.14/20.19 | COMBINE_EQS: (9), (18) imply: % 136.14/20.19 | (19) all_57_11 = e2 % 136.14/20.19 | % 136.14/20.19 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (13), (14), (15), % 136.14/20.19 | (16), (19) are inconsistent by sub-proof #633. % 136.14/20.19 | % 136.14/20.19 End of proof % 136.14/20.19 % 136.14/20.19 Sub-proof #298 shows that the following formulas are inconsistent: % 136.14/20.19 ---------------------------------------------------------------- % 136.14/20.19 (1) all_57_9 = e1 & op(e3, e0) = e1 % 136.14/20.19 (2) all_57_9 = e0 % 136.14/20.19 (3) ~ (e1 = e0) % 136.14/20.19 % 136.14/20.19 Begin of proof % 136.14/20.19 | % 136.14/20.19 | ALPHA: (1) implies: % 136.14/20.19 | (4) all_57_9 = e1 % 136.14/20.19 | % 136.14/20.19 | COMBINE_EQS: (2), (4) imply: % 136.14/20.19 | (5) e1 = e0 % 136.14/20.19 | % 136.14/20.19 | REDUCE: (3), (5) imply: % 136.14/20.19 | (6) $false % 136.14/20.19 | % 136.14/20.19 | CLOSE: (6) is inconsistent. % 136.14/20.19 | % 136.14/20.19 End of proof % 136.14/20.19 % 136.14/20.19 Sub-proof #299 shows that the following formulas are inconsistent: % 136.14/20.19 ---------------------------------------------------------------- % 136.14/20.19 (1) all_57_9 = e0 & op(e3, e0) = e0 % 136.14/20.19 (2) all_57_9 = e3 % 136.14/20.19 (3) ~ (e3 = e0) % 136.14/20.19 % 136.14/20.19 Begin of proof % 136.14/20.19 | % 136.14/20.19 | ALPHA: (1) implies: % 136.14/20.19 | (4) all_57_9 = e0 % 136.14/20.19 | % 136.14/20.19 | COMBINE_EQS: (2), (4) imply: % 136.14/20.19 | (5) e3 = e0 % 136.14/20.19 | % 136.14/20.19 | REDUCE: (3), (5) imply: % 136.14/20.19 | (6) $false % 136.14/20.19 | % 136.14/20.19 | CLOSE: (6) is inconsistent. % 136.14/20.19 | % 136.14/20.19 End of proof % 136.14/20.19 % 136.14/20.19 Sub-proof #300 shows that the following formulas are inconsistent: % 136.14/20.19 ---------------------------------------------------------------- % 136.14/20.19 (1) op(e0, e0) = e0 % 136.14/20.19 (2) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.19 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 136.14/20.19 (3) ~ (e2 = e0) % 136.14/20.19 (4) all_57_1 = e2 % 136.14/20.19 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.19 (6) ~ (e2 = e1) % 136.14/20.19 (7) ~ (e3 = e0) % 136.14/20.19 (8) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) | % 136.14/20.19 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2) % 136.14/20.19 (9) ~ (e3 = e2) % 136.14/20.19 (10) op(e1, e1) = e3 % 136.14/20.19 (11) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.19 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.19 (12) all_57_12 = e3 % 136.14/20.19 (13) all_57_3 = e3 % 136.14/20.19 (14) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.14/20.19 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.19 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 136.14/20.19 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.19 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 136.14/20.19 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 136.14/20.19 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.14/20.19 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.14/20.19 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.14/20.19 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.14/20.19 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 136.14/20.19 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.14/20.19 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 136.14/20.19 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.14/20.19 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 136.14/20.19 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 136.14/20.19 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.19 $i(all_56_21) & $i(all_56_29)) % 136.14/20.19 (15) ~ (e3 = e1) % 136.14/20.19 (16) ~ (e1 = e0) % 136.14/20.19 (17) op(e0, e0) = all_56_31 % 136.14/20.19 % 136.14/20.19 Begin of proof % 136.14/20.19 | % 136.14/20.19 | BETA: splitting (14) gives: % 136.14/20.19 | % 136.14/20.19 | Case 1: % 136.14/20.19 | | % 136.14/20.19 | | (18) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.14/20.19 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.19 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.14/20.19 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 136.14/20.19 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 136.14/20.19 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 136.14/20.19 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.14/20.19 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.14/20.19 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.14/20.19 | | $i(all_56_27)) % 136.14/20.19 | | % 136.14/20.19 | | REF_CLOSE: (1), (3), (5), (7), (17), (18) are inconsistent by sub-proof % 136.14/20.19 | | #713. % 136.14/20.19 | | % 136.14/20.19 | Case 2: % 136.14/20.19 | | % 136.14/20.19 | | (19) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.14/20.19 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.14/20.19 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.14/20.19 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.14/20.19 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.14/20.19 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.14/20.19 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.14/20.19 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.14/20.19 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.14/20.19 | | $i(all_56_29)) % 136.14/20.19 | | % 136.14/20.19 | | BETA: splitting (19) gives: % 136.14/20.19 | | % 136.14/20.19 | | Case 1: % 136.14/20.19 | | | % 136.14/20.19 | | | (20) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.14/20.19 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.14/20.19 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.14/20.19 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.14/20.19 | | | $i(all_56_15) & $i(all_56_23) % 136.14/20.19 | | | % 136.14/20.19 | | | ALPHA: (20) implies: % 136.14/20.19 | | | (21) op(e1, e1) = e0 % 136.14/20.19 | | | % 136.14/20.19 | | | REF_CLOSE: (5), (7), (10), (21) are inconsistent by sub-proof #753. % 136.14/20.19 | | | % 136.14/20.19 | | Case 2: % 136.14/20.19 | | | % 136.14/20.19 | | | (22) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.14/20.19 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.14/20.19 | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.14/20.19 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.14/20.19 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.14/20.19 | | | % 136.14/20.19 | | | ALPHA: (22) implies: % 136.14/20.19 | | | (23) all_56_31 = e1 % 136.14/20.19 | | | (24) op(e0, e1) = e0 % 136.14/20.19 | | | % 136.14/20.19 | | | REDUCE: (17), (23) imply: % 136.14/20.19 | | | (25) op(e0, e0) = e1 % 136.14/20.19 | | | % 136.14/20.19 | | | BETA: splitting (8) gives: % 136.14/20.19 | | | % 136.14/20.19 | | | Case 1: % 136.14/20.19 | | | | % 136.14/20.19 | | | | (26) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, % 136.14/20.19 | | | | e2) = e2) % 136.14/20.19 | | | | % 136.14/20.19 | | | | BETA: splitting (26) gives: % 136.14/20.19 | | | | % 136.14/20.19 | | | | Case 1: % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | (27) all_57_12 = e2 & op(e0, e3) = e2 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | ALPHA: (27) implies: % 136.14/20.19 | | | | | (28) all_57_12 = e2 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | REF_CLOSE: (9), (12), (28) are inconsistent by sub-proof #518. % 136.14/20.19 | | | | | % 136.14/20.19 | | | | Case 2: % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | (29) all_57_13 = e2 & op(e0, e2) = e2 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | ALPHA: (29) implies: % 136.14/20.19 | | | | | (30) all_57_13 = e2 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (11), (13), (15), (16), (30) are % 136.14/20.19 | | | | | inconsistent by sub-proof #301. % 136.14/20.19 | | | | | % 136.14/20.19 | | | | End of split % 136.14/20.19 | | | | % 136.14/20.19 | | | Case 2: % 136.14/20.19 | | | | % 136.14/20.19 | | | | (31) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, % 136.14/20.19 | | | | e0) = e2) % 136.14/20.19 | | | | % 136.14/20.19 | | | | BETA: splitting (31) gives: % 136.14/20.19 | | | | % 136.14/20.19 | | | | Case 1: % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | (32) all_57_14 = e2 & op(e0, e1) = e2 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | ALPHA: (32) implies: % 136.14/20.19 | | | | | (33) op(e0, e1) = e2 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | REF_CLOSE: (3), (5), (24), (33) are inconsistent by sub-proof #660. % 136.14/20.19 | | | | | % 136.14/20.19 | | | | Case 2: % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | (34) all_57_15 = e2 & op(e0, e0) = e2 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | ALPHA: (34) implies: % 136.14/20.19 | | | | | (35) op(e0, e0) = e2 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | REF_CLOSE: (5), (6), (25), (35) are inconsistent by sub-proof #636. % 136.14/20.19 | | | | | % 136.14/20.19 | | | | End of split % 136.14/20.19 | | | | % 136.14/20.19 | | | End of split % 136.14/20.19 | | | % 136.14/20.19 | | End of split % 136.14/20.19 | | % 136.14/20.19 | End of split % 136.14/20.19 | % 136.14/20.19 End of proof % 136.14/20.19 % 136.14/20.19 Sub-proof #301 shows that the following formulas are inconsistent: % 136.14/20.19 ---------------------------------------------------------------- % 136.14/20.19 (1) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.19 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 136.14/20.19 (2) ~ (e2 = e0) % 136.14/20.19 (3) all_57_1 = e2 % 136.14/20.19 (4) ~ (e2 = e1) % 136.14/20.19 (5) ~ (e3 = e0) % 136.14/20.19 (6) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.19 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.19 (7) all_57_13 = e2 % 136.14/20.19 (8) all_57_3 = e3 % 136.14/20.19 (9) ~ (e3 = e1) % 136.14/20.19 (10) ~ (e1 = e0) % 136.14/20.19 % 136.14/20.19 Begin of proof % 136.14/20.19 | % 136.14/20.19 | BETA: splitting (6) gives: % 136.14/20.19 | % 136.14/20.19 | Case 1: % 136.14/20.19 | | % 136.14/20.19 | | (11) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = % 136.14/20.19 | | e1) % 136.14/20.19 | | % 136.14/20.19 | | BETA: splitting (11) gives: % 136.14/20.19 | | % 136.14/20.19 | | Case 1: % 136.14/20.19 | | | % 136.14/20.19 | | | (12) all_57_1 = e1 & op(e3, e2) = e1 % 136.14/20.19 | | | % 136.14/20.19 | | | REF_CLOSE: (3), (4), (12) are inconsistent by sub-proof #465. % 136.14/20.19 | | | % 136.14/20.19 | | Case 2: % 136.14/20.19 | | | % 136.14/20.19 | | | (13) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.19 | | | % 136.14/20.19 | | | REF_CLOSE: (8), (9), (13) are inconsistent by sub-proof #303. % 136.14/20.19 | | | % 136.14/20.19 | | End of split % 136.14/20.19 | | % 136.14/20.19 | Case 2: % 136.14/20.19 | | % 136.14/20.19 | | (14) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = % 136.14/20.19 | | e1) % 136.14/20.19 | | % 136.14/20.19 | | BETA: splitting (14) gives: % 136.14/20.19 | | % 136.14/20.19 | | Case 1: % 136.14/20.19 | | | % 136.14/20.19 | | | (15) all_57_7 = e1 & op(e1, e2) = e1 % 136.14/20.19 | | | % 136.14/20.19 | | | ALPHA: (15) implies: % 136.14/20.19 | | | (16) all_57_7 = e1 % 136.14/20.19 | | | % 136.14/20.19 | | | BETA: splitting (1) gives: % 136.14/20.19 | | | % 136.14/20.19 | | | Case 1: % 136.14/20.19 | | | | % 136.14/20.19 | | | | (17) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) % 136.14/20.19 | | | | = e0) % 136.14/20.19 | | | | % 136.14/20.19 | | | | BETA: splitting (17) gives: % 136.14/20.19 | | | | % 136.14/20.19 | | | | Case 1: % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | (18) all_57_1 = e0 & op(e3, e2) = e0 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | REF_CLOSE: (2), (3), (18) are inconsistent by sub-proof #466. % 136.14/20.19 | | | | | % 136.14/20.19 | | | | Case 2: % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | (19) all_57_3 = e0 & op(e2, e2) = e0 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | REF_CLOSE: (5), (8), (19) are inconsistent by sub-proof #302. % 136.14/20.19 | | | | | % 136.14/20.19 | | | | End of split % 136.14/20.19 | | | | % 136.14/20.19 | | | Case 2: % 136.14/20.19 | | | | % 136.14/20.19 | | | | (20) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) % 136.14/20.19 | | | | = e0) % 136.14/20.19 | | | | % 136.14/20.19 | | | | BETA: splitting (20) gives: % 136.14/20.19 | | | | % 136.14/20.19 | | | | Case 1: % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | (21) all_57_7 = e0 & op(e1, e2) = e0 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | ALPHA: (21) implies: % 136.14/20.19 | | | | | (22) all_57_7 = e0 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | REF_CLOSE: (10), (16), (22) are inconsistent by sub-proof #464. % 136.14/20.19 | | | | | % 136.14/20.19 | | | | Case 2: % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | (23) all_57_13 = e0 & op(e0, e2) = e0 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | ALPHA: (23) implies: % 136.14/20.19 | | | | | (24) all_57_13 = e0 % 136.14/20.19 | | | | | % 136.14/20.19 | | | | | REF_CLOSE: (2), (7), (24) are inconsistent by sub-proof #404. % 136.14/20.19 | | | | | % 136.14/20.19 | | | | End of split % 136.14/20.19 | | | | % 136.14/20.19 | | | End of split % 136.14/20.19 | | | % 136.14/20.19 | | Case 2: % 136.14/20.19 | | | % 136.14/20.19 | | | (25) all_57_13 = e1 & op(e0, e2) = e1 % 136.14/20.19 | | | % 136.14/20.19 | | | ALPHA: (25) implies: % 136.14/20.19 | | | (26) all_57_13 = e1 % 136.14/20.19 | | | % 136.14/20.19 | | | REF_CLOSE: (4), (7), (26) are inconsistent by sub-proof #567. % 136.14/20.19 | | | % 136.14/20.19 | | End of split % 136.14/20.19 | | % 136.14/20.19 | End of split % 136.14/20.19 | % 136.14/20.19 End of proof % 136.14/20.19 % 136.14/20.19 Sub-proof #302 shows that the following formulas are inconsistent: % 136.14/20.19 ---------------------------------------------------------------- % 136.14/20.19 (1) all_57_3 = e0 & op(e2, e2) = e0 % 136.14/20.19 (2) all_57_3 = e3 % 136.14/20.19 (3) ~ (e3 = e0) % 136.14/20.19 % 136.14/20.19 Begin of proof % 136.14/20.19 | % 136.14/20.19 | ALPHA: (1) implies: % 136.14/20.20 | (4) all_57_3 = e0 % 136.14/20.20 | % 136.14/20.20 | COMBINE_EQS: (2), (4) imply: % 136.14/20.20 | (5) e3 = e0 % 136.14/20.20 | % 136.14/20.20 | SIMP: (5) implies: % 136.14/20.20 | (6) e3 = e0 % 136.14/20.20 | % 136.14/20.20 | REDUCE: (3), (6) imply: % 136.14/20.20 | (7) $false % 136.14/20.20 | % 136.14/20.20 | CLOSE: (7) is inconsistent. % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #303 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.20 (2) all_57_3 = e3 % 136.14/20.20 (3) ~ (e3 = e1) % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | ALPHA: (1) implies: % 136.14/20.20 | (4) all_57_3 = e1 % 136.14/20.20 | % 136.14/20.20 | COMBINE_EQS: (2), (4) imply: % 136.14/20.20 | (5) e3 = e1 % 136.14/20.20 | % 136.14/20.20 | SIMP: (5) implies: % 136.14/20.20 | (6) e3 = e1 % 136.14/20.20 | % 136.14/20.20 | REDUCE: (3), (6) imply: % 136.14/20.20 | (7) $false % 136.14/20.20 | % 136.14/20.20 | CLOSE: (7) is inconsistent. % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #304 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.14/20.20 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.14/20.20 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.14/20.20 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.20 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ % 136.14/20.20 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 136.14/20.20 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = % 136.14/20.20 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.14/20.20 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.14/20.20 $i(all_56_29)) % 136.14/20.20 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.20 (3) ~ (all_52_2 = e1) % 136.14/20.20 (4) op(e2, e2) = e3 % 136.14/20.20 (5) op(e1, e3) = all_52_2 % 136.14/20.20 (6) ~ (e3 = e1) % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | BETA: splitting (1) gives: % 136.14/20.20 | % 136.14/20.20 | Case 1: % 136.14/20.20 | | % 136.14/20.20 | | (7) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.14/20.20 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.20 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.14/20.20 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) % 136.14/20.20 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.14/20.20 | | % 136.14/20.20 | | ALPHA: (7) implies: % 136.14/20.20 | | (8) op(e1, e3) = e1 % 136.14/20.20 | | % 136.14/20.20 | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #725. % 136.14/20.20 | | % 136.14/20.20 | Case 2: % 136.14/20.20 | | % 136.14/20.20 | | (9) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.14/20.20 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 % 136.14/20.20 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.14/20.20 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.14/20.20 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.14/20.20 | | % 136.14/20.20 | | ALPHA: (9) implies: % 136.14/20.20 | | (10) op(e2, e2) = e1 % 136.14/20.20 | | % 136.14/20.20 | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #325. % 136.14/20.20 | | % 136.14/20.20 | End of split % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #305 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) ~ (all_22_1 = e1) & op(e3, e3) = all_22_1 & $i(all_22_1) % 136.14/20.20 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.20 (3) op(e3, e3) = e1 % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | ALPHA: (1) implies: % 136.14/20.20 | (4) ~ (all_22_1 = e1) % 136.14/20.20 | (5) op(e3, e3) = all_22_1 % 136.14/20.20 | % 136.14/20.20 | GROUND_INST: instantiating (2) with e1, all_22_1, e3, e3, simplifying with % 136.14/20.20 | (3), (5) gives: % 136.14/20.20 | (6) all_22_1 = e1 % 136.14/20.20 | % 136.14/20.20 | REDUCE: (4), (6) imply: % 136.14/20.20 | (7) $false % 136.14/20.20 | % 136.14/20.20 | CLOSE: (7) is inconsistent. % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #306 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) all_54_1 = e1 | all_54_1 = e0 % 136.14/20.20 (2) all_54_1 = all_22_0 % 136.14/20.20 (3) ~ (all_22_0 = e1) % 136.14/20.20 (4) ~ (all_22_0 = e0) % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | BETA: splitting (1) gives: % 136.14/20.20 | % 136.14/20.20 | Case 1: % 136.14/20.20 | | % 136.14/20.20 | | (5) all_54_1 = e1 % 136.14/20.20 | | % 136.14/20.20 | | COMBINE_EQS: (2), (5) imply: % 136.14/20.20 | | (6) all_22_0 = e1 % 136.14/20.20 | | % 136.14/20.20 | | SIMP: (6) implies: % 136.14/20.20 | | (7) all_22_0 = e1 % 136.14/20.20 | | % 136.14/20.20 | | REDUCE: (3), (7) imply: % 136.14/20.20 | | (8) $false % 136.14/20.20 | | % 136.14/20.20 | | CLOSE: (8) is inconsistent. % 136.14/20.20 | | % 136.14/20.20 | Case 2: % 136.14/20.20 | | % 136.14/20.20 | | (9) all_54_1 = e0 % 136.14/20.20 | | % 136.14/20.20 | | COMBINE_EQS: (2), (9) imply: % 136.14/20.20 | | (10) all_22_0 = e0 % 136.14/20.20 | | % 136.14/20.20 | | SIMP: (10) implies: % 136.14/20.20 | | (11) all_22_0 = e0 % 136.14/20.20 | | % 136.14/20.20 | | REDUCE: (4), (11) imply: % 136.14/20.20 | | (12) $false % 136.14/20.20 | | % 136.14/20.20 | | CLOSE: (12) is inconsistent. % 136.14/20.20 | | % 136.14/20.20 | End of split % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #307 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) ~ (all_22_0 = e0) % 136.14/20.20 (2) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) % 136.14/20.20 (3) op(e3, e3) = e1 % 136.14/20.20 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.20 (5) ~ (e1 = e0) % 136.14/20.20 (6) op(e3, e2) = all_22_0 % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | BETA: splitting (2) gives: % 136.14/20.20 | % 136.14/20.20 | Case 1: % 136.14/20.20 | | % 136.14/20.20 | | (7) all_57_0 = e0 & op(e3, e3) = e0 % 136.14/20.20 | | % 136.14/20.20 | | ALPHA: (7) implies: % 136.14/20.20 | | (8) op(e3, e3) = e0 % 136.14/20.20 | | % 136.14/20.20 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #717. % 136.14/20.20 | | % 136.14/20.20 | Case 2: % 136.14/20.20 | | % 136.14/20.20 | | (9) all_57_1 = e0 & op(e3, e2) = e0 % 136.14/20.20 | | % 136.14/20.20 | | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #309. % 136.14/20.20 | | % 136.14/20.20 | End of split % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #308 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) ~ (all_22_0 = e0) % 136.14/20.20 (2) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.20 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 136.14/20.20 (3) ~ (e2 = e0) % 136.14/20.20 (4) op(e3, e3) = e1 % 136.14/20.20 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.14/20.20 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.20 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.20 (7) ~ (e2 = e1) % 136.14/20.20 (8) ~ (e3 = e0) % 136.14/20.20 (9) ~ (e3 = e2) % 136.14/20.20 (10) op(e2, e2) = e3 % 136.14/20.20 (11) ~ (all_52_4 = e3) % 136.14/20.20 (12) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 136.14/20.20 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 136.14/20.20 (13) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.20 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.20 (14) op(e3, e2) = all_52_4 % 136.14/20.20 (15) ~ (e3 = e1) % 136.14/20.20 (16) ~ (e1 = e0) % 136.14/20.20 (17) all_57_7 = e2 % 136.14/20.20 (18) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.14/20.20 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.14/20.20 (19) op(e3, e2) = all_22_0 % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | BETA: splitting (2) gives: % 136.14/20.20 | % 136.14/20.20 | Case 1: % 136.14/20.20 | | % 136.14/20.20 | | (20) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = % 136.14/20.20 | | e0) % 136.14/20.20 | | % 136.14/20.20 | | BETA: splitting (20) gives: % 136.14/20.20 | | % 136.14/20.20 | | Case 1: % 136.14/20.20 | | | % 136.14/20.20 | | | (21) all_57_1 = e0 & op(e3, e2) = e0 % 136.14/20.20 | | | % 136.14/20.20 | | | REF_CLOSE: (1), (6), (19), (21) are inconsistent by sub-proof #309. % 136.14/20.20 | | | % 136.14/20.20 | | Case 2: % 136.14/20.20 | | | % 136.14/20.20 | | | (22) all_57_3 = e0 & op(e2, e2) = e0 % 136.14/20.20 | | | % 136.14/20.20 | | | ALPHA: (22) implies: % 136.14/20.20 | | | (23) op(e2, e2) = e0 % 136.14/20.20 | | | % 136.14/20.20 | | | REF_CLOSE: (6), (8), (10), (23) are inconsistent by sub-proof #641. % 136.14/20.20 | | | % 136.14/20.20 | | End of split % 136.14/20.20 | | % 136.14/20.20 | Case 2: % 136.14/20.20 | | % 136.14/20.20 | | (24) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = % 136.14/20.20 | | e0) % 136.14/20.20 | | % 136.14/20.20 | | BETA: splitting (24) gives: % 136.14/20.20 | | % 136.14/20.20 | | Case 1: % 136.14/20.20 | | | % 136.14/20.20 | | | (25) all_57_7 = e0 & op(e1, e2) = e0 % 136.14/20.20 | | | % 136.14/20.20 | | | REF_CLOSE: (3), (17), (25) are inconsistent by sub-proof #664. % 136.14/20.20 | | | % 136.14/20.20 | | Case 2: % 136.14/20.20 | | | % 136.14/20.20 | | | (26) all_57_13 = e0 & op(e0, e2) = e0 % 136.14/20.20 | | | % 136.14/20.20 | | | ALPHA: (26) implies: % 136.14/20.20 | | | (27) all_57_13 = e0 % 136.14/20.20 | | | % 136.14/20.20 | | | BETA: splitting (13) gives: % 136.14/20.20 | | | % 136.14/20.20 | | | Case 1: % 136.14/20.20 | | | | % 136.14/20.20 | | | | (28) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) % 136.14/20.20 | | | | = e1) % 136.14/20.20 | | | | % 136.14/20.20 | | | | BETA: splitting (28) gives: % 136.14/20.20 | | | | % 136.14/20.20 | | | | Case 1: % 136.14/20.20 | | | | | % 136.14/20.20 | | | | | (29) all_57_1 = e1 & op(e3, e2) = e1 % 136.14/20.20 | | | | | % 136.14/20.20 | | | | | ALPHA: (29) implies: % 136.14/20.20 | | | | | (30) all_57_1 = e1 % 136.14/20.20 | | | | | (31) op(e3, e2) = e1 % 136.14/20.20 | | | | | % 136.14/20.20 | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12), (14), (15), % 136.14/20.20 | | | | | (16), (18), (30), (31) are inconsistent by sub-proof #610. % 136.14/20.20 | | | | | % 136.14/20.20 | | | | Case 2: % 136.14/20.20 | | | | | % 136.14/20.20 | | | | | (32) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.20 | | | | | % 136.14/20.20 | | | | | ALPHA: (32) implies: % 136.14/20.20 | | | | | (33) op(e2, e2) = e1 % 136.14/20.20 | | | | | % 136.14/20.20 | | | | | REF_CLOSE: (6), (10), (15), (33) are inconsistent by sub-proof #325. % 136.14/20.20 | | | | | % 136.14/20.20 | | | | End of split % 136.14/20.20 | | | | % 136.14/20.20 | | | Case 2: % 136.14/20.20 | | | | % 136.14/20.20 | | | | (34) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) % 136.14/20.20 | | | | = e1) % 136.14/20.20 | | | | % 136.14/20.20 | | | | BETA: splitting (34) gives: % 136.14/20.20 | | | | % 136.14/20.20 | | | | Case 1: % 136.14/20.20 | | | | | % 136.14/20.20 | | | | | (35) all_57_7 = e1 & op(e1, e2) = e1 % 136.14/20.20 | | | | | % 136.14/20.20 | | | | | REF_CLOSE: (7), (17), (35) are inconsistent by sub-proof #727. % 136.14/20.20 | | | | | % 136.14/20.20 | | | | Case 2: % 136.14/20.20 | | | | | % 136.14/20.20 | | | | | (36) all_57_13 = e1 & op(e0, e2) = e1 % 136.14/20.20 | | | | | % 136.14/20.20 | | | | | ALPHA: (36) implies: % 136.14/20.20 | | | | | (37) all_57_13 = e1 % 136.14/20.20 | | | | | % 136.14/20.20 | | | | | REF_CLOSE: (16), (27), (37) are inconsistent by sub-proof #681. % 136.14/20.20 | | | | | % 136.14/20.20 | | | | End of split % 136.14/20.20 | | | | % 136.14/20.20 | | | End of split % 136.14/20.20 | | | % 136.14/20.20 | | End of split % 136.14/20.20 | | % 136.14/20.20 | End of split % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #309 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) all_57_1 = e0 & op(e3, e2) = e0 % 136.14/20.20 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.20 (3) op(e3, e2) = all_22_0 % 136.14/20.20 (4) ~ (all_22_0 = e0) % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | ALPHA: (1) implies: % 136.14/20.20 | (5) op(e3, e2) = e0 % 136.14/20.20 | % 136.14/20.20 | GROUND_INST: instantiating (2) with e0, all_22_0, e2, e3, simplifying with % 136.14/20.20 | (3), (5) gives: % 136.14/20.20 | (6) all_22_0 = e0 % 136.14/20.20 | % 136.14/20.20 | REDUCE: (4), (6) imply: % 136.14/20.20 | (7) $false % 136.14/20.20 | % 136.14/20.20 | CLOSE: (7) is inconsistent. % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #310 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.20 (2) ~ (all_52_9 = e3) % 136.14/20.20 (3) op(e2, e1) = all_52_9 % 136.14/20.20 (4) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) % 136.14/20.20 (5) op(e3, e1) = all_52_8 % 136.14/20.20 (6) ~ (all_52_8 = e3) % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | BETA: splitting (4) gives: % 136.14/20.20 | % 136.14/20.20 | Case 1: % 136.14/20.20 | | % 136.14/20.20 | | (7) all_57_4 = e3 & op(e3, e1) = e3 % 136.14/20.20 | | % 136.14/20.20 | | ALPHA: (7) implies: % 136.14/20.20 | | (8) op(e3, e1) = e3 % 136.14/20.20 | | % 136.14/20.20 | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #705. % 136.14/20.20 | | % 136.14/20.20 | Case 2: % 136.14/20.20 | | % 136.14/20.20 | | (9) all_57_5 = e3 & op(e2, e1) = e3 % 136.14/20.20 | | % 136.14/20.20 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #547. % 136.14/20.20 | | % 136.14/20.20 | End of split % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #311 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) ~ (all_52_13 = e0) % 136.14/20.20 (2) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 136.14/20.20 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.20 (4) ~ (all_52_1 = all_52_13) % 136.14/20.20 (5) ~ (all_52_13 = e3) % 136.14/20.20 (6) all_54_6 = all_52_9 % 136.14/20.20 (7) op(e2, e3) = all_52_1 % 136.14/20.20 (8) all_54_7 = all_52_13 % 136.14/20.20 (9) ~ (all_52_9 = e0) % 136.14/20.20 (10) op(e2, e3) = e2 % 136.14/20.20 (11) all_54_6 = e1 | all_54_6 = e0 % 136.14/20.20 (12) ~ (all_52_9 = all_52_13) % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | BETA: splitting (11) gives: % 136.14/20.20 | % 136.14/20.20 | Case 1: % 136.14/20.20 | | % 136.14/20.20 | | (13) all_54_6 = e1 % 136.14/20.20 | | % 136.14/20.20 | | COMBINE_EQS: (6), (13) imply: % 136.14/20.20 | | (14) all_52_9 = e1 % 136.14/20.20 | | % 136.14/20.20 | | SIMP: (14) implies: % 136.14/20.20 | | (15) all_52_9 = e1 % 136.14/20.20 | | % 136.14/20.20 | | REDUCE: (12), (15) imply: % 136.14/20.20 | | (16) ~ (all_52_13 = e1) % 136.14/20.20 | | % 136.14/20.20 | | SIMP: (16) implies: % 136.14/20.20 | | (17) ~ (all_52_13 = e1) % 136.14/20.20 | | % 136.14/20.20 | | BETA: splitting (2) gives: % 136.14/20.20 | | % 136.14/20.20 | | Case 1: % 136.14/20.20 | | | % 136.14/20.20 | | | (18) all_54_7 = e3 % 136.14/20.20 | | | % 136.14/20.20 | | | REF_CLOSE: (5), (8), (18) are inconsistent by sub-proof #338. % 136.14/20.20 | | | % 136.14/20.20 | | Case 2: % 136.14/20.20 | | | % 136.14/20.20 | | | (19) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 136.14/20.20 | | | % 136.14/20.20 | | | REF_CLOSE: (1), (3), (4), (7), (8), (10), (17), (19) are inconsistent by % 136.14/20.20 | | | sub-proof #312. % 136.14/20.20 | | | % 136.14/20.20 | | End of split % 136.14/20.20 | | % 136.14/20.20 | Case 2: % 136.14/20.20 | | % 136.14/20.20 | | (20) all_54_6 = e0 % 136.14/20.20 | | % 136.14/20.20 | | REF_CLOSE: (6), (9), (20) are inconsistent by sub-proof #480. % 136.14/20.20 | | % 136.14/20.20 | End of split % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #312 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) ~ (all_52_13 = e0) % 136.14/20.20 (2) ~ (all_52_13 = e1) % 136.14/20.20 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.20 (4) ~ (all_52_1 = all_52_13) % 136.14/20.20 (5) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0 % 136.14/20.20 (6) op(e2, e3) = all_52_1 % 136.14/20.20 (7) all_54_7 = all_52_13 % 136.14/20.20 (8) op(e2, e3) = e2 % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | BETA: splitting (5) gives: % 136.14/20.20 | % 136.14/20.20 | Case 1: % 136.14/20.20 | | % 136.14/20.20 | | (9) all_54_7 = e2 % 136.14/20.20 | | % 136.14/20.20 | | COMBINE_EQS: (7), (9) imply: % 136.14/20.20 | | (10) all_52_13 = e2 % 136.14/20.20 | | % 136.14/20.20 | | SIMP: (10) implies: % 136.14/20.20 | | (11) all_52_13 = e2 % 136.14/20.20 | | % 136.14/20.20 | | REDUCE: (4), (11) imply: % 136.14/20.20 | | (12) ~ (all_52_1 = e2) % 136.14/20.20 | | % 136.14/20.20 | | REF_CLOSE: (3), (6), (8), (12) are inconsistent by sub-proof #779. % 136.14/20.20 | | % 136.14/20.20 | Case 2: % 136.14/20.20 | | % 136.14/20.20 | | (13) all_54_7 = e1 | all_54_7 = e0 % 136.14/20.20 | | % 136.14/20.20 | | REF_CLOSE: (1), (2), (7), (13) are inconsistent by sub-proof #313. % 136.14/20.20 | | % 136.14/20.20 | End of split % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #313 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) all_54_7 = e1 | all_54_7 = e0 % 136.14/20.20 (2) all_54_7 = all_52_13 % 136.14/20.20 (3) ~ (all_52_13 = e1) % 136.14/20.20 (4) ~ (all_52_13 = e0) % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | BETA: splitting (1) gives: % 136.14/20.20 | % 136.14/20.20 | Case 1: % 136.14/20.20 | | % 136.14/20.20 | | (5) all_54_7 = e1 % 136.14/20.20 | | % 136.14/20.20 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #314. % 136.14/20.20 | | % 136.14/20.20 | Case 2: % 136.14/20.20 | | % 136.14/20.20 | | (6) all_54_7 = e0 % 136.14/20.20 | | % 136.14/20.20 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #326. % 136.14/20.20 | | % 136.14/20.20 | End of split % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #314 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) all_54_7 = all_52_13 % 136.14/20.20 (2) all_54_7 = e1 % 136.14/20.20 (3) ~ (all_52_13 = e1) % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | COMBINE_EQS: (1), (2) imply: % 136.14/20.20 | (4) all_52_13 = e1 % 136.14/20.20 | % 136.14/20.20 | SIMP: (4) implies: % 136.14/20.20 | (5) all_52_13 = e1 % 136.14/20.20 | % 136.14/20.20 | REDUCE: (3), (5) imply: % 136.14/20.20 | (6) $false % 136.14/20.20 | % 136.14/20.20 | CLOSE: (6) is inconsistent. % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #315 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) all_54_6 = all_52_9 % 136.14/20.20 (2) all_54_6 = e3 % 136.14/20.20 (3) ~ (all_52_9 = e3) % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | COMBINE_EQS: (1), (2) imply: % 136.14/20.20 | (4) all_52_9 = e3 % 136.14/20.20 | % 136.14/20.20 | SIMP: (4) implies: % 136.14/20.20 | (5) all_52_9 = e3 % 136.14/20.20 | % 136.14/20.20 | REDUCE: (3), (5) imply: % 136.14/20.20 | (6) $false % 136.14/20.20 | % 136.14/20.20 | CLOSE: (6) is inconsistent. % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #316 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) all_54_2 = all_52_8 % 136.14/20.20 (2) all_54_2 = e1 % 136.14/20.20 (3) ~ (all_52_8 = e1) % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | COMBINE_EQS: (1), (2) imply: % 136.14/20.20 | (4) all_52_8 = e1 % 136.14/20.20 | % 136.14/20.20 | SIMP: (4) implies: % 136.14/20.20 | (5) all_52_8 = e1 % 136.14/20.20 | % 136.14/20.20 | REDUCE: (3), (5) imply: % 136.14/20.20 | (6) $false % 136.14/20.20 | % 136.14/20.20 | CLOSE: (6) is inconsistent. % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #317 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) all_54_2 = all_52_8 % 136.14/20.20 (2) all_54_2 = e2 % 136.14/20.20 (3) ~ (all_52_8 = e2) % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | COMBINE_EQS: (1), (2) imply: % 136.14/20.20 | (4) all_52_8 = e2 % 136.14/20.20 | % 136.14/20.20 | SIMP: (4) implies: % 136.14/20.20 | (5) all_52_8 = e2 % 136.14/20.20 | % 136.14/20.20 | REDUCE: (3), (5) imply: % 136.14/20.20 | (6) $false % 136.14/20.20 | % 136.14/20.20 | CLOSE: (6) is inconsistent. % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #318 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) ~ (all_52_12 = e1) % 136.14/20.20 (2) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 136.14/20.20 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 136.14/20.20 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.14/20.20 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.14/20.20 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.14/20.20 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.20 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 136.14/20.20 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.14/20.20 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.20 $i(all_56_21) & $i(all_56_29)) % 136.14/20.20 (3) op(e3, e3) = e1 % 136.14/20.20 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.20 (5) ~ (e2 = e1) % 136.14/20.20 (6) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 136.14/20.20 (7) all_54_3 = all_52_12 % 136.14/20.20 (8) ~ (all_52_12 = e0) % 136.14/20.20 (9) ~ (all_52_8 = all_52_12) % 136.14/20.20 (10) ~ (all_52_12 = e2) % 136.14/20.20 (11) op(e3, e1) = all_52_8 % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | BETA: splitting (2) gives: % 136.14/20.20 | % 136.14/20.20 | Case 1: % 136.14/20.20 | | % 136.14/20.20 | | (12) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.14/20.20 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 % 136.14/20.20 | | & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.14/20.20 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.14/20.20 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.14/20.20 | | % 136.14/20.20 | | ALPHA: (12) implies: % 136.14/20.20 | | (13) op(e3, e3) = e2 % 136.14/20.20 | | % 136.14/20.20 | | REF_CLOSE: (3), (4), (5), (13) are inconsistent by sub-proof #743. % 136.14/20.20 | | % 136.14/20.20 | Case 2: % 136.14/20.20 | | % 136.14/20.20 | | (14) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.14/20.20 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = % 136.14/20.20 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.14/20.20 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.14/20.20 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.14/20.20 | | % 136.14/20.20 | | ALPHA: (14) implies: % 136.14/20.20 | | (15) op(e3, e1) = e3 % 136.14/20.20 | | % 136.14/20.20 | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (11), (15) are inconsistent % 136.14/20.20 | | by sub-proof #319. % 136.14/20.20 | | % 136.14/20.20 | End of split % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #319 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) ~ (all_52_12 = e1) % 136.14/20.20 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.20 (3) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 136.14/20.20 (4) all_54_3 = all_52_12 % 136.14/20.20 (5) ~ (all_52_12 = e0) % 136.14/20.20 (6) ~ (all_52_8 = all_52_12) % 136.14/20.20 (7) ~ (all_52_12 = e2) % 136.14/20.20 (8) op(e3, e1) = all_52_8 % 136.14/20.20 (9) op(e3, e1) = e3 % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | BETA: splitting (3) gives: % 136.14/20.20 | % 136.14/20.20 | Case 1: % 136.14/20.20 | | % 136.14/20.20 | | (10) all_54_3 = e3 % 136.14/20.20 | | % 136.14/20.20 | | COMBINE_EQS: (4), (10) imply: % 136.14/20.20 | | (11) all_52_12 = e3 % 136.14/20.20 | | % 136.14/20.20 | | REDUCE: (6), (11) imply: % 136.14/20.20 | | (12) ~ (all_52_8 = e3) % 136.14/20.20 | | % 136.14/20.20 | | REF_CLOSE: (2), (8), (9), (12) are inconsistent by sub-proof #705. % 136.14/20.20 | | % 136.14/20.20 | Case 2: % 136.14/20.20 | | % 136.14/20.20 | | (13) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 136.14/20.20 | | % 136.14/20.20 | | REF_CLOSE: (1), (4), (5), (7), (13) are inconsistent by sub-proof #320. % 136.14/20.20 | | % 136.14/20.20 | End of split % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #320 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) ~ (all_52_12 = e1) % 136.14/20.20 (2) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0 % 136.14/20.20 (3) all_54_3 = all_52_12 % 136.14/20.20 (4) ~ (all_52_12 = e0) % 136.14/20.20 (5) ~ (all_52_12 = e2) % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | BETA: splitting (2) gives: % 136.14/20.20 | % 136.14/20.20 | Case 1: % 136.14/20.20 | | % 136.14/20.20 | | (6) all_54_3 = e2 % 136.14/20.20 | | % 136.14/20.20 | | COMBINE_EQS: (3), (6) imply: % 136.14/20.20 | | (7) all_52_12 = e2 % 136.14/20.20 | | % 136.14/20.20 | | REDUCE: (5), (7) imply: % 136.14/20.20 | | (8) $false % 136.14/20.20 | | % 136.14/20.20 | | CLOSE: (8) is inconsistent. % 136.14/20.20 | | % 136.14/20.20 | Case 2: % 136.14/20.20 | | % 136.14/20.20 | | (9) all_54_3 = e1 | all_54_3 = e0 % 136.14/20.20 | | % 136.14/20.20 | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #321. % 136.14/20.20 | | % 136.14/20.20 | End of split % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #321 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) all_54_3 = e1 | all_54_3 = e0 % 136.14/20.20 (2) all_54_3 = all_52_12 % 136.14/20.20 (3) ~ (all_52_12 = e1) % 136.14/20.20 (4) ~ (all_52_12 = e0) % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | BETA: splitting (1) gives: % 136.14/20.20 | % 136.14/20.20 | Case 1: % 136.14/20.20 | | % 136.14/20.20 | | (5) all_54_3 = e1 % 136.14/20.20 | | % 136.14/20.20 | | COMBINE_EQS: (2), (5) imply: % 136.14/20.20 | | (6) all_52_12 = e1 % 136.14/20.20 | | % 136.14/20.20 | | REDUCE: (3), (6) imply: % 136.14/20.20 | | (7) $false % 136.14/20.20 | | % 136.14/20.20 | | CLOSE: (7) is inconsistent. % 136.14/20.20 | | % 136.14/20.20 | Case 2: % 136.14/20.20 | | % 136.14/20.20 | | (8) all_54_3 = e0 % 136.14/20.20 | | % 136.14/20.20 | | COMBINE_EQS: (2), (8) imply: % 136.14/20.20 | | (9) all_52_12 = e0 % 136.14/20.20 | | % 136.14/20.20 | | REDUCE: (4), (9) imply: % 136.14/20.20 | | (10) $false % 136.14/20.20 | | % 136.14/20.20 | | CLOSE: (10) is inconsistent. % 136.14/20.20 | | % 136.14/20.20 | End of split % 136.14/20.20 | % 136.14/20.20 End of proof % 136.14/20.20 % 136.14/20.20 Sub-proof #322 shows that the following formulas are inconsistent: % 136.14/20.20 ---------------------------------------------------------------- % 136.14/20.20 (1) ~ (all_4_2 = e2) % 136.14/20.20 (2) ~ (all_4_2 = e1) % 136.14/20.20 (3) ~ (all_4_2 = e3) % 136.14/20.20 (4) all_54_15 = all_4_2 % 136.14/20.20 (5) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 136.14/20.20 (6) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.14/20.20 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.14/20.20 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.14/20.20 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.14/20.20 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) % 136.14/20.20 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.14/20.20 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 136.14/20.20 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 136.14/20.20 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & % 136.14/20.20 all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ % 136.14/20.20 (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = % 136.14/20.20 e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 136.14/20.20 all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 % 136.14/20.20 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.20 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, % 136.14/20.20 e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.14/20.20 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.14/20.20 $i(all_56_29)) % 136.14/20.20 (7) all_56_31 = all_4_2 % 136.14/20.20 % 136.14/20.20 Begin of proof % 136.14/20.20 | % 136.14/20.20 | BETA: splitting (5) gives: % 136.14/20.20 | % 136.14/20.20 | Case 1: % 136.14/20.20 | | % 136.14/20.20 | | (8) all_54_15 = e3 % 136.14/20.20 | | % 136.14/20.21 | | COMBINE_EQS: (4), (8) imply: % 136.14/20.21 | | (9) all_4_2 = e3 % 136.14/20.21 | | % 136.14/20.21 | | REDUCE: (3), (9) imply: % 136.14/20.21 | | (10) $false % 136.14/20.21 | | % 136.14/20.21 | | CLOSE: (10) is inconsistent. % 136.14/20.21 | | % 136.14/20.21 | Case 2: % 136.14/20.21 | | % 136.14/20.21 | | (11) ~ (all_54_15 = e3) % 136.14/20.21 | | (12) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 136.14/20.21 | | % 136.14/20.21 | | BETA: splitting (6) gives: % 136.14/20.21 | | % 136.14/20.21 | | Case 1: % 136.14/20.21 | | | % 136.14/20.21 | | | (13) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.14/20.21 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.14/20.21 | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.14/20.21 | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.14/20.21 | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.14/20.21 | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.14/20.21 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.14/20.21 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.14/20.21 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.14/20.21 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 136.14/20.21 | | | % 136.14/20.21 | | | BETA: splitting (13) gives: % 136.14/20.21 | | | % 136.14/20.21 | | | Case 1: % 136.14/20.21 | | | | % 136.14/20.21 | | | | (14) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.14/20.21 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.14/20.21 | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.14/20.21 | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.14/20.21 | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.14/20.21 | | | | % 136.14/20.21 | | | | ALPHA: (14) implies: % 136.14/20.21 | | | | (15) all_56_31 = e3 % 136.14/20.21 | | | | % 136.14/20.21 | | | | COMBINE_EQS: (7), (15) imply: % 136.14/20.21 | | | | (16) all_4_2 = e3 % 136.14/20.21 | | | | % 136.14/20.21 | | | | REDUCE: (3), (16) imply: % 136.14/20.21 | | | | (17) $false % 136.14/20.21 | | | | % 136.14/20.21 | | | | CLOSE: (17) is inconsistent. % 136.14/20.21 | | | | % 136.14/20.21 | | | Case 2: % 136.14/20.21 | | | | % 136.14/20.21 | | | | (18) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.14/20.21 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.14/20.21 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.14/20.21 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.14/20.21 | | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.14/20.21 | | | | % 136.14/20.21 | | | | REF_CLOSE: (1), (7), (18) are inconsistent by sub-proof #765. % 136.14/20.21 | | | | % 136.14/20.21 | | | End of split % 136.14/20.21 | | | % 136.14/20.21 | | Case 2: % 136.14/20.21 | | | % 136.14/20.21 | | | (19) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.14/20.21 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.14/20.21 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 136.14/20.21 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.14/20.21 | | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = % 136.14/20.21 | | | e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 136.14/20.21 | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 136.14/20.21 | | | = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.14/20.21 | | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.14/20.21 | | | $i(all_56_29)) % 136.14/20.21 | | | % 136.14/20.21 | | | BETA: splitting (19) gives: % 136.14/20.21 | | | % 136.14/20.21 | | | Case 1: % 136.14/20.21 | | | | % 136.14/20.21 | | | | (20) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.14/20.21 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.14/20.21 | | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 136.14/20.21 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.14/20.21 | | | | $i(all_56_15) & $i(all_56_23) % 136.14/20.21 | | | | % 136.14/20.21 | | | | ALPHA: (20) implies: % 136.14/20.21 | | | | (21) ~ (all_56_31 = e0) % 136.14/20.21 | | | | % 136.14/20.21 | | | | REDUCE: (7), (21) imply: % 136.14/20.21 | | | | (22) ~ (all_4_2 = e0) % 136.14/20.21 | | | | % 136.14/20.21 | | | | REF_CLOSE: (1), (2), (4), (12), (22) are inconsistent by sub-proof #746. % 136.14/20.21 | | | | % 136.14/20.21 | | | Case 2: % 136.14/20.21 | | | | % 136.14/20.21 | | | | (23) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.14/20.21 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.14/20.21 | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.14/20.21 | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.14/20.21 | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.14/20.21 | | | | % 136.14/20.21 | | | | REF_CLOSE: (2), (7), (23) are inconsistent by sub-proof #745. % 136.14/20.21 | | | | % 136.14/20.21 | | | End of split % 136.14/20.21 | | | % 136.14/20.21 | | End of split % 136.14/20.21 | | % 136.14/20.21 | End of split % 136.14/20.21 | % 136.14/20.21 End of proof % 136.14/20.21 % 136.14/20.21 Sub-proof #323 shows that the following formulas are inconsistent: % 136.14/20.21 ---------------------------------------------------------------- % 136.14/20.21 (1) ~ (all_52_6 = e3) % 136.14/20.21 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.21 (3) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) % 136.14/20.21 (4) op(e1, e2) = all_52_6 % 136.14/20.21 (5) ~ (all_52_2 = e3) % 136.14/20.21 (6) op(e1, e3) = all_52_2 % 136.14/20.21 % 136.14/20.21 Begin of proof % 136.14/20.21 | % 136.14/20.21 | BETA: splitting (3) gives: % 136.14/20.21 | % 136.14/20.21 | Case 1: % 136.14/20.21 | | % 136.14/20.21 | | (7) all_57_6 = e3 & op(e1, e3) = e3 % 136.14/20.21 | | % 136.14/20.21 | | REF_CLOSE: (2), (5), (6), (7) are inconsistent by sub-proof #761. % 136.14/20.21 | | % 136.14/20.21 | Case 2: % 136.14/20.21 | | % 136.14/20.21 | | (8) all_57_7 = e3 & op(e1, e2) = e3 % 136.14/20.21 | | % 136.14/20.21 | | ALPHA: (8) implies: % 136.14/20.21 | | (9) op(e1, e2) = e3 % 136.14/20.21 | | % 136.14/20.21 | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #654. % 136.14/20.21 | | % 136.14/20.21 | End of split % 136.14/20.21 | % 136.14/20.21 End of proof % 136.14/20.21 % 136.14/20.21 Sub-proof #324 shows that the following formulas are inconsistent: % 136.14/20.21 ---------------------------------------------------------------- % 136.14/20.21 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.14/20.21 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.14/20.21 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.14/20.21 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.21 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ % 136.14/20.21 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 136.14/20.21 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = % 136.14/20.21 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.14/20.21 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.14/20.21 $i(all_56_29)) % 136.14/20.21 (2) op(e1, e1) = all_6_2 % 136.14/20.21 (3) ~ (all_6_2 = e3) % 136.14/20.21 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.21 (5) op(e2, e2) = e3 % 136.14/20.21 (6) ~ (e3 = e1) % 136.14/20.21 % 136.14/20.21 Begin of proof % 136.14/20.21 | % 136.14/20.21 | BETA: splitting (1) gives: % 136.14/20.21 | % 136.14/20.21 | Case 1: % 136.14/20.21 | | % 136.14/20.21 | | (7) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.14/20.21 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.21 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.14/20.21 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) % 136.14/20.21 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.14/20.21 | | % 136.14/20.21 | | ALPHA: (7) implies: % 136.14/20.21 | | (8) op(e1, e1) = e3 % 136.14/20.21 | | % 136.14/20.21 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #771. % 136.14/20.21 | | % 136.14/20.21 | Case 2: % 136.14/20.21 | | % 136.14/20.21 | | (9) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.14/20.21 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 % 136.14/20.21 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.14/20.21 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.14/20.21 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.14/20.21 | | % 136.14/20.21 | | ALPHA: (9) implies: % 136.14/20.21 | | (10) op(e2, e2) = e1 % 136.14/20.21 | | % 136.14/20.21 | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #325. % 136.14/20.21 | | % 136.14/20.21 | End of split % 136.14/20.21 | % 136.14/20.21 End of proof % 136.14/20.21 % 136.14/20.21 Sub-proof #325 shows that the following formulas are inconsistent: % 136.14/20.21 ---------------------------------------------------------------- % 136.14/20.21 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.21 (2) op(e2, e2) = e3 % 136.14/20.21 (3) op(e2, e2) = e1 % 136.14/20.21 (4) ~ (e3 = e1) % 136.14/20.21 % 136.14/20.21 Begin of proof % 136.14/20.21 | % 136.14/20.21 | GROUND_INST: instantiating (1) with e3, e1, e2, e2, simplifying with (2), (3) % 136.14/20.21 | gives: % 136.14/20.21 | (5) e3 = e1 % 136.14/20.21 | % 136.14/20.21 | REDUCE: (4), (5) imply: % 136.14/20.21 | (6) $false % 136.14/20.21 | % 136.14/20.21 | CLOSE: (6) is inconsistent. % 136.14/20.21 | % 136.14/20.21 End of proof % 136.14/20.21 % 136.14/20.21 Sub-proof #326 shows that the following formulas are inconsistent: % 136.14/20.21 ---------------------------------------------------------------- % 136.14/20.21 (1) all_54_7 = all_52_13 % 136.14/20.21 (2) all_54_7 = e0 % 136.14/20.21 (3) ~ (all_52_13 = e0) % 136.14/20.21 % 136.14/20.21 Begin of proof % 136.14/20.21 | % 136.14/20.21 | COMBINE_EQS: (1), (2) imply: % 136.14/20.21 | (4) all_52_13 = e0 % 136.14/20.21 | % 136.14/20.21 | SIMP: (4) implies: % 136.14/20.21 | (5) all_52_13 = e0 % 136.14/20.21 | % 136.14/20.21 | REDUCE: (3), (5) imply: % 136.14/20.21 | (6) $false % 136.14/20.21 | % 136.14/20.21 | CLOSE: (6) is inconsistent. % 136.14/20.21 | % 136.14/20.21 End of proof % 136.14/20.21 % 136.14/20.21 Sub-proof #327 shows that the following formulas are inconsistent: % 136.14/20.21 ---------------------------------------------------------------- % 136.14/20.21 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.21 (2) op(e1, e0) = all_52_14 % 136.14/20.21 (3) op(e1, e0) = e1 % 136.14/20.21 (4) ~ (all_52_14 = e1) % 136.14/20.21 % 136.14/20.21 Begin of proof % 136.14/20.21 | % 136.14/20.21 | GROUND_INST: instantiating (1) with all_52_14, e1, e0, e1, simplifying with % 136.14/20.21 | (2), (3) gives: % 136.14/20.21 | (5) all_52_14 = e1 % 136.14/20.21 | % 136.14/20.21 | REDUCE: (4), (5) imply: % 136.14/20.21 | (6) $false % 136.14/20.21 | % 136.14/20.21 | CLOSE: (6) is inconsistent. % 136.14/20.21 | % 136.14/20.21 End of proof % 136.14/20.21 % 136.14/20.21 Sub-proof #328 shows that the following formulas are inconsistent: % 136.14/20.21 ---------------------------------------------------------------- % 136.14/20.21 (1) op(e2, e0) = all_52_13 % 136.14/20.21 (2) ~ (all_52_14 = e3) % 136.14/20.21 (3) op(e3, e3) = e2 % 136.14/20.21 (4) op(e3, e1) = all_56_17 % 136.14/20.21 (5) ( ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 & $i(all_36_0)) | ( ~ % 136.14/20.21 (all_36_1 = e2) & op(e3, e3) = all_36_1 & $i(all_36_1)) % 136.14/20.21 (6) ~ (e2 = e0) % 136.14/20.21 (7) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.14/20.21 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.21 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.21 (9) ~ (e2 = e1) % 136.14/20.21 (10) ~ (e3 = e2) % 136.14/20.21 (11) ~ (all_52_12 = e0) % 136.14/20.21 (12) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) | % 136.14/20.21 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.21 (13) op(e3, e0) = all_52_12 % 136.14/20.21 (14) ~ (all_52_13 = e3) % 136.14/20.21 (15) op(e0, e0) = e2 % 136.14/20.21 (16) ~ (all_56_17 = e1) % 136.14/20.21 (17) ~ (e3 = e1) % 136.14/20.21 (18) ~ (e1 = e0) % 136.14/20.21 (19) op(e1, e0) = all_52_14 % 136.14/20.21 (20) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) | % 136.14/20.21 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1) % 136.14/20.21 % 136.14/20.21 Begin of proof % 136.14/20.21 | % 136.14/20.21 | BETA: splitting (20) gives: % 136.14/20.21 | % 136.14/20.21 | Case 1: % 136.14/20.21 | | % 136.14/20.21 | | (21) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = % 136.14/20.21 | | e1) % 136.14/20.21 | | % 136.14/20.21 | | BETA: splitting (21) gives: % 136.14/20.21 | | % 136.14/20.21 | | Case 1: % 136.14/20.21 | | | % 136.14/20.21 | | | (22) all_57_0 = e1 & op(e3, e3) = e1 % 136.14/20.21 | | | % 136.14/20.21 | | | ALPHA: (22) implies: % 136.14/20.21 | | | (23) op(e3, e3) = e1 % 136.14/20.21 | | | % 136.14/20.21 | | | REF_CLOSE: (3), (8), (9), (23) are inconsistent by sub-proof #743. % 136.14/20.21 | | | % 136.14/20.21 | | Case 2: % 136.14/20.21 | | | % 136.14/20.21 | | | (24) all_57_1 = e1 & op(e3, e2) = e1 % 136.14/20.21 | | | % 136.14/20.21 | | | ALPHA: (24) implies: % 136.14/20.21 | | | (25) op(e3, e2) = e1 % 136.14/20.21 | | | % 136.14/20.21 | | | BETA: splitting (5) gives: % 136.14/20.21 | | | % 136.14/20.21 | | | Case 1: % 136.14/20.21 | | | | % 136.14/20.21 | | | | (26) ~ (all_36_0 = e0) & op(e3, e1) = all_36_0 & $i(all_36_0) % 136.14/20.21 | | | | % 136.14/20.21 | | | | ALPHA: (26) implies: % 136.14/20.21 | | | | (27) ~ (all_36_0 = e0) % 136.14/20.21 | | | | (28) op(e3, e1) = all_36_0 % 136.14/20.21 | | | | % 136.14/20.21 | | | | BETA: splitting (7) gives: % 136.14/20.21 | | | | % 136.14/20.21 | | | | Case 1: % 136.14/20.21 | | | | | % 136.14/20.21 | | | | | (29) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, % 136.14/20.21 | | | | | e2) = e0) % 136.14/20.21 | | | | | % 136.14/20.21 | | | | | REF_CLOSE: (3), (6), (8), (18), (25), (29) are inconsistent by % 136.14/20.21 | | | | | sub-proof #333. % 136.14/20.21 | | | | | % 136.14/20.21 | | | | Case 2: % 136.14/20.21 | | | | | % 136.14/20.21 | | | | | (30) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, % 136.14/20.21 | | | | | e0) = e0) % 136.14/20.21 | | | | | % 136.14/20.21 | | | | | BETA: splitting (30) gives: % 136.14/20.21 | | | | | % 136.14/20.21 | | | | | Case 1: % 136.14/20.21 | | | | | | % 136.14/20.21 | | | | | | (31) all_57_4 = e0 & op(e3, e1) = e0 % 136.14/20.21 | | | | | | % 136.14/20.21 | | | | | | REF_CLOSE: (8), (27), (28), (31) are inconsistent by sub-proof #332. % 136.14/20.21 | | | | | | % 136.14/20.21 | | | | | Case 2: % 136.14/20.21 | | | | | | % 136.14/20.21 | | | | | | (32) all_57_9 = e0 & op(e3, e0) = e0 % 136.14/20.21 | | | | | | % 136.14/20.21 | | | | | | REF_CLOSE: (8), (11), (13), (32) are inconsistent by sub-proof #618. % 136.14/20.21 | | | | | | % 136.14/20.21 | | | | | End of split % 136.14/20.21 | | | | | % 136.14/20.21 | | | | End of split % 136.14/20.21 | | | | % 136.14/20.21 | | | Case 2: % 136.14/20.21 | | | | % 136.14/20.21 | | | | (33) ~ (all_36_1 = e2) & op(e3, e3) = all_36_1 & $i(all_36_1) % 136.14/20.21 | | | | % 136.14/20.21 | | | | REF_CLOSE: (3), (8), (33) are inconsistent by sub-proof #342. % 136.14/20.21 | | | | % 136.14/20.21 | | | End of split % 136.14/20.21 | | | % 136.14/20.21 | | End of split % 136.14/20.21 | | % 136.14/20.21 | Case 2: % 136.14/20.21 | | % 136.14/20.21 | | (34) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = % 136.14/20.21 | | e1) % 136.14/20.21 | | % 136.14/20.21 | | BETA: splitting (34) gives: % 136.14/20.21 | | % 136.14/20.21 | | Case 1: % 136.14/20.21 | | | % 136.14/20.21 | | | (35) all_57_4 = e1 & op(e3, e1) = e1 % 136.14/20.21 | | | % 136.14/20.21 | | | ALPHA: (35) implies: % 136.14/20.21 | | | (36) op(e3, e1) = e1 % 136.14/20.21 | | | % 136.14/20.21 | | | REF_CLOSE: (4), (8), (16), (36) are inconsistent by sub-proof #349. % 136.14/20.21 | | | % 136.14/20.21 | | Case 2: % 136.14/20.21 | | | % 136.14/20.21 | | | (37) all_57_9 = e1 & op(e3, e0) = e1 % 136.14/20.21 | | | % 136.14/20.21 | | | ALPHA: (37) implies: % 136.14/20.21 | | | (38) all_57_9 = e1 % 136.14/20.21 | | | % 136.14/20.21 | | | REF_CLOSE: (1), (2), (8), (10), (12), (14), (15), (17), (19), (38) are % 136.14/20.21 | | | inconsistent by sub-proof #329. % 136.14/20.21 | | | % 136.14/20.21 | | End of split % 136.14/20.21 | | % 136.14/20.21 | End of split % 136.14/20.21 | % 136.14/20.21 End of proof % 136.14/20.21 % 136.14/20.21 Sub-proof #329 shows that the following formulas are inconsistent: % 136.14/20.21 ---------------------------------------------------------------- % 136.14/20.21 (1) op(e2, e0) = all_52_13 % 136.14/20.21 (2) ~ (all_52_14 = e3) % 136.14/20.21 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.21 (4) ~ (e3 = e2) % 136.14/20.21 (5) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) | % 136.14/20.21 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.21 (6) ~ (all_52_13 = e3) % 136.14/20.21 (7) op(e0, e0) = e2 % 136.14/20.21 (8) all_57_9 = e1 % 136.14/20.21 (9) ~ (e3 = e1) % 136.14/20.21 (10) op(e1, e0) = all_52_14 % 136.14/20.21 % 136.14/20.21 Begin of proof % 136.14/20.21 | % 136.14/20.21 | BETA: splitting (5) gives: % 136.14/20.21 | % 136.14/20.21 | Case 1: % 136.14/20.21 | | % 136.14/20.21 | | (11) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = % 136.14/20.21 | | e3) % 136.14/20.21 | | % 136.14/20.21 | | REF_CLOSE: (1), (3), (6), (8), (9), (11) are inconsistent by sub-proof #331. % 136.14/20.21 | | % 136.14/20.21 | Case 2: % 136.14/20.21 | | % 136.14/20.21 | | (12) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = % 136.14/20.21 | | e3) % 136.14/20.21 | | % 136.14/20.21 | | REF_CLOSE: (2), (3), (4), (7), (10), (12) are inconsistent by sub-proof % 136.14/20.21 | | #330. % 136.14/20.21 | | % 136.14/20.21 | End of split % 136.14/20.21 | % 136.14/20.21 End of proof % 136.14/20.21 % 136.14/20.21 Sub-proof #330 shows that the following formulas are inconsistent: % 136.14/20.21 ---------------------------------------------------------------- % 136.14/20.21 (1) ~ (all_52_14 = e3) % 136.14/20.21 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.21 (3) ~ (e3 = e2) % 136.14/20.21 (4) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.21 (5) op(e0, e0) = e2 % 136.14/20.21 (6) op(e1, e0) = all_52_14 % 136.14/20.21 % 136.14/20.21 Begin of proof % 136.14/20.21 | % 136.14/20.21 | BETA: splitting (4) gives: % 136.14/20.21 | % 136.14/20.21 | Case 1: % 136.14/20.21 | | % 136.14/20.21 | | (7) all_57_11 = e3 & op(e1, e0) = e3 % 136.14/20.21 | | % 136.14/20.21 | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #750. % 136.14/20.21 | | % 136.14/20.21 | Case 2: % 136.14/20.21 | | % 136.14/20.21 | | (8) all_57_15 = e3 & op(e0, e0) = e3 % 136.14/20.21 | | % 136.14/20.21 | | ALPHA: (8) implies: % 136.14/20.21 | | (9) op(e0, e0) = e3 % 136.14/20.21 | | % 136.14/20.21 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #634. % 136.14/20.21 | | % 136.14/20.21 | End of split % 136.14/20.21 | % 136.14/20.21 End of proof % 136.14/20.21 % 136.14/20.21 Sub-proof #331 shows that the following formulas are inconsistent: % 136.14/20.21 ---------------------------------------------------------------- % 136.14/20.21 (1) op(e2, e0) = all_52_13 % 136.14/20.21 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.21 (3) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) % 136.14/20.21 (4) ~ (all_52_13 = e3) % 136.14/20.21 (5) all_57_9 = e1 % 136.14/20.21 (6) ~ (e3 = e1) % 136.14/20.21 % 136.14/20.21 Begin of proof % 136.14/20.21 | % 136.14/20.21 | BETA: splitting (3) gives: % 136.14/20.21 | % 136.14/20.21 | Case 1: % 136.14/20.21 | | % 136.14/20.21 | | (7) all_57_9 = e3 & op(e3, e0) = e3 % 136.14/20.21 | | % 136.14/20.21 | | ALPHA: (7) implies: % 136.14/20.21 | | (8) all_57_9 = e3 % 136.14/20.21 | | % 136.14/20.21 | | REF_CLOSE: (5), (6), (8) are inconsistent by sub-proof #690. % 136.14/20.21 | | % 136.14/20.21 | Case 2: % 136.14/20.21 | | % 136.14/20.21 | | (9) all_57_10 = e3 & op(e2, e0) = e3 % 136.14/20.21 | | % 136.14/20.21 | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #749. % 136.14/20.21 | | % 136.14/20.21 | End of split % 136.14/20.21 | % 136.14/20.21 End of proof % 136.14/20.21 % 136.14/20.21 Sub-proof #332 shows that the following formulas are inconsistent: % 136.14/20.21 ---------------------------------------------------------------- % 136.14/20.21 (1) all_57_4 = e0 & op(e3, e1) = e0 % 136.14/20.21 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.21 (3) op(e3, e1) = all_36_0 % 136.14/20.21 (4) ~ (all_36_0 = e0) % 136.14/20.21 % 136.14/20.21 Begin of proof % 136.14/20.21 | % 136.14/20.21 | ALPHA: (1) implies: % 136.14/20.21 | (5) op(e3, e1) = e0 % 136.14/20.21 | % 136.14/20.21 | GROUND_INST: instantiating (2) with e0, all_36_0, e1, e3, simplifying with % 136.14/20.21 | (3), (5) gives: % 136.14/20.21 | (6) all_36_0 = e0 % 136.14/20.21 | % 136.14/20.21 | REDUCE: (4), (6) imply: % 136.14/20.21 | (7) $false % 136.14/20.21 | % 136.14/20.21 | CLOSE: (7) is inconsistent. % 136.14/20.21 | % 136.14/20.21 End of proof % 136.14/20.21 % 136.14/20.21 Sub-proof #333 shows that the following formulas are inconsistent: % 136.14/20.21 ---------------------------------------------------------------- % 136.14/20.21 (1) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) % 136.14/20.21 (2) op(e3, e2) = e1 % 136.14/20.21 (3) op(e3, e3) = e2 % 136.14/20.21 (4) ~ (e2 = e0) % 136.14/20.22 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.22 (6) ~ (e1 = e0) % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | BETA: splitting (1) gives: % 136.14/20.22 | % 136.14/20.22 | Case 1: % 136.14/20.22 | | % 136.14/20.22 | | (7) all_57_0 = e0 & op(e3, e3) = e0 % 136.14/20.22 | | % 136.14/20.22 | | ALPHA: (7) implies: % 136.14/20.22 | | (8) op(e3, e3) = e0 % 136.14/20.22 | | % 136.14/20.22 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #495. % 136.14/20.22 | | % 136.14/20.22 | Case 2: % 136.14/20.22 | | % 136.14/20.22 | | (9) all_57_1 = e0 & op(e3, e2) = e0 % 136.14/20.22 | | % 136.14/20.22 | | ALPHA: (9) implies: % 136.14/20.22 | | (10) op(e3, e2) = e0 % 136.14/20.22 | | % 136.14/20.22 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #730. % 136.14/20.22 | | % 136.14/20.22 | End of split % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #334 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.22 (2) op(e2, e2) = all_26_1 % 136.14/20.22 (3) op(e2, e2) = e3 % 136.14/20.22 (4) ~ (all_26_1 = e3) % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | GROUND_INST: instantiating (1) with e3, all_26_1, e2, e2, simplifying with % 136.14/20.22 | (2), (3) gives: % 136.14/20.22 | (5) all_26_1 = e3 % 136.14/20.22 | % 136.14/20.22 | REDUCE: (4), (5) imply: % 136.14/20.22 | (6) $false % 136.14/20.22 | % 136.14/20.22 | CLOSE: (6) is inconsistent. % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #335 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 136.14/20.22 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 136.14/20.22 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.14/20.22 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.14/20.22 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.14/20.22 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.22 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 136.14/20.22 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.14/20.22 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.22 $i(all_56_21) & $i(all_56_29)) % 136.14/20.22 (2) op(e3, e3) = e2 % 136.14/20.22 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.22 (4) ~ (e2 = e1) % 136.14/20.22 (5) op(e2, e3) = e3 % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | BETA: splitting (1) gives: % 136.14/20.22 | % 136.14/20.22 | Case 1: % 136.14/20.22 | | % 136.14/20.22 | | (6) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.14/20.22 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.14/20.22 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.14/20.22 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.14/20.22 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.14/20.22 | | % 136.14/20.22 | | ALPHA: (6) implies: % 136.14/20.22 | | (7) ~ (all_56_3 = e3) % 136.14/20.22 | | (8) op(e2, e3) = all_56_3 % 136.14/20.22 | | % 136.14/20.22 | | REF_CLOSE: (3), (5), (7), (8) are inconsistent by sub-proof #347. % 136.14/20.22 | | % 136.14/20.22 | Case 2: % 136.14/20.22 | | % 136.14/20.22 | | (9) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.14/20.22 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 136.14/20.22 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.14/20.22 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.14/20.22 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.14/20.22 | | % 136.14/20.22 | | ALPHA: (9) implies: % 136.14/20.22 | | (10) op(e3, e3) = e1 % 136.14/20.22 | | % 136.14/20.22 | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #743. % 136.14/20.22 | | % 136.14/20.22 | End of split % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #336 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.22 (2) op(e2, e0) = all_26_0 % 136.14/20.22 (3) op(e2, e0) = e1 % 136.14/20.22 (4) ~ (all_26_0 = e1) % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | GROUND_INST: instantiating (1) with e1, all_26_0, e0, e2, simplifying with % 136.14/20.22 | (2), (3) gives: % 136.14/20.22 | (5) all_26_0 = e1 % 136.14/20.22 | % 136.14/20.22 | REDUCE: (4), (5) imply: % 136.14/20.22 | (6) $false % 136.14/20.22 | % 136.14/20.22 | CLOSE: (6) is inconsistent. % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #337 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) all_54_7 = all_52_13 % 136.14/20.22 (2) all_54_7 = e2 % 136.14/20.22 (3) ~ (all_52_13 = e2) % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | COMBINE_EQS: (1), (2) imply: % 136.14/20.22 | (4) all_52_13 = e2 % 136.14/20.22 | % 136.14/20.22 | SIMP: (4) implies: % 136.14/20.22 | (5) all_52_13 = e2 % 136.14/20.22 | % 136.14/20.22 | REDUCE: (3), (5) imply: % 136.14/20.22 | (6) $false % 136.14/20.22 | % 136.14/20.22 | CLOSE: (6) is inconsistent. % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #338 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) all_54_7 = all_52_13 % 136.14/20.22 (2) all_54_7 = e3 % 136.14/20.22 (3) ~ (all_52_13 = e3) % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | COMBINE_EQS: (1), (2) imply: % 136.14/20.22 | (4) all_52_13 = e3 % 136.14/20.22 | % 136.14/20.22 | SIMP: (4) implies: % 136.14/20.22 | (5) all_52_13 = e3 % 136.14/20.22 | % 136.14/20.22 | REDUCE: (3), (5) imply: % 136.14/20.22 | (6) $false % 136.14/20.22 | % 136.14/20.22 | CLOSE: (6) is inconsistent. % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #339 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) all_54_5 = all_8_2 % 136.14/20.22 (2) all_54_5 = e1 % 136.14/20.22 (3) ~ (all_8_2 = e1) % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | COMBINE_EQS: (1), (2) imply: % 136.14/20.22 | (4) all_8_2 = e1 % 136.14/20.22 | % 136.14/20.22 | SIMP: (4) implies: % 136.14/20.22 | (5) all_8_2 = e1 % 136.14/20.22 | % 136.14/20.22 | REDUCE: (3), (5) imply: % 136.14/20.22 | (6) $false % 136.14/20.22 | % 136.14/20.22 | CLOSE: (6) is inconsistent. % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #340 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) all_54_5 = all_8_2 % 136.14/20.22 (2) all_54_5 = e2 % 136.14/20.22 (3) ~ (all_8_2 = e2) % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | COMBINE_EQS: (1), (2) imply: % 136.14/20.22 | (4) all_8_2 = e2 % 136.14/20.22 | % 136.14/20.22 | SIMP: (4) implies: % 136.14/20.22 | (5) all_8_2 = e2 % 136.14/20.22 | % 136.14/20.22 | REDUCE: (3), (5) imply: % 136.14/20.22 | (6) $false % 136.14/20.22 | % 136.14/20.22 | CLOSE: (6) is inconsistent. % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #341 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) all_57_6 = e2 & op(e1, e3) = e2 % 136.14/20.22 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.22 (3) op(e1, e3) = all_52_2 % 136.14/20.22 (4) ~ (all_52_2 = e2) % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | ALPHA: (1) implies: % 136.14/20.22 | (5) op(e1, e3) = e2 % 136.14/20.22 | % 136.14/20.22 | GROUND_INST: instantiating (2) with all_52_2, e2, e3, e1, simplifying with % 136.14/20.22 | (3), (5) gives: % 136.14/20.22 | (6) all_52_2 = e2 % 136.14/20.22 | % 136.14/20.22 | REDUCE: (4), (6) imply: % 136.14/20.22 | (7) $false % 136.14/20.22 | % 136.14/20.22 | CLOSE: (7) is inconsistent. % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #342 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) ~ (all_36_1 = e2) & op(e3, e3) = all_36_1 & $i(all_36_1) % 136.14/20.22 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.22 (3) op(e3, e3) = e2 % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | ALPHA: (1) implies: % 136.14/20.22 | (4) ~ (all_36_1 = e2) % 136.14/20.22 | (5) op(e3, e3) = all_36_1 % 136.14/20.22 | % 136.14/20.22 | GROUND_INST: instantiating (2) with e2, all_36_1, e3, e3, simplifying with % 136.14/20.22 | (3), (5) gives: % 136.14/20.22 | (6) all_36_1 = e2 % 136.14/20.22 | % 136.14/20.22 | REDUCE: (4), (6) imply: % 136.14/20.22 | (7) $false % 136.14/20.22 | % 136.14/20.22 | CLOSE: (7) is inconsistent. % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #343 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.22 (2) op(e3, e1) = e1 % 136.14/20.22 (3) op(e3, e1) = e0 % 136.14/20.22 (4) ~ (e1 = e0) % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | GROUND_INST: instantiating (1) with e0, e1, e1, e3, simplifying with (2), (3) % 136.14/20.22 | gives: % 136.14/20.22 | (5) e1 = e0 % 136.14/20.22 | % 136.14/20.22 | REDUCE: (4), (5) imply: % 136.14/20.22 | (6) $false % 136.14/20.22 | % 136.14/20.22 | CLOSE: (6) is inconsistent. % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #344 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) op(e3, e3) = e2 % 136.14/20.22 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.22 (3) ~ (e3 = e0) % 136.14/20.22 (4) ~ (e3 = e2) % 136.14/20.22 (5) op(e3, e1) = all_36_0 % 136.14/20.22 (6) all_57_1 = e0 % 136.14/20.22 (7) op(e3, e1) = all_52_8 % 136.14/20.22 (8) all_57_9 = e1 % 136.14/20.22 (9) ~ (e3 = e1) % 136.14/20.22 (10) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.14/20.22 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.14/20.22 (11) ~ (all_52_8 = e3) % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | BETA: splitting (10) gives: % 136.14/20.22 | % 136.14/20.22 | Case 1: % 136.14/20.22 | | % 136.14/20.22 | | (12) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = % 136.14/20.22 | | e3) % 136.14/20.22 | | % 136.14/20.22 | | BETA: splitting (12) gives: % 136.14/20.22 | | % 136.14/20.22 | | Case 1: % 136.14/20.22 | | | % 136.14/20.22 | | | (13) all_57_0 = e3 & op(e3, e3) = e3 % 136.14/20.22 | | | % 136.14/20.22 | | | ALPHA: (13) implies: % 136.14/20.22 | | | (14) op(e3, e3) = e3 % 136.14/20.22 | | | % 136.14/20.22 | | | REF_CLOSE: (1), (2), (4), (14) are inconsistent by sub-proof #778. % 136.14/20.22 | | | % 136.14/20.22 | | Case 2: % 136.14/20.22 | | | % 136.14/20.22 | | | (15) all_57_1 = e3 & op(e3, e2) = e3 % 136.14/20.22 | | | % 136.14/20.22 | | | REF_CLOSE: (3), (6), (15) are inconsistent by sub-proof #376. % 136.14/20.22 | | | % 136.14/20.22 | | End of split % 136.14/20.22 | | % 136.14/20.22 | Case 2: % 136.14/20.22 | | % 136.14/20.22 | | (16) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = % 136.14/20.22 | | e3) % 136.14/20.22 | | % 136.14/20.22 | | BETA: splitting (16) gives: % 136.14/20.22 | | % 136.14/20.22 | | Case 1: % 136.14/20.22 | | | % 136.14/20.22 | | | (17) all_57_4 = e3 & op(e3, e1) = e3 % 136.14/20.22 | | | % 136.14/20.22 | | | REF_CLOSE: (2), (5), (7), (11), (17) are inconsistent by sub-proof #379. % 136.14/20.22 | | | % 136.14/20.22 | | Case 2: % 136.14/20.22 | | | % 136.14/20.22 | | | (18) all_57_9 = e3 & op(e3, e0) = e3 % 136.14/20.22 | | | % 136.14/20.22 | | | REF_CLOSE: (8), (9), (18) are inconsistent by sub-proof #345. % 136.14/20.22 | | | % 136.14/20.22 | | End of split % 136.14/20.22 | | % 136.14/20.22 | End of split % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #345 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) all_57_9 = e3 & op(e3, e0) = e3 % 136.14/20.22 (2) all_57_9 = e1 % 136.14/20.22 (3) ~ (e3 = e1) % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | ALPHA: (1) implies: % 136.14/20.22 | (4) all_57_9 = e3 % 136.14/20.22 | % 136.14/20.22 | COMBINE_EQS: (2), (4) imply: % 136.14/20.22 | (5) e3 = e1 % 136.14/20.22 | % 136.14/20.22 | REDUCE: (3), (5) imply: % 136.14/20.22 | (6) $false % 136.14/20.22 | % 136.14/20.22 | CLOSE: (6) is inconsistent. % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #346 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.14/20.22 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.14/20.22 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.14/20.22 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.14/20.22 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) % 136.14/20.22 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.14/20.22 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 136.14/20.22 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 136.14/20.22 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 136.14/20.22 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.22 (3) op(e3, e1) = e1 % 136.14/20.22 (4) op(e2, e3) = e3 % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | BETA: splitting (1) gives: % 136.14/20.22 | % 136.14/20.22 | Case 1: % 136.14/20.22 | | % 136.14/20.22 | | (5) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.14/20.22 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.22 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.14/20.22 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.22 | | $i(all_56_17) & $i(all_56_25) % 136.14/20.22 | | % 136.14/20.22 | | ALPHA: (5) implies: % 136.14/20.22 | | (6) ~ (all_56_17 = e1) % 136.14/20.22 | | (7) op(e3, e1) = all_56_17 % 136.14/20.22 | | % 136.14/20.22 | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #349. % 136.14/20.22 | | % 136.14/20.22 | Case 2: % 136.14/20.22 | | % 136.14/20.22 | | (8) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.14/20.22 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.14/20.22 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.14/20.22 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 136.14/20.22 | | $i(all_56_19) & $i(all_56_27) % 136.14/20.22 | | % 136.14/20.22 | | ALPHA: (8) implies: % 136.14/20.22 | | (9) ~ (all_56_3 = e3) % 136.14/20.22 | | (10) op(e2, e3) = all_56_3 % 136.14/20.22 | | % 136.14/20.22 | | REF_CLOSE: (2), (4), (9), (10) are inconsistent by sub-proof #347. % 136.14/20.22 | | % 136.14/20.22 | End of split % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #347 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.22 (2) op(e2, e3) = all_56_3 % 136.14/20.22 (3) op(e2, e3) = e3 % 136.14/20.22 (4) ~ (all_56_3 = e3) % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | GROUND_INST: instantiating (1) with e3, all_56_3, e3, e2, simplifying with % 136.14/20.22 | (2), (3) gives: % 136.14/20.22 | (5) all_56_3 = e3 % 136.14/20.22 | % 136.14/20.22 | REDUCE: (4), (5) imply: % 136.14/20.22 | (6) $false % 136.14/20.22 | % 136.14/20.22 | CLOSE: (6) is inconsistent. % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #348 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.14/20.22 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.14/20.22 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.14/20.22 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.22 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ % 136.14/20.22 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 136.14/20.22 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = % 136.14/20.22 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.14/20.22 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.14/20.22 $i(all_56_29)) % 136.14/20.22 (2) op(e3, e1) = e1 % 136.14/20.22 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.22 (4) ~ (all_52_9 = e2) % 136.14/20.22 (5) op(e2, e1) = all_52_9 % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | BETA: splitting (1) gives: % 136.14/20.22 | % 136.14/20.22 | Case 1: % 136.14/20.22 | | % 136.14/20.22 | | (6) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.14/20.22 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.22 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.14/20.22 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) % 136.14/20.22 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.14/20.22 | | % 136.14/20.22 | | ALPHA: (6) implies: % 136.14/20.22 | | (7) ~ (all_56_17 = e1) % 136.14/20.22 | | (8) op(e3, e1) = all_56_17 % 136.14/20.22 | | % 136.14/20.22 | | REF_CLOSE: (2), (3), (7), (8) are inconsistent by sub-proof #349. % 136.14/20.22 | | % 136.14/20.22 | Case 2: % 136.14/20.22 | | % 136.14/20.22 | | (9) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.14/20.22 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 % 136.14/20.22 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.14/20.22 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.14/20.22 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.14/20.22 | | % 136.14/20.22 | | ALPHA: (9) implies: % 136.14/20.22 | | (10) op(e2, e1) = e2 % 136.14/20.22 | | % 136.14/20.22 | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #770. % 136.14/20.22 | | % 136.14/20.22 | End of split % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #349 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.22 (2) op(e3, e1) = all_56_17 % 136.14/20.22 (3) op(e3, e1) = e1 % 136.14/20.22 (4) ~ (all_56_17 = e1) % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | GROUND_INST: instantiating (1) with e1, all_56_17, e1, e3, simplifying with % 136.14/20.22 | (2), (3) gives: % 136.14/20.22 | (5) all_56_17 = e1 % 136.14/20.22 | % 136.14/20.22 | REDUCE: (4), (5) imply: % 136.14/20.22 | (6) $false % 136.14/20.22 | % 136.14/20.22 | CLOSE: (6) is inconsistent. % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #350 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) op(e0, e0) = all_4_2 % 136.14/20.22 (2) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.22 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.22 (4) ~ (e2 = e1) % 136.14/20.22 (5) ~ (all_4_2 = e1) % 136.14/20.22 (6) all_57_14 = e2 % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | BETA: splitting (2) gives: % 136.14/20.22 | % 136.14/20.22 | Case 1: % 136.14/20.22 | | % 136.14/20.22 | | (7) all_57_14 = e1 & op(e0, e1) = e1 % 136.14/20.22 | | % 136.14/20.22 | | ALPHA: (7) implies: % 136.14/20.22 | | (8) all_57_14 = e1 % 136.14/20.22 | | % 136.14/20.22 | | REF_CLOSE: (4), (6), (8) are inconsistent by sub-proof #560. % 136.14/20.22 | | % 136.14/20.22 | Case 2: % 136.14/20.22 | | % 136.14/20.22 | | (9) all_57_15 = e1 & op(e0, e0) = e1 % 136.14/20.22 | | % 136.14/20.22 | | ALPHA: (9) implies: % 136.14/20.22 | | (10) op(e0, e0) = e1 % 136.14/20.22 | | % 136.14/20.22 | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #354. % 136.14/20.22 | | % 136.14/20.22 | End of split % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #351 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) ~ (all_52_11 = e1) % 136.14/20.22 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.22 (3) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 136.14/20.22 (4) op(e0, e1) = all_52_11 % 136.14/20.22 (5) op(e0, e1) = e0 % 136.14/20.22 (6) ~ (all_52_11 = e0) % 136.14/20.22 (7) all_54_14 = all_52_11 % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | BETA: splitting (3) gives: % 136.14/20.22 | % 136.14/20.22 | Case 1: % 136.14/20.22 | | % 136.14/20.22 | | (8) all_54_14 = e2 % 136.14/20.22 | | % 136.14/20.22 | | COMBINE_EQS: (7), (8) imply: % 136.14/20.22 | | (9) all_52_11 = e2 % 136.14/20.22 | | % 136.14/20.22 | | SIMP: (9) implies: % 136.14/20.22 | | (10) all_52_11 = e2 % 136.14/20.22 | | % 136.14/20.22 | | REDUCE: (6), (10) imply: % 136.14/20.22 | | (11) ~ (e2 = e0) % 136.14/20.22 | | % 136.14/20.22 | | REDUCE: (4), (10) imply: % 136.14/20.22 | | (12) op(e0, e1) = e2 % 136.14/20.22 | | % 136.14/20.22 | | REF_CLOSE: (2), (5), (11), (12) are inconsistent by sub-proof #660. % 136.14/20.22 | | % 136.14/20.22 | Case 2: % 136.14/20.22 | | % 136.14/20.22 | | (13) all_54_14 = e1 | all_54_14 = e0 % 136.14/20.22 | | % 136.14/20.22 | | REF_CLOSE: (1), (6), (7), (13) are inconsistent by sub-proof #755. % 136.14/20.22 | | % 136.14/20.22 | End of split % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #352 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) op(e0, e0) = all_4_2 % 136.14/20.22 (2) op(e1, e1) = all_6_2 % 136.14/20.22 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.22 (4) ~ (all_4_2 = e2) % 136.14/20.22 (5) ~ (all_6_2 = e2) % 136.14/20.22 (6) op(e0, e0) = e2 % 136.14/20.22 (7) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.14/20.22 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.14/20.22 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) % 136.14/20.22 = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 136.14/20.22 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 136.14/20.22 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 136.14/20.22 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 136.14/20.22 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 136.14/20.22 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.14/20.22 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.14/20.22 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.14/20.22 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.14/20.22 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.14/20.22 e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) % 136.14/20.22 & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 % 136.14/20.22 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 136.14/20.22 ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) % 136.14/20.22 = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.14/20.22 $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & % 136.14/20.22 all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.22 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 136.14/20.22 op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.14/20.22 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.22 $i(all_56_21) & $i(all_56_29)))) % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | BETA: splitting (7) gives: % 136.14/20.22 | % 136.14/20.22 | Case 1: % 136.14/20.22 | | % 136.14/20.22 | | (8) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.14/20.22 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.14/20.22 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.14/20.22 | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) % 136.14/20.22 | | & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.14/20.22 | | % 136.14/20.22 | | ALPHA: (8) implies: % 136.14/20.22 | | (9) op(e1, e1) = e2 % 136.14/20.22 | | % 136.14/20.22 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #767. % 136.14/20.22 | | % 136.14/20.22 | Case 2: % 136.14/20.22 | | % 136.14/20.22 | | (10) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 % 136.14/20.22 | | = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 136.14/20.22 | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) % 136.14/20.22 | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.14/20.22 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.14/20.22 | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 % 136.14/20.22 | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 136.14/20.22 | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.14/20.22 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.14/20.22 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.14/20.22 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 % 136.14/20.22 | | = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.14/20.22 | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, % 136.14/20.22 | | e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 136.14/20.22 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 136.14/20.22 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.14/20.22 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.14/20.22 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.14/20.22 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.14/20.22 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29))) % 136.14/20.22 | | % 136.14/20.22 | | ALPHA: (10) implies: % 136.14/20.22 | | (11) op(e0, e0) = all_56_31 % 136.14/20.22 | | % 136.14/20.22 | | REF_CLOSE: (1), (3), (4), (6), (11) are inconsistent by sub-proof #427. % 136.14/20.22 | | % 136.14/20.22 | End of split % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #353 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) op(e1, e0) = e2 % 136.14/20.22 (2) op(e0, e0) = all_4_2 % 136.14/20.22 (3) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.22 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.22 (5) ~ (e2 = e1) % 136.14/20.22 (6) ~ (all_4_2 = e1) % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | BETA: splitting (3) gives: % 136.14/20.22 | % 136.14/20.22 | Case 1: % 136.14/20.22 | | % 136.14/20.22 | | (7) all_57_11 = e1 & op(e1, e0) = e1 % 136.14/20.22 | | % 136.14/20.22 | | ALPHA: (7) implies: % 136.14/20.22 | | (8) op(e1, e0) = e1 % 136.14/20.22 | | % 136.14/20.22 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #720. % 136.14/20.22 | | % 136.14/20.22 | Case 2: % 136.14/20.22 | | % 136.14/20.22 | | (9) all_57_15 = e1 & op(e0, e0) = e1 % 136.14/20.22 | | % 136.14/20.22 | | ALPHA: (9) implies: % 136.14/20.22 | | (10) op(e0, e0) = e1 % 136.14/20.22 | | % 136.14/20.22 | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #354. % 136.14/20.22 | | % 136.14/20.22 | End of split % 136.14/20.22 | % 136.14/20.22 End of proof % 136.14/20.22 % 136.14/20.22 Sub-proof #354 shows that the following formulas are inconsistent: % 136.14/20.22 ---------------------------------------------------------------- % 136.14/20.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.22 (2) op(e0, e0) = all_4_2 % 136.14/20.22 (3) op(e0, e0) = e1 % 136.14/20.22 (4) ~ (all_4_2 = e1) % 136.14/20.22 % 136.14/20.22 Begin of proof % 136.14/20.22 | % 136.14/20.22 | GROUND_INST: instantiating (1) with all_4_2, e1, e0, e0, simplifying with (2), % 136.14/20.23 | (3) gives: % 136.14/20.23 | (5) all_4_2 = e1 % 136.14/20.23 | % 136.14/20.23 | REDUCE: (4), (5) imply: % 136.14/20.23 | (6) $false % 136.14/20.23 | % 136.14/20.23 | CLOSE: (6) is inconsistent. % 136.14/20.23 | % 136.14/20.23 End of proof % 136.14/20.23 % 136.14/20.23 Sub-proof #355 shows that the following formulas are inconsistent: % 136.14/20.23 ---------------------------------------------------------------- % 136.14/20.23 (1) all_57_10 = e3 & op(e2, e0) = e3 % 136.14/20.23 (2) all_57_10 = e1 % 136.14/20.23 (3) ~ (e3 = e1) % 136.14/20.23 % 136.14/20.23 Begin of proof % 136.14/20.23 | % 136.14/20.23 | ALPHA: (1) implies: % 136.14/20.23 | (4) all_57_10 = e3 % 136.14/20.23 | % 136.14/20.23 | COMBINE_EQS: (2), (4) imply: % 136.14/20.23 | (5) e3 = e1 % 136.14/20.23 | % 136.14/20.23 | SIMP: (5) implies: % 136.14/20.23 | (6) e3 = e1 % 136.14/20.23 | % 136.14/20.23 | REDUCE: (3), (6) imply: % 136.14/20.23 | (7) $false % 136.14/20.23 | % 136.14/20.23 | CLOSE: (7) is inconsistent. % 136.14/20.23 | % 136.14/20.23 End of proof % 136.14/20.23 % 136.14/20.23 Sub-proof #356 shows that the following formulas are inconsistent: % 136.14/20.23 ---------------------------------------------------------------- % 136.14/20.23 (1) op(e3, e3) = e2 % 136.14/20.23 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.23 (3) ~ (e2 = e1) % 136.14/20.23 (4) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) % 136.14/20.23 (5) all_57_2 = e3 % 136.14/20.23 (6) ~ (e3 = e1) % 136.14/20.23 % 136.14/20.23 Begin of proof % 136.14/20.23 | % 136.14/20.23 | BETA: splitting (4) gives: % 136.14/20.23 | % 136.14/20.23 | Case 1: % 136.14/20.23 | | % 136.14/20.23 | | (7) all_57_0 = e1 & op(e3, e3) = e1 % 136.14/20.23 | | % 136.14/20.23 | | ALPHA: (7) implies: % 136.14/20.23 | | (8) op(e3, e3) = e1 % 136.14/20.23 | | % 136.14/20.23 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #743. % 136.14/20.23 | | % 136.14/20.23 | Case 2: % 136.14/20.23 | | % 136.14/20.23 | | (9) all_57_2 = e1 & op(e2, e3) = e1 % 136.14/20.23 | | % 136.14/20.23 | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #453. % 136.14/20.23 | | % 136.14/20.23 | End of split % 136.14/20.23 | % 136.14/20.23 End of proof % 136.14/20.23 % 136.14/20.23 Sub-proof #357 shows that the following formulas are inconsistent: % 136.14/20.23 ---------------------------------------------------------------- % 136.14/20.23 (1) ~ (e2 = e0) % 136.14/20.23 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.23 (3) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) | % 136.14/20.23 (all_57_11 = e0 & op(e1, e0) = e0) % 136.14/20.23 (4) ~ (all_52_9 = e2) % 136.14/20.23 (5) op(e2, e1) = all_52_9 % 136.14/20.23 (6) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 136.14/20.23 (7) all_57_11 = e2 % 136.14/20.23 (8) all_57_9 = e1 % 136.14/20.23 (9) ~ (e1 = e0) % 136.14/20.23 % 136.14/20.23 Begin of proof % 136.14/20.23 | % 136.14/20.23 | BETA: splitting (6) gives: % 136.14/20.23 | % 136.14/20.23 | Case 1: % 136.14/20.23 | | % 136.14/20.23 | | (10) all_57_5 = e2 & op(e2, e1) = e2 % 136.14/20.23 | | % 136.14/20.23 | | ALPHA: (10) implies: % 136.14/20.23 | | (11) op(e2, e1) = e2 % 136.14/20.23 | | % 136.14/20.23 | | REF_CLOSE: (2), (4), (5), (11) are inconsistent by sub-proof #770. % 136.14/20.23 | | % 136.14/20.23 | Case 2: % 136.14/20.23 | | % 136.14/20.23 | | (12) all_57_10 = e2 & op(e2, e0) = e2 % 136.14/20.23 | | % 136.14/20.23 | | ALPHA: (12) implies: % 136.14/20.23 | | (13) all_57_10 = e2 % 136.14/20.23 | | % 136.14/20.23 | | BETA: splitting (3) gives: % 136.14/20.23 | | % 136.14/20.23 | | Case 1: % 136.14/20.23 | | | % 136.14/20.23 | | | (14) all_57_9 = e0 & op(e3, e0) = e0 % 136.14/20.23 | | | % 136.14/20.23 | | | ALPHA: (14) implies: % 136.14/20.23 | | | (15) all_57_9 = e0 % 136.14/20.23 | | | % 136.14/20.23 | | | REF_CLOSE: (8), (9), (15) are inconsistent by sub-proof #383. % 136.14/20.23 | | | % 136.14/20.23 | | Case 2: % 136.14/20.23 | | | % 136.14/20.23 | | | (16) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.14/20.23 | | | = e0) % 136.14/20.23 | | | % 136.14/20.23 | | | BETA: splitting (16) gives: % 136.14/20.23 | | | % 136.14/20.23 | | | Case 1: % 136.14/20.23 | | | | % 136.14/20.23 | | | | (17) all_57_10 = e0 & op(e2, e0) = e0 % 136.14/20.23 | | | | % 136.14/20.23 | | | | REF_CLOSE: (1), (13), (17) are inconsistent by sub-proof #363. % 136.14/20.23 | | | | % 136.14/20.23 | | | Case 2: % 136.14/20.23 | | | | % 136.14/20.23 | | | | (18) all_57_11 = e0 & op(e1, e0) = e0 % 136.14/20.23 | | | | % 136.14/20.23 | | | | REF_CLOSE: (1), (7), (18) are inconsistent by sub-proof #656. % 136.14/20.23 | | | | % 136.14/20.23 | | | End of split % 136.14/20.23 | | | % 136.14/20.23 | | End of split % 136.14/20.23 | | % 136.14/20.23 | End of split % 136.14/20.23 | % 136.14/20.23 End of proof % 136.14/20.23 % 136.14/20.23 Sub-proof #358 shows that the following formulas are inconsistent: % 136.14/20.23 ---------------------------------------------------------------- % 136.14/20.23 (1) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 136.14/20.23 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 136.14/20.23 (2) op(e2, e0) = all_52_13 % 136.14/20.23 (3) op(e3, e3) = e2 % 136.14/20.23 (4) ~ (e2 = e0) % 136.14/20.23 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.23 (6) ~ (e3 = e0) % 136.14/20.23 (7) ~ (all_52_9 = e2) % 136.14/20.23 (8) ~ (all_52_13 = e2) % 136.14/20.23 (9) op(e2, e1) = all_52_9 % 136.14/20.23 (10) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.14/20.23 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.14/20.23 (11) ~ (all_52_1 = e2) % 136.14/20.23 (12) all_57_2 = e3 % 136.14/20.23 (13) op(e2, e3) = all_52_1 % 136.14/20.23 (14) ~ (e1 = e0) % 136.14/20.23 (15) all_57_3 = e2 % 136.14/20.23 (16) all_57_6 = e2 % 136.14/20.23 (17) all_57_12 = e1 % 136.14/20.23 % 136.14/20.23 Begin of proof % 136.14/20.23 | % 136.14/20.23 | BETA: splitting (10) gives: % 136.14/20.23 | % 136.14/20.23 | Case 1: % 136.14/20.23 | | % 136.14/20.23 | | (18) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = % 136.14/20.23 | | e0) % 136.14/20.23 | | % 136.14/20.23 | | REF_CLOSE: (3), (4), (5), (6), (12), (18) are inconsistent by sub-proof % 136.14/20.23 | | #426. % 136.14/20.23 | | % 136.14/20.23 | Case 2: % 136.14/20.23 | | % 136.14/20.23 | | (19) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = % 136.14/20.23 | | e0) % 136.14/20.23 | | % 136.14/20.23 | | BETA: splitting (19) gives: % 136.14/20.23 | | % 136.14/20.23 | | Case 1: % 136.14/20.23 | | | % 136.14/20.23 | | | (20) all_57_6 = e0 & op(e1, e3) = e0 % 136.14/20.23 | | | % 136.14/20.23 | | | ALPHA: (20) implies: % 136.14/20.23 | | | (21) all_57_6 = e0 % 136.14/20.23 | | | % 136.14/20.23 | | | COMBINE_EQS: (16), (21) imply: % 136.14/20.23 | | | (22) e2 = e0 % 136.14/20.23 | | | % 136.14/20.23 | | | SIMP: (22) implies: % 136.14/20.23 | | | (23) e2 = e0 % 136.14/20.23 | | | % 136.14/20.23 | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (11), (13), (15), (23) are % 136.14/20.23 | | | inconsistent by sub-proof #359. % 136.14/20.23 | | | % 136.14/20.23 | | Case 2: % 136.14/20.23 | | | % 136.14/20.23 | | | (24) all_57_12 = e0 & op(e0, e3) = e0 % 136.14/20.23 | | | % 136.14/20.23 | | | ALPHA: (24) implies: % 136.14/20.23 | | | (25) all_57_12 = e0 % 136.14/20.23 | | | % 136.14/20.23 | | | REF_CLOSE: (14), (17), (25) are inconsistent by sub-proof #581. % 136.14/20.23 | | | % 136.14/20.23 | | End of split % 136.14/20.23 | | % 136.14/20.23 | End of split % 136.14/20.23 | % 136.14/20.23 End of proof % 136.14/20.23 % 136.14/20.23 Sub-proof #359 shows that the following formulas are inconsistent: % 136.14/20.23 ---------------------------------------------------------------- % 136.14/20.23 (1) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 136.14/20.23 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 136.14/20.23 (2) op(e2, e0) = all_52_13 % 136.14/20.23 (3) ~ (e2 = e0) % 136.14/20.23 (4) e2 = e0 % 136.14/20.23 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.23 (6) ~ (all_52_9 = e2) % 136.14/20.23 (7) ~ (all_52_13 = e2) % 136.14/20.23 (8) op(e2, e1) = all_52_9 % 136.14/20.23 (9) ~ (all_52_1 = e2) % 136.14/20.23 (10) op(e2, e3) = all_52_1 % 136.14/20.23 (11) all_57_3 = e2 % 136.14/20.23 % 136.14/20.23 Begin of proof % 136.14/20.23 | % 136.14/20.23 | COMBINE_EQS: (4), (11) imply: % 136.14/20.23 | (12) all_57_3 = e0 % 136.14/20.23 | % 136.14/20.23 | BETA: splitting (1) gives: % 136.14/20.23 | % 136.14/20.23 | Case 1: % 136.14/20.23 | | % 136.14/20.23 | | (13) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = % 136.14/20.23 | | e2) % 136.14/20.23 | | % 136.14/20.23 | | BETA: splitting (13) gives: % 136.14/20.23 | | % 136.14/20.23 | | Case 1: % 136.14/20.23 | | | % 136.14/20.23 | | | (14) all_57_2 = e2 & op(e2, e3) = e2 % 136.14/20.23 | | | % 136.14/20.23 | | | ALPHA: (14) implies: % 136.14/20.23 | | | (15) op(e2, e3) = e2 % 136.14/20.23 | | | % 136.14/20.23 | | | REF_CLOSE: (5), (9), (10), (15) are inconsistent by sub-proof #779. % 136.14/20.23 | | | % 136.14/20.23 | | Case 2: % 136.14/20.23 | | | % 136.14/20.23 | | | (16) all_57_3 = e2 & op(e2, e2) = e2 % 136.14/20.23 | | | % 136.14/20.23 | | | REF_CLOSE: (3), (11), (12) are inconsistent by sub-proof #679. % 136.14/20.23 | | | % 136.14/20.23 | | End of split % 136.14/20.23 | | % 136.14/20.23 | Case 2: % 136.14/20.23 | | % 136.14/20.23 | | (17) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = % 136.14/20.23 | | e2) % 136.14/20.23 | | % 136.14/20.23 | | REF_CLOSE: (2), (5), (6), (7), (8), (17) are inconsistent by sub-proof #625. % 136.14/20.23 | | % 136.14/20.23 | End of split % 136.14/20.23 | % 136.14/20.23 End of proof % 136.14/20.23 % 136.14/20.23 Sub-proof #360 shows that the following formulas are inconsistent: % 136.14/20.23 ---------------------------------------------------------------- % 136.14/20.23 (1) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 136.14/20.23 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 136.14/20.23 (2) op(e3, e3) = e2 % 136.14/20.23 (3) ~ (e2 = e0) % 136.14/20.23 (4) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 136.14/20.23 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 136.14/20.23 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.23 (6) ~ (e2 = e1) % 136.14/20.23 (7) ~ (e3 = e0) % 136.14/20.23 (8) ~ (e3 = e2) % 136.14/20.23 (9) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.14/20.23 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.14/20.23 (10) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.14/20.23 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.14/20.23 (11) all_57_3 = e3 % 136.14/20.23 (12) ~ (e3 = e1) % 136.14/20.23 (13) ~ (e1 = e0) % 136.14/20.23 (14) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.23 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.14/20.23 (15) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.23 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 136.14/20.23 (16) all_57_6 = e2 % 136.14/20.23 % 136.14/20.23 Begin of proof % 136.14/20.23 | % 136.14/20.23 | BETA: splitting (1) gives: % 136.14/20.23 | % 136.14/20.23 | Case 1: % 136.14/20.23 | | % 136.14/20.23 | | (17) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = % 136.14/20.23 | | e2) % 136.14/20.23 | | % 136.14/20.23 | | BETA: splitting (17) gives: % 136.14/20.23 | | % 136.14/20.23 | | Case 1: % 136.14/20.23 | | | % 136.14/20.23 | | | (18) all_57_2 = e2 & op(e2, e3) = e2 % 136.14/20.23 | | | % 136.14/20.23 | | | ALPHA: (18) implies: % 136.14/20.23 | | | (19) all_57_2 = e2 % 136.14/20.23 | | | % 136.14/20.23 | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (12), (16), (19) are inconsistent % 136.14/20.23 | | | by sub-proof #393. % 136.14/20.23 | | | % 136.14/20.23 | | Case 2: % 136.14/20.23 | | | % 136.14/20.23 | | | (20) all_57_3 = e2 & op(e2, e2) = e2 % 136.14/20.23 | | | % 136.14/20.23 | | | REF_CLOSE: (8), (11), (20) are inconsistent by sub-proof #375. % 136.14/20.23 | | | % 136.14/20.23 | | End of split % 136.14/20.23 | | % 136.14/20.23 | Case 2: % 136.14/20.23 | | % 136.14/20.23 | | (21) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = % 136.14/20.23 | | e2) % 136.14/20.23 | | % 136.14/20.23 | | BETA: splitting (21) gives: % 136.14/20.23 | | % 136.14/20.23 | | Case 1: % 136.14/20.23 | | | % 136.14/20.23 | | | (22) all_57_5 = e2 & op(e2, e1) = e2 % 136.14/20.23 | | | % 136.14/20.23 | | | ALPHA: (22) implies: % 136.14/20.23 | | | (23) all_57_5 = e2 % 136.14/20.23 | | | % 136.14/20.23 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 136.14/20.23 | | | (14), (15), (16), (23) are inconsistent by sub-proof #366. % 136.14/20.23 | | | % 136.14/20.23 | | Case 2: % 136.14/20.23 | | | % 136.14/20.23 | | | (24) all_57_10 = e2 & op(e2, e0) = e2 % 136.14/20.23 | | | % 136.14/20.23 | | | ALPHA: (24) implies: % 136.14/20.23 | | | (25) all_57_10 = e2 % 136.14/20.23 | | | % 136.14/20.23 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 136.14/20.23 | | | (14), (15), (16), (25) are inconsistent by sub-proof #361. % 136.14/20.23 | | | % 136.14/20.23 | | End of split % 136.14/20.23 | | % 136.14/20.23 | End of split % 136.14/20.23 | % 136.14/20.23 End of proof % 136.14/20.23 % 136.14/20.23 Sub-proof #361 shows that the following formulas are inconsistent: % 136.14/20.23 ---------------------------------------------------------------- % 136.14/20.23 (1) op(e3, e3) = e2 % 136.14/20.23 (2) ~ (e2 = e0) % 136.14/20.23 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 136.14/20.23 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 136.14/20.23 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.23 (5) ~ (e2 = e1) % 136.14/20.23 (6) ~ (e3 = e0) % 136.14/20.23 (7) ~ (e3 = e2) % 136.14/20.23 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.14/20.23 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.14/20.23 (9) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.14/20.23 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.14/20.23 (10) all_57_3 = e3 % 136.14/20.23 (11) ~ (e3 = e1) % 136.14/20.23 (12) ~ (e1 = e0) % 136.14/20.23 (13) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.23 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.14/20.23 (14) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.23 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 136.14/20.23 (15) all_57_6 = e2 % 136.14/20.23 (16) all_57_10 = e2 % 136.14/20.23 % 136.14/20.23 Begin of proof % 136.14/20.23 | % 136.14/20.23 | BETA: splitting (8) gives: % 136.14/20.23 | % 136.14/20.23 | Case 1: % 136.14/20.23 | | % 136.14/20.23 | | (17) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = % 136.14/20.23 | | e3) % 136.14/20.23 | | % 136.14/20.23 | | BETA: splitting (17) gives: % 136.14/20.23 | | % 136.14/20.23 | | Case 1: % 136.14/20.23 | | | % 136.14/20.23 | | | (18) all_57_0 = e3 & op(e3, e3) = e3 % 136.14/20.23 | | | % 136.14/20.23 | | | ALPHA: (18) implies: % 136.14/20.23 | | | (19) op(e3, e3) = e3 % 136.14/20.23 | | | % 136.14/20.23 | | | REF_CLOSE: (1), (4), (7), (19) are inconsistent by sub-proof #778. % 136.14/20.23 | | | % 136.14/20.23 | | Case 2: % 136.14/20.23 | | | % 136.14/20.23 | | | (20) all_57_2 = e3 & op(e2, e3) = e3 % 136.14/20.23 | | | % 136.14/20.23 | | | ALPHA: (20) implies: % 136.14/20.23 | | | (21) all_57_2 = e3 % 136.14/20.23 | | | % 136.14/20.23 | | | REF_CLOSE: (2), (5), (6), (10), (11), (12), (13), (14), (16), (21) are % 136.14/20.23 | | | inconsistent by sub-proof #362. % 136.14/20.23 | | | % 136.14/20.23 | | End of split % 136.14/20.23 | | % 136.14/20.23 | Case 2: % 136.14/20.23 | | % 136.14/20.23 | | (22) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = % 136.14/20.23 | | e3) % 136.14/20.23 | | % 136.14/20.23 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (12), (15), (22) % 136.14/20.23 | | are inconsistent by sub-proof #367. % 136.14/20.23 | | % 136.14/20.23 | End of split % 136.14/20.23 | % 136.14/20.23 End of proof % 136.14/20.23 % 136.14/20.23 Sub-proof #362 shows that the following formulas are inconsistent: % 136.14/20.23 ---------------------------------------------------------------- % 136.14/20.23 (1) ~ (e2 = e0) % 136.14/20.23 (2) ~ (e2 = e1) % 136.14/20.23 (3) ~ (e3 = e0) % 136.14/20.23 (4) all_57_2 = e3 % 136.14/20.23 (5) all_57_3 = e3 % 136.14/20.23 (6) ~ (e3 = e1) % 136.14/20.23 (7) ~ (e1 = e0) % 136.14/20.23 (8) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.23 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.14/20.23 (9) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.23 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 136.14/20.23 (10) all_57_10 = e2 % 136.14/20.23 % 136.14/20.23 Begin of proof % 136.14/20.23 | % 136.14/20.23 | BETA: splitting (9) gives: % 136.14/20.23 | % 136.14/20.23 | Case 1: % 136.14/20.23 | | % 136.14/20.23 | | (11) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = % 136.14/20.23 | | e0) % 136.14/20.23 | | % 136.14/20.23 | | REF_CLOSE: (3), (4), (5), (11) are inconsistent by sub-proof #373. % 136.14/20.23 | | % 136.14/20.23 | Case 2: % 136.14/20.23 | | % 136.14/20.23 | | (12) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = % 136.14/20.23 | | e0) % 136.14/20.23 | | % 136.14/20.23 | | BETA: splitting (12) gives: % 136.14/20.23 | | % 136.14/20.23 | | Case 1: % 136.14/20.23 | | | % 136.14/20.23 | | | (13) all_57_5 = e0 & op(e2, e1) = e0 % 136.14/20.23 | | | % 136.14/20.23 | | | ALPHA: (13) implies: % 136.14/20.23 | | | (14) all_57_5 = e0 % 136.14/20.23 | | | % 136.14/20.23 | | | BETA: splitting (8) gives: % 136.14/20.23 | | | % 136.14/20.23 | | | Case 1: % 136.14/20.23 | | | | % 136.14/20.23 | | | | (15) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) % 136.14/20.23 | | | | = e1) % 136.14/20.23 | | | | % 136.14/20.23 | | | | BETA: splitting (15) gives: % 136.14/20.23 | | | | % 136.14/20.23 | | | | Case 1: % 136.14/20.23 | | | | | % 136.14/20.23 | | | | | (16) all_57_2 = e1 & op(e2, e3) = e1 % 136.14/20.23 | | | | | % 136.14/20.23 | | | | | REF_CLOSE: (4), (6), (16) are inconsistent by sub-proof #371. % 136.14/20.23 | | | | | % 136.14/20.23 | | | | Case 2: % 136.14/20.23 | | | | | % 136.14/20.23 | | | | | (17) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.23 | | | | | % 136.14/20.23 | | | | | REF_CLOSE: (5), (6), (17) are inconsistent by sub-proof #370. % 136.14/20.23 | | | | | % 136.14/20.23 | | | | End of split % 136.14/20.23 | | | | % 136.14/20.23 | | | Case 2: % 136.14/20.23 | | | | % 136.14/20.23 | | | | (18) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) % 136.14/20.23 | | | | = e1) % 136.14/20.23 | | | | % 136.14/20.23 | | | | REF_CLOSE: (2), (7), (10), (14), (18) are inconsistent by sub-proof % 136.14/20.23 | | | | #364. % 136.14/20.23 | | | | % 136.14/20.23 | | | End of split % 136.14/20.23 | | | % 136.14/20.23 | | Case 2: % 136.14/20.23 | | | % 136.14/20.23 | | | (19) all_57_10 = e0 & op(e2, e0) = e0 % 136.14/20.23 | | | % 136.14/20.23 | | | REF_CLOSE: (1), (10), (19) are inconsistent by sub-proof #363. % 136.14/20.23 | | | % 136.14/20.23 | | End of split % 136.14/20.23 | | % 136.14/20.23 | End of split % 136.14/20.23 | % 136.14/20.23 End of proof % 136.14/20.23 % 136.14/20.23 Sub-proof #363 shows that the following formulas are inconsistent: % 136.14/20.23 ---------------------------------------------------------------- % 136.14/20.23 (1) all_57_10 = e0 & op(e2, e0) = e0 % 136.14/20.23 (2) all_57_10 = e2 % 136.14/20.23 (3) ~ (e2 = e0) % 136.14/20.23 % 136.14/20.23 Begin of proof % 136.14/20.23 | % 136.14/20.23 | ALPHA: (1) implies: % 136.14/20.23 | (4) all_57_10 = e0 % 136.14/20.23 | % 136.14/20.23 | COMBINE_EQS: (2), (4) imply: % 136.14/20.23 | (5) e2 = e0 % 136.14/20.23 | % 136.14/20.23 | SIMP: (5) implies: % 136.14/20.23 | (6) e2 = e0 % 136.14/20.23 | % 136.14/20.23 | REDUCE: (3), (6) imply: % 136.14/20.23 | (7) $false % 136.14/20.23 | % 136.14/20.23 | CLOSE: (7) is inconsistent. % 136.14/20.23 | % 136.14/20.23 End of proof % 136.14/20.23 % 136.14/20.23 Sub-proof #364 shows that the following formulas are inconsistent: % 136.14/20.23 ---------------------------------------------------------------- % 136.14/20.23 (1) ~ (e2 = e1) % 136.14/20.23 (2) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.14/20.23 (3) ~ (e1 = e0) % 136.14/20.23 (4) all_57_5 = e0 % 136.14/20.23 (5) all_57_10 = e2 % 136.14/20.23 % 136.14/20.23 Begin of proof % 136.14/20.23 | % 136.14/20.23 | BETA: splitting (2) gives: % 136.14/20.23 | % 136.14/20.23 | Case 1: % 136.14/20.23 | | % 136.14/20.23 | | (6) all_57_5 = e1 & op(e2, e1) = e1 % 136.14/20.23 | | % 136.14/20.23 | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #365. % 136.14/20.23 | | % 136.14/20.23 | Case 2: % 136.14/20.23 | | % 136.14/20.23 | | (7) all_57_10 = e1 & op(e2, e0) = e1 % 136.14/20.23 | | % 136.14/20.23 | | ALPHA: (7) implies: % 136.14/20.23 | | (8) all_57_10 = e1 % 136.14/20.23 | | % 136.14/20.23 | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #414. % 136.14/20.23 | | % 136.14/20.23 | End of split % 136.14/20.23 | % 136.14/20.23 End of proof % 136.14/20.23 % 136.14/20.23 Sub-proof #365 shows that the following formulas are inconsistent: % 136.14/20.23 ---------------------------------------------------------------- % 136.14/20.23 (1) all_57_5 = e1 & op(e2, e1) = e1 % 136.14/20.23 (2) all_57_5 = e0 % 136.14/20.23 (3) ~ (e1 = e0) % 136.14/20.23 % 136.14/20.23 Begin of proof % 136.14/20.23 | % 136.14/20.23 | ALPHA: (1) implies: % 136.14/20.23 | (4) all_57_5 = e1 % 136.14/20.23 | % 136.14/20.23 | COMBINE_EQS: (2), (4) imply: % 136.14/20.23 | (5) e1 = e0 % 136.14/20.23 | % 136.14/20.23 | REDUCE: (3), (5) imply: % 136.14/20.23 | (6) $false % 136.14/20.23 | % 136.14/20.23 | CLOSE: (6) is inconsistent. % 136.14/20.23 | % 136.14/20.23 End of proof % 136.14/20.23 % 136.14/20.23 Sub-proof #366 shows that the following formulas are inconsistent: % 136.14/20.23 ---------------------------------------------------------------- % 136.14/20.23 (1) op(e3, e3) = e2 % 136.14/20.23 (2) ~ (e2 = e0) % 136.14/20.23 (3) all_57_5 = e2 % 136.14/20.23 (4) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 136.14/20.23 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 136.14/20.23 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.23 (6) ~ (e2 = e1) % 136.14/20.23 (7) ~ (e3 = e0) % 136.14/20.23 (8) ~ (e3 = e2) % 136.14/20.23 (9) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.14/20.23 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.14/20.23 (10) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.14/20.23 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.14/20.23 (11) all_57_3 = e3 % 136.14/20.23 (12) ~ (e3 = e1) % 136.14/20.23 (13) ~ (e1 = e0) % 136.14/20.23 (14) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.23 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.14/20.23 (15) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.23 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 136.14/20.23 (16) all_57_6 = e2 % 136.14/20.23 % 136.14/20.23 Begin of proof % 136.14/20.23 | % 136.14/20.23 | BETA: splitting (9) gives: % 136.14/20.23 | % 136.14/20.23 | Case 1: % 136.14/20.23 | | % 136.14/20.23 | | (17) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = % 136.14/20.23 | | e3) % 136.14/20.23 | | % 136.14/20.23 | | BETA: splitting (17) gives: % 136.14/20.23 | | % 136.14/20.23 | | Case 1: % 136.14/20.23 | | | % 136.14/20.23 | | | (18) all_57_0 = e3 & op(e3, e3) = e3 % 136.14/20.23 | | | % 136.14/20.23 | | | ALPHA: (18) implies: % 136.14/20.23 | | | (19) op(e3, e3) = e3 % 136.14/20.23 | | | % 136.14/20.23 | | | REF_CLOSE: (1), (5), (8), (19) are inconsistent by sub-proof #778. % 136.14/20.23 | | | % 136.14/20.23 | | Case 2: % 136.14/20.23 | | | % 136.14/20.23 | | | (20) all_57_2 = e3 & op(e2, e3) = e3 % 136.14/20.23 | | | % 136.14/20.23 | | | ALPHA: (20) implies: % 136.14/20.23 | | | (21) all_57_2 = e3 % 136.14/20.23 | | | % 136.14/20.23 | | | REF_CLOSE: (2), (3), (6), (7), (11), (12), (13), (14), (15), (21) are % 136.14/20.23 | | | inconsistent by sub-proof #368. % 136.14/20.23 | | | % 136.14/20.23 | | End of split % 136.14/20.23 | | % 136.14/20.23 | Case 2: % 136.14/20.23 | | % 136.14/20.23 | | (22) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = % 136.14/20.23 | | e3) % 136.14/20.23 | | % 136.14/20.23 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (12), (13), (16), (22) % 136.14/20.23 | | are inconsistent by sub-proof #367. % 136.14/20.23 | | % 136.14/20.23 | End of split % 136.14/20.23 | % 136.14/20.23 End of proof % 136.14/20.23 % 136.14/20.23 Sub-proof #367 shows that the following formulas are inconsistent: % 136.14/20.23 ---------------------------------------------------------------- % 136.14/20.23 (1) op(e3, e3) = e2 % 136.14/20.23 (2) ~ (e2 = e0) % 136.14/20.23 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 136.14/20.23 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 136.14/20.23 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.23 (5) ~ (e2 = e1) % 136.14/20.23 (6) ~ (e3 = e0) % 136.14/20.23 (7) ~ (e3 = e2) % 136.14/20.23 (8) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.14/20.23 (9) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.14/20.23 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.14/20.23 (10) ~ (e3 = e1) % 136.14/20.23 (11) ~ (e1 = e0) % 136.14/20.23 (12) all_57_6 = e2 % 136.14/20.23 % 136.14/20.23 Begin of proof % 136.14/20.23 | % 136.14/20.23 | BETA: splitting (8) gives: % 136.14/20.23 | % 136.14/20.23 | Case 1: % 136.14/20.23 | | % 136.14/20.23 | | (13) all_57_6 = e3 & op(e1, e3) = e3 % 136.14/20.23 | | % 136.14/20.23 | | ALPHA: (13) implies: % 136.14/20.23 | | (14) all_57_6 = e3 % 136.14/20.23 | | % 136.14/20.23 | | REF_CLOSE: (7), (12), (14) are inconsistent by sub-proof #592. % 136.14/20.23 | | % 136.14/20.23 | Case 2: % 136.14/20.23 | | % 136.14/20.23 | | (15) all_57_12 = e3 & op(e0, e3) = e3 % 136.14/20.23 | | % 136.14/20.23 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (12), (15) are % 136.14/20.23 | | inconsistent by sub-proof #391. % 136.14/20.23 | | % 136.14/20.23 | End of split % 136.14/20.23 | % 136.14/20.23 End of proof % 136.14/20.23 % 136.14/20.23 Sub-proof #368 shows that the following formulas are inconsistent: % 136.14/20.23 ---------------------------------------------------------------- % 136.14/20.23 (1) ~ (e2 = e0) % 136.14/20.23 (2) all_57_5 = e2 % 136.14/20.23 (3) ~ (e2 = e1) % 136.14/20.23 (4) ~ (e3 = e0) % 136.14/20.23 (5) all_57_2 = e3 % 136.14/20.23 (6) all_57_3 = e3 % 136.14/20.23 (7) ~ (e3 = e1) % 136.14/20.23 (8) ~ (e1 = e0) % 136.14/20.23 (9) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.23 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.14/20.23 (10) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.23 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) % 136.14/20.23 % 136.14/20.23 Begin of proof % 136.14/20.23 | % 136.14/20.23 | BETA: splitting (10) gives: % 136.14/20.23 | % 136.14/20.23 | Case 1: % 136.14/20.23 | | % 136.14/20.23 | | (11) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = % 136.14/20.23 | | e0) % 136.14/20.23 | | % 136.14/20.23 | | REF_CLOSE: (4), (5), (6), (11) are inconsistent by sub-proof #373. % 136.14/20.23 | | % 136.14/20.23 | Case 2: % 136.14/20.23 | | % 136.14/20.23 | | (12) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = % 136.14/20.23 | | e0) % 136.14/20.23 | | % 136.14/20.23 | | BETA: splitting (12) gives: % 136.14/20.23 | | % 136.14/20.23 | | Case 1: % 136.14/20.23 | | | % 136.14/20.23 | | | (13) all_57_5 = e0 & op(e2, e1) = e0 % 136.14/20.23 | | | % 136.14/20.23 | | | ALPHA: (13) implies: % 136.14/20.23 | | | (14) all_57_5 = e0 % 136.14/20.23 | | | % 136.14/20.23 | | | REF_CLOSE: (1), (2), (14) are inconsistent by sub-proof #372. % 136.14/20.23 | | | % 136.14/20.23 | | Case 2: % 136.14/20.23 | | | % 136.14/20.23 | | | (15) all_57_10 = e0 & op(e2, e0) = e0 % 136.14/20.23 | | | % 136.14/20.23 | | | ALPHA: (15) implies: % 136.14/20.23 | | | (16) all_57_10 = e0 % 136.14/20.23 | | | % 136.14/20.23 | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (16) are inconsistent by % 136.14/20.23 | | | sub-proof #369. % 136.14/20.23 | | | % 136.14/20.23 | | End of split % 136.14/20.23 | | % 136.14/20.23 | End of split % 136.14/20.23 | % 136.14/20.23 End of proof % 136.14/20.23 % 136.14/20.23 Sub-proof #369 shows that the following formulas are inconsistent: % 136.14/20.23 ---------------------------------------------------------------- % 136.14/20.23 (1) all_57_5 = e2 % 136.14/20.23 (2) ~ (e2 = e1) % 136.14/20.23 (3) all_57_10 = e0 % 136.14/20.23 (4) all_57_2 = e3 % 136.14/20.24 (5) all_57_3 = e3 % 136.14/20.24 (6) ~ (e3 = e1) % 136.14/20.24 (7) ~ (e1 = e0) % 136.14/20.24 (8) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.24 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | BETA: splitting (8) gives: % 136.14/20.24 | % 136.14/20.24 | Case 1: % 136.14/20.24 | | % 136.14/20.24 | | (9) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) % 136.14/20.24 | | % 136.14/20.24 | | BETA: splitting (9) gives: % 136.14/20.24 | | % 136.14/20.24 | | Case 1: % 136.14/20.24 | | | % 136.14/20.24 | | | (10) all_57_2 = e1 & op(e2, e3) = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #371. % 136.14/20.24 | | | % 136.14/20.24 | | Case 2: % 136.14/20.24 | | | % 136.14/20.24 | | | (11) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | REF_CLOSE: (5), (6), (11) are inconsistent by sub-proof #370. % 136.14/20.24 | | | % 136.14/20.24 | | End of split % 136.14/20.24 | | % 136.14/20.24 | Case 2: % 136.14/20.24 | | % 136.14/20.24 | | (12) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = % 136.14/20.24 | | e1) % 136.14/20.24 | | % 136.14/20.24 | | BETA: splitting (12) gives: % 136.14/20.24 | | % 136.14/20.24 | | Case 1: % 136.14/20.24 | | | % 136.14/20.24 | | | (13) all_57_5 = e1 & op(e2, e1) = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | ALPHA: (13) implies: % 136.14/20.24 | | | (14) all_57_5 = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | REF_CLOSE: (1), (2), (14) are inconsistent by sub-proof #418. % 136.14/20.24 | | | % 136.14/20.24 | | Case 2: % 136.14/20.24 | | | % 136.14/20.24 | | | (15) all_57_10 = e1 & op(e2, e0) = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | ALPHA: (15) implies: % 136.14/20.24 | | | (16) all_57_10 = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | COMBINE_EQS: (3), (16) imply: % 136.14/20.24 | | | (17) e1 = e0 % 136.14/20.24 | | | % 136.14/20.24 | | | REDUCE: (7), (17) imply: % 136.14/20.24 | | | (18) $false % 136.14/20.24 | | | % 136.14/20.24 | | | CLOSE: (18) is inconsistent. % 136.14/20.24 | | | % 136.14/20.24 | | End of split % 136.14/20.24 | | % 136.14/20.24 | End of split % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #370 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.24 (2) all_57_3 = e3 % 136.14/20.24 (3) ~ (e3 = e1) % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | ALPHA: (1) implies: % 136.14/20.24 | (4) all_57_3 = e1 % 136.14/20.24 | % 136.14/20.24 | COMBINE_EQS: (2), (4) imply: % 136.14/20.24 | (5) e3 = e1 % 136.14/20.24 | % 136.14/20.24 | REDUCE: (3), (5) imply: % 136.14/20.24 | (6) $false % 136.14/20.24 | % 136.14/20.24 | CLOSE: (6) is inconsistent. % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #371 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) all_57_2 = e1 & op(e2, e3) = e1 % 136.14/20.24 (2) all_57_2 = e3 % 136.14/20.24 (3) ~ (e3 = e1) % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | ALPHA: (1) implies: % 136.14/20.24 | (4) all_57_2 = e1 % 136.14/20.24 | % 136.14/20.24 | COMBINE_EQS: (2), (4) imply: % 136.14/20.24 | (5) e3 = e1 % 136.14/20.24 | % 136.14/20.24 | SIMP: (5) implies: % 136.14/20.24 | (6) e3 = e1 % 136.14/20.24 | % 136.14/20.24 | REDUCE: (3), (6) imply: % 136.14/20.24 | (7) $false % 136.14/20.24 | % 136.14/20.24 | CLOSE: (7) is inconsistent. % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #372 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) all_57_5 = e2 % 136.14/20.24 (2) all_57_5 = e0 % 136.14/20.24 (3) ~ (e2 = e0) % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | COMBINE_EQS: (1), (2) imply: % 136.14/20.24 | (4) e2 = e0 % 136.14/20.24 | % 136.14/20.24 | SIMP: (4) implies: % 136.14/20.24 | (5) e2 = e0 % 136.14/20.24 | % 136.14/20.24 | REDUCE: (3), (5) imply: % 136.14/20.24 | (6) $false % 136.14/20.24 | % 136.14/20.24 | CLOSE: (6) is inconsistent. % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #373 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) % 136.14/20.24 (2) all_57_2 = e3 % 136.14/20.24 (3) ~ (e3 = e0) % 136.14/20.24 (4) all_57_3 = e3 % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | BETA: splitting (1) gives: % 136.14/20.24 | % 136.14/20.24 | Case 1: % 136.14/20.24 | | % 136.14/20.24 | | (5) all_57_2 = e0 & op(e2, e3) = e0 % 136.14/20.24 | | % 136.14/20.24 | | ALPHA: (5) implies: % 136.14/20.24 | | (6) all_57_2 = e0 % 136.14/20.24 | | % 136.14/20.24 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #593. % 136.14/20.24 | | % 136.14/20.24 | Case 2: % 136.14/20.24 | | % 136.14/20.24 | | (7) all_57_3 = e0 & op(e2, e2) = e0 % 136.14/20.24 | | % 136.14/20.24 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #374. % 136.14/20.24 | | % 136.14/20.24 | End of split % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #374 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) all_57_3 = e0 & op(e2, e2) = e0 % 136.14/20.24 (2) all_57_3 = e3 % 136.14/20.24 (3) ~ (e3 = e0) % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | ALPHA: (1) implies: % 136.14/20.24 | (4) all_57_3 = e0 % 136.14/20.24 | % 136.14/20.24 | COMBINE_EQS: (2), (4) imply: % 136.14/20.24 | (5) e3 = e0 % 136.14/20.24 | % 136.14/20.24 | REDUCE: (3), (5) imply: % 136.14/20.24 | (6) $false % 136.14/20.24 | % 136.14/20.24 | CLOSE: (6) is inconsistent. % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #375 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) all_57_3 = e2 & op(e2, e2) = e2 % 136.14/20.24 (2) all_57_3 = e3 % 136.14/20.24 (3) ~ (e3 = e2) % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | ALPHA: (1) implies: % 136.14/20.24 | (4) all_57_3 = e2 % 136.14/20.24 | % 136.14/20.24 | COMBINE_EQS: (2), (4) imply: % 136.14/20.24 | (5) e3 = e2 % 136.14/20.24 | % 136.14/20.24 | REDUCE: (3), (5) imply: % 136.14/20.24 | (6) $false % 136.14/20.24 | % 136.14/20.24 | CLOSE: (6) is inconsistent. % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #376 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) all_57_1 = e3 & op(e3, e2) = e3 % 136.14/20.24 (2) all_57_1 = e0 % 136.14/20.24 (3) ~ (e3 = e0) % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | ALPHA: (1) implies: % 136.14/20.24 | (4) all_57_1 = e3 % 136.14/20.24 | % 136.14/20.24 | COMBINE_EQS: (2), (4) imply: % 136.14/20.24 | (5) e3 = e0 % 136.14/20.24 | % 136.14/20.24 | SIMP: (5) implies: % 136.14/20.24 | (6) e3 = e0 % 136.14/20.24 | % 136.14/20.24 | REDUCE: (3), (6) imply: % 136.14/20.24 | (7) $false % 136.14/20.24 | % 136.14/20.24 | CLOSE: (7) is inconsistent. % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #377 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) all_57_10 = e3 & op(e2, e0) = e3 % 136.14/20.24 (2) all_57_10 = e0 % 136.14/20.24 (3) ~ (e3 = e0) % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | ALPHA: (1) implies: % 136.14/20.24 | (4) all_57_10 = e3 % 136.14/20.24 | % 136.14/20.24 | COMBINE_EQS: (2), (4) imply: % 136.14/20.24 | (5) e3 = e0 % 136.14/20.24 | % 136.14/20.24 | REDUCE: (3), (5) imply: % 136.14/20.24 | (6) $false % 136.14/20.24 | % 136.14/20.24 | CLOSE: (6) is inconsistent. % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #378 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) op(e3, e3) = e2 % 136.14/20.24 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.24 (3) ~ (e2 = e1) % 136.14/20.24 (4) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) % 136.14/20.24 (5) op(e3, e2) = all_52_4 % 136.14/20.24 (6) ~ (all_52_4 = e1) % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | BETA: splitting (4) gives: % 136.14/20.24 | % 136.14/20.24 | Case 1: % 136.14/20.24 | | % 136.14/20.24 | | (7) all_57_0 = e1 & op(e3, e3) = e1 % 136.14/20.24 | | % 136.14/20.24 | | ALPHA: (7) implies: % 136.14/20.24 | | (8) op(e3, e3) = e1 % 136.14/20.24 | | % 136.14/20.24 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #743. % 136.14/20.24 | | % 136.14/20.24 | Case 2: % 136.14/20.24 | | % 136.14/20.24 | | (9) all_57_1 = e1 & op(e3, e2) = e1 % 136.14/20.24 | | % 136.14/20.24 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #684. % 136.14/20.24 | | % 136.14/20.24 | End of split % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #379 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) all_57_4 = e3 & op(e3, e1) = e3 % 136.14/20.24 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.24 (3) op(e3, e1) = all_36_0 % 136.14/20.24 (4) op(e3, e1) = all_52_8 % 136.14/20.24 (5) ~ (all_52_8 = e3) % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | ALPHA: (1) implies: % 136.14/20.24 | (6) op(e3, e1) = e3 % 136.14/20.24 | % 136.14/20.24 | GROUND_INST: instantiating (2) with all_52_8, e3, e1, e3, simplifying with % 136.14/20.24 | (4), (6) gives: % 136.14/20.24 | (7) all_52_8 = e3 % 136.14/20.24 | % 136.14/20.24 | GROUND_INST: instantiating (2) with all_52_8, all_36_0, e1, e3, simplifying % 136.14/20.24 | with (3), (4) gives: % 136.14/20.24 | (8) all_52_8 = all_36_0 % 136.14/20.24 | % 136.14/20.24 | COMBINE_EQS: (7), (8) imply: % 136.14/20.24 | (9) all_36_0 = e3 % 136.14/20.24 | % 136.14/20.24 | REDUCE: (5), (7) imply: % 136.14/20.24 | (10) $false % 136.14/20.24 | % 136.14/20.24 | CLOSE: (10) is inconsistent. % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #380 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) ~ (all_16_1 = e0) & op(e2, e2) = all_16_1 & $i(all_16_1) % 136.14/20.24 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.24 (3) op(e2, e2) = e0 % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | ALPHA: (1) implies: % 136.14/20.24 | (4) ~ (all_16_1 = e0) % 136.14/20.24 | (5) op(e2, e2) = all_16_1 % 136.14/20.24 | % 136.14/20.24 | GROUND_INST: instantiating (2) with e0, all_16_1, e2, e2, simplifying with % 136.14/20.24 | (3), (5) gives: % 136.14/20.24 | (6) all_16_1 = e0 % 136.14/20.24 | % 136.14/20.24 | REDUCE: (4), (6) imply: % 136.14/20.24 | (7) $false % 136.14/20.24 | % 136.14/20.24 | CLOSE: (7) is inconsistent. % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #381 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) ~ (all_16_0 = e0) % 136.14/20.24 (2) ~ (all_16_0 = e1) % 136.14/20.24 (3) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0 % 136.14/20.24 (4) ~ (all_16_0 = e2) % 136.14/20.24 (5) all_54_4 = all_16_0 % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | BETA: splitting (3) gives: % 136.14/20.24 | % 136.14/20.24 | Case 1: % 136.14/20.24 | | % 136.14/20.24 | | (6) all_54_4 = e2 % 136.14/20.24 | | % 136.14/20.24 | | COMBINE_EQS: (5), (6) imply: % 136.14/20.24 | | (7) all_16_0 = e2 % 136.14/20.24 | | % 136.14/20.24 | | REDUCE: (4), (7) imply: % 136.14/20.24 | | (8) $false % 136.14/20.24 | | % 136.14/20.24 | | CLOSE: (8) is inconsistent. % 136.14/20.24 | | % 136.14/20.24 | Case 2: % 136.14/20.24 | | % 136.14/20.24 | | (9) all_54_4 = e1 | all_54_4 = e0 % 136.14/20.24 | | % 136.14/20.24 | | BETA: splitting (9) gives: % 136.14/20.24 | | % 136.14/20.24 | | Case 1: % 136.14/20.24 | | | % 136.14/20.24 | | | (10) all_54_4 = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | COMBINE_EQS: (5), (10) imply: % 136.14/20.24 | | | (11) all_16_0 = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | REDUCE: (2), (11) imply: % 136.14/20.24 | | | (12) $false % 136.14/20.24 | | | % 136.14/20.24 | | | CLOSE: (12) is inconsistent. % 136.14/20.24 | | | % 136.14/20.24 | | Case 2: % 136.14/20.24 | | | % 136.14/20.24 | | | (13) all_54_4 = e0 % 136.14/20.24 | | | % 136.14/20.24 | | | COMBINE_EQS: (5), (13) imply: % 136.14/20.24 | | | (14) all_16_0 = e0 % 136.14/20.24 | | | % 136.14/20.24 | | | REDUCE: (1), (14) imply: % 136.14/20.24 | | | (15) $false % 136.14/20.24 | | | % 136.14/20.24 | | | CLOSE: (15) is inconsistent. % 136.14/20.24 | | | % 136.14/20.24 | | End of split % 136.14/20.24 | | % 136.14/20.24 | End of split % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #382 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) all_57_4 = e1 & op(e3, e1) = e1 % 136.14/20.24 (2) all_57_4 = e3 % 136.14/20.24 (3) ~ (e3 = e1) % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | ALPHA: (1) implies: % 136.14/20.24 | (4) all_57_4 = e1 % 136.14/20.24 | % 136.14/20.24 | COMBINE_EQS: (2), (4) imply: % 136.14/20.24 | (5) e3 = e1 % 136.14/20.24 | % 136.14/20.24 | REDUCE: (3), (5) imply: % 136.14/20.24 | (6) $false % 136.14/20.24 | % 136.14/20.24 | CLOSE: (6) is inconsistent. % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #383 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) all_57_9 = e1 % 136.14/20.24 (2) all_57_9 = e0 % 136.14/20.24 (3) ~ (e1 = e0) % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | COMBINE_EQS: (1), (2) imply: % 136.14/20.24 | (4) e1 = e0 % 136.14/20.24 | % 136.14/20.24 | SIMP: (4) implies: % 136.14/20.24 | (5) e1 = e0 % 136.14/20.24 | % 136.14/20.24 | REDUCE: (3), (5) imply: % 136.14/20.24 | (6) $false % 136.14/20.24 | % 136.14/20.24 | CLOSE: (6) is inconsistent. % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #384 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) all_57_4 = e0 & op(e3, e1) = e0 % 136.14/20.24 (2) all_57_4 = e3 % 136.14/20.24 (3) ~ (e3 = e0) % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | ALPHA: (1) implies: % 136.14/20.24 | (4) all_57_4 = e0 % 136.14/20.24 | % 136.14/20.24 | COMBINE_EQS: (2), (4) imply: % 136.14/20.24 | (5) e3 = e0 % 136.14/20.24 | % 136.14/20.24 | REDUCE: (3), (5) imply: % 136.14/20.24 | (6) $false % 136.14/20.24 | % 136.14/20.24 | CLOSE: (6) is inconsistent. % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #385 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) all_57_7 = e2 & op(e1, e2) = e2 % 136.14/20.24 (2) all_57_7 = e3 % 136.14/20.24 (3) ~ (e3 = e2) % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | ALPHA: (1) implies: % 136.14/20.24 | (4) all_57_7 = e2 % 136.14/20.24 | % 136.14/20.24 | COMBINE_EQS: (2), (4) imply: % 136.14/20.24 | (5) e3 = e2 % 136.14/20.24 | % 136.14/20.24 | REDUCE: (3), (5) imply: % 136.14/20.24 | (6) $false % 136.14/20.24 | % 136.14/20.24 | CLOSE: (6) is inconsistent. % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #386 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) op(e0, e0) = e0 % 136.14/20.24 (2) op(e2, e0) = all_52_13 % 136.14/20.24 (3) ~ (all_52_14 = e3) % 136.14/20.24 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.24 (5) ~ (e3 = e0) % 136.14/20.24 (6) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) | % 136.14/20.24 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.24 (7) ~ (all_52_13 = e3) % 136.14/20.24 (8) op(e1, e0) = all_52_14 % 136.14/20.24 (9) all_57_9 = e0 % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | BETA: splitting (6) gives: % 136.14/20.24 | % 136.14/20.24 | Case 1: % 136.14/20.24 | | % 136.14/20.24 | | (10) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = % 136.14/20.24 | | e3) % 136.14/20.24 | | % 136.14/20.24 | | BETA: splitting (10) gives: % 136.14/20.24 | | % 136.14/20.24 | | Case 1: % 136.14/20.24 | | | % 136.14/20.24 | | | (11) all_57_9 = e3 & op(e3, e0) = e3 % 136.14/20.24 | | | % 136.14/20.24 | | | ALPHA: (11) implies: % 136.14/20.24 | | | (12) all_57_9 = e3 % 136.14/20.24 | | | % 136.14/20.24 | | | REF_CLOSE: (5), (9), (12) are inconsistent by sub-proof #670. % 136.14/20.24 | | | % 136.14/20.24 | | Case 2: % 136.14/20.24 | | | % 136.14/20.24 | | | (13) all_57_10 = e3 & op(e2, e0) = e3 % 136.14/20.24 | | | % 136.14/20.24 | | | REF_CLOSE: (2), (4), (7), (13) are inconsistent by sub-proof #749. % 136.14/20.24 | | | % 136.14/20.24 | | End of split % 136.14/20.24 | | % 136.14/20.24 | Case 2: % 136.14/20.24 | | % 136.14/20.24 | | (14) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = % 136.14/20.24 | | e3) % 136.14/20.24 | | % 136.14/20.24 | | REF_CLOSE: (1), (3), (4), (5), (8), (14) are inconsistent by sub-proof #387. % 136.14/20.24 | | % 136.14/20.24 | End of split % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #387 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) op(e0, e0) = e0 % 136.14/20.24 (2) ~ (all_52_14 = e3) % 136.14/20.24 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.24 (4) ~ (e3 = e0) % 136.14/20.24 (5) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.24 (6) op(e1, e0) = all_52_14 % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | BETA: splitting (5) gives: % 136.14/20.24 | % 136.14/20.24 | Case 1: % 136.14/20.24 | | % 136.14/20.24 | | (7) all_57_11 = e3 & op(e1, e0) = e3 % 136.14/20.24 | | % 136.14/20.24 | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #750. % 136.14/20.24 | | % 136.14/20.24 | Case 2: % 136.14/20.24 | | % 136.14/20.24 | | (8) all_57_15 = e3 & op(e0, e0) = e3 % 136.14/20.24 | | % 136.14/20.24 | | ALPHA: (8) implies: % 136.14/20.24 | | (9) op(e0, e0) = e3 % 136.14/20.24 | | % 136.14/20.24 | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #715. % 136.14/20.24 | | % 136.14/20.24 | End of split % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #388 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) ~ (e2 = e0) % 136.14/20.24 (2) all_57_3 = e0 % 136.14/20.24 (3) ~ (e2 = e1) % 136.14/20.24 (4) ~ (e3 = e2) % 136.14/20.24 (5) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 136.14/20.24 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) % 136.14/20.24 (6) all_57_13 = e3 & op(e0, e2) = e3 % 136.14/20.24 (7) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.24 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.24 (8) all_57_7 = e3 % 136.14/20.24 (9) ~ (e3 = e1) % 136.14/20.24 (10) ~ (e1 = e0) % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | ALPHA: (6) implies: % 136.14/20.24 | (11) all_57_13 = e3 % 136.14/20.24 | % 136.14/20.24 | BETA: splitting (5) gives: % 136.14/20.24 | % 136.14/20.24 | Case 1: % 136.14/20.24 | | % 136.14/20.24 | | (12) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = % 136.14/20.24 | | e2) % 136.14/20.24 | | % 136.14/20.24 | | BETA: splitting (12) gives: % 136.14/20.24 | | % 136.14/20.24 | | Case 1: % 136.14/20.24 | | | % 136.14/20.24 | | | (13) all_57_1 = e2 & op(e3, e2) = e2 % 136.14/20.24 | | | % 136.14/20.24 | | | ALPHA: (13) implies: % 136.14/20.24 | | | (14) all_57_1 = e2 % 136.14/20.24 | | | % 136.14/20.24 | | | BETA: splitting (7) gives: % 136.14/20.24 | | | % 136.14/20.24 | | | Case 1: % 136.14/20.24 | | | | % 136.14/20.24 | | | | (15) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) % 136.14/20.24 | | | | = e1) % 136.14/20.24 | | | | % 136.14/20.24 | | | | BETA: splitting (15) gives: % 136.14/20.24 | | | | % 136.14/20.24 | | | | Case 1: % 136.14/20.24 | | | | | % 136.14/20.24 | | | | | (16) all_57_1 = e1 & op(e3, e2) = e1 % 136.14/20.24 | | | | | % 136.14/20.24 | | | | | REF_CLOSE: (3), (14), (16) are inconsistent by sub-proof #465. % 136.14/20.24 | | | | | % 136.14/20.24 | | | | Case 2: % 136.14/20.24 | | | | | % 136.14/20.24 | | | | | (17) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.24 | | | | | % 136.14/20.24 | | | | | REF_CLOSE: (2), (10), (17) are inconsistent by sub-proof #449. % 136.14/20.24 | | | | | % 136.14/20.24 | | | | End of split % 136.14/20.24 | | | | % 136.14/20.24 | | | Case 2: % 136.14/20.24 | | | | % 136.14/20.24 | | | | (18) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) % 136.14/20.24 | | | | = e1) % 136.14/20.24 | | | | % 136.14/20.24 | | | | BETA: splitting (18) gives: % 136.14/20.24 | | | | % 136.14/20.24 | | | | Case 1: % 136.14/20.24 | | | | | % 136.14/20.24 | | | | | (19) all_57_7 = e1 & op(e1, e2) = e1 % 136.14/20.24 | | | | | % 136.14/20.24 | | | | | ALPHA: (19) implies: % 136.14/20.24 | | | | | (20) all_57_7 = e1 % 136.14/20.24 | | | | | % 136.14/20.24 | | | | | REF_CLOSE: (8), (9), (20) are inconsistent by sub-proof #390. % 136.14/20.24 | | | | | % 136.14/20.24 | | | | Case 2: % 136.14/20.24 | | | | | % 136.14/20.24 | | | | | (21) all_57_13 = e1 & op(e0, e2) = e1 % 136.14/20.24 | | | | | % 136.14/20.24 | | | | | REF_CLOSE: (9), (11), (21) are inconsistent by sub-proof #389. % 136.14/20.24 | | | | | % 136.14/20.24 | | | | End of split % 136.14/20.24 | | | | % 136.14/20.24 | | | End of split % 136.14/20.24 | | | % 136.14/20.24 | | Case 2: % 136.14/20.24 | | | % 136.14/20.24 | | | (22) all_57_3 = e2 & op(e2, e2) = e2 % 136.14/20.24 | | | % 136.14/20.24 | | | ALPHA: (22) implies: % 136.14/20.24 | | | (23) all_57_3 = e2 % 136.14/20.24 | | | % 136.14/20.24 | | | REF_CLOSE: (1), (2), (23) are inconsistent by sub-proof #679. % 136.14/20.24 | | | % 136.14/20.24 | | End of split % 136.14/20.24 | | % 136.14/20.24 | Case 2: % 136.14/20.24 | | % 136.14/20.24 | | (24) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = % 136.14/20.24 | | e2) % 136.14/20.24 | | % 136.14/20.24 | | BETA: splitting (24) gives: % 136.14/20.24 | | % 136.14/20.24 | | Case 1: % 136.14/20.24 | | | % 136.14/20.24 | | | (25) all_57_7 = e2 & op(e1, e2) = e2 % 136.14/20.24 | | | % 136.14/20.24 | | | ALPHA: (25) implies: % 136.14/20.24 | | | (26) all_57_7 = e2 % 136.14/20.24 | | | % 136.14/20.24 | | | REF_CLOSE: (4), (8), (26) are inconsistent by sub-proof #486. % 136.14/20.24 | | | % 136.14/20.24 | | Case 2: % 136.14/20.24 | | | % 136.14/20.24 | | | (27) all_57_13 = e2 & op(e0, e2) = e2 % 136.14/20.24 | | | % 136.14/20.24 | | | ALPHA: (27) implies: % 136.14/20.24 | | | (28) all_57_13 = e2 % 136.14/20.24 | | | % 136.14/20.24 | | | REF_CLOSE: (4), (11), (28) are inconsistent by sub-proof #408. % 136.14/20.24 | | | % 136.14/20.24 | | End of split % 136.14/20.24 | | % 136.14/20.24 | End of split % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #389 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) all_57_13 = e1 & op(e0, e2) = e1 % 136.14/20.24 (2) all_57_13 = e3 % 136.14/20.24 (3) ~ (e3 = e1) % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | ALPHA: (1) implies: % 136.14/20.24 | (4) all_57_13 = e1 % 136.14/20.24 | % 136.14/20.24 | COMBINE_EQS: (2), (4) imply: % 136.14/20.24 | (5) e3 = e1 % 136.14/20.24 | % 136.14/20.24 | SIMP: (5) implies: % 136.14/20.24 | (6) e3 = e1 % 136.14/20.24 | % 136.14/20.24 | REDUCE: (3), (6) imply: % 136.14/20.24 | (7) $false % 136.14/20.24 | % 136.14/20.24 | CLOSE: (7) is inconsistent. % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #390 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) all_57_7 = e3 % 136.14/20.24 (2) all_57_7 = e1 % 136.14/20.24 (3) ~ (e3 = e1) % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | COMBINE_EQS: (1), (2) imply: % 136.14/20.24 | (4) e3 = e1 % 136.14/20.24 | % 136.14/20.24 | SIMP: (4) implies: % 136.14/20.24 | (5) e3 = e1 % 136.14/20.24 | % 136.14/20.24 | REDUCE: (3), (5) imply: % 136.14/20.24 | (6) $false % 136.14/20.24 | % 136.14/20.24 | CLOSE: (6) is inconsistent. % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #391 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) op(e3, e3) = e2 % 136.14/20.24 (2) ~ (e2 = e0) % 136.14/20.24 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 136.14/20.24 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 136.14/20.24 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.24 (5) ~ (e2 = e1) % 136.14/20.24 (6) ~ (e3 = e0) % 136.14/20.24 (7) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.14/20.24 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.14/20.24 (8) all_57_12 = e3 & op(e0, e3) = e3 % 136.14/20.24 (9) ~ (e3 = e1) % 136.14/20.24 (10) ~ (e1 = e0) % 136.14/20.24 (11) all_57_6 = e2 % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | ALPHA: (8) implies: % 136.14/20.24 | (12) all_57_12 = e3 % 136.14/20.24 | % 136.14/20.24 | BETA: splitting (3) gives: % 136.14/20.24 | % 136.14/20.24 | Case 1: % 136.14/20.24 | | % 136.14/20.24 | | (13) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = % 136.14/20.24 | | e1) % 136.14/20.24 | | % 136.14/20.24 | | BETA: splitting (13) gives: % 136.14/20.24 | | % 136.14/20.24 | | Case 1: % 136.14/20.24 | | | % 136.14/20.24 | | | (14) all_57_0 = e1 & op(e3, e3) = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | ALPHA: (14) implies: % 136.14/20.24 | | | (15) op(e3, e3) = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | REF_CLOSE: (1), (4), (5), (15) are inconsistent by sub-proof #743. % 136.14/20.24 | | | % 136.14/20.24 | | Case 2: % 136.14/20.24 | | | % 136.14/20.24 | | | (16) all_57_2 = e1 & op(e2, e3) = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | ALPHA: (16) implies: % 136.14/20.24 | | | (17) all_57_2 = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | REF_CLOSE: (1), (2), (4), (6), (7), (10), (11), (12), (17) are % 136.14/20.24 | | | inconsistent by sub-proof #392. % 136.14/20.24 | | | % 136.14/20.24 | | End of split % 136.14/20.24 | | % 136.14/20.24 | Case 2: % 136.14/20.24 | | % 136.14/20.24 | | (18) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = % 136.14/20.24 | | e1) % 136.14/20.24 | | % 136.14/20.24 | | BETA: splitting (18) gives: % 136.14/20.24 | | % 136.14/20.24 | | Case 1: % 136.14/20.24 | | | % 136.14/20.24 | | | (19) all_57_6 = e1 & op(e1, e3) = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | ALPHA: (19) implies: % 136.14/20.24 | | | (20) all_57_6 = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | COMBINE_EQS: (11), (20) imply: % 136.14/20.24 | | | (21) e2 = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | SIMP: (21) implies: % 136.14/20.24 | | | (22) e2 = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | REDUCE: (5), (22) imply: % 136.14/20.24 | | | (23) $false % 136.14/20.24 | | | % 136.14/20.24 | | | CLOSE: (23) is inconsistent. % 136.14/20.24 | | | % 136.14/20.24 | | Case 2: % 136.14/20.24 | | | % 136.14/20.24 | | | (24) all_57_12 = e1 & op(e0, e3) = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | ALPHA: (24) implies: % 136.14/20.24 | | | (25) all_57_12 = e1 % 136.14/20.24 | | | % 136.14/20.24 | | | REF_CLOSE: (9), (12), (25) are inconsistent by sub-proof #591. % 136.14/20.24 | | | % 136.14/20.24 | | End of split % 136.14/20.24 | | % 136.14/20.24 | End of split % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #392 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) all_57_2 = e1 % 136.14/20.24 (2) op(e3, e3) = e2 % 136.14/20.24 (3) ~ (e2 = e0) % 136.14/20.24 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.24 (5) ~ (e3 = e0) % 136.14/20.24 (6) all_57_12 = e3 % 136.14/20.24 (7) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.14/20.24 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.14/20.24 (8) ~ (e1 = e0) % 136.14/20.24 (9) all_57_6 = e2 % 136.14/20.24 % 136.14/20.24 Begin of proof % 136.14/20.24 | % 136.14/20.24 | BETA: splitting (7) gives: % 136.14/20.24 | % 136.14/20.24 | Case 1: % 136.14/20.24 | | % 136.14/20.24 | | (10) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = % 136.14/20.24 | | e0) % 136.14/20.24 | | % 136.14/20.24 | | BETA: splitting (10) gives: % 136.14/20.24 | | % 136.14/20.24 | | Case 1: % 136.14/20.24 | | | % 136.14/20.24 | | | (11) all_57_0 = e0 & op(e3, e3) = e0 % 136.14/20.24 | | | % 136.14/20.24 | | | ALPHA: (11) implies: % 136.14/20.24 | | | (12) op(e3, e3) = e0 % 136.14/20.24 | | | % 136.14/20.24 | | | REF_CLOSE: (2), (3), (4), (12) are inconsistent by sub-proof #495. % 136.14/20.24 | | | % 136.14/20.24 | | Case 2: % 136.14/20.24 | | | % 136.14/20.24 | | | (13) all_57_2 = e0 & op(e2, e3) = e0 % 136.14/20.24 | | | % 136.14/20.24 | | | ALPHA: (13) implies: % 136.14/20.24 | | | (14) all_57_2 = e0 % 136.14/20.24 | | | % 136.14/20.24 | | | REF_CLOSE: (1), (8), (14) are inconsistent by sub-proof #646. % 136.14/20.24 | | | % 136.14/20.24 | | End of split % 136.14/20.24 | | % 136.14/20.24 | Case 2: % 136.14/20.24 | | % 136.14/20.24 | | (15) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = % 136.14/20.24 | | e0) % 136.14/20.24 | | % 136.14/20.24 | | BETA: splitting (15) gives: % 136.14/20.24 | | % 136.14/20.24 | | Case 1: % 136.14/20.24 | | | % 136.14/20.24 | | | (16) all_57_6 = e0 & op(e1, e3) = e0 % 136.14/20.24 | | | % 136.14/20.24 | | | ALPHA: (16) implies: % 136.14/20.24 | | | (17) all_57_6 = e0 % 136.14/20.24 | | | % 136.14/20.24 | | | REF_CLOSE: (3), (9), (17) are inconsistent by sub-proof #586. % 136.14/20.24 | | | % 136.14/20.24 | | Case 2: % 136.14/20.24 | | | % 136.14/20.24 | | | (18) all_57_12 = e0 & op(e0, e3) = e0 % 136.14/20.24 | | | % 136.14/20.24 | | | REF_CLOSE: (5), (6), (18) are inconsistent by sub-proof #436. % 136.14/20.24 | | | % 136.14/20.24 | | End of split % 136.14/20.24 | | % 136.14/20.24 | End of split % 136.14/20.24 | % 136.14/20.24 End of proof % 136.14/20.24 % 136.14/20.24 Sub-proof #393 shows that the following formulas are inconsistent: % 136.14/20.24 ---------------------------------------------------------------- % 136.14/20.24 (1) op(e3, e3) = e2 % 136.14/20.24 (2) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 136.14/20.24 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 136.14/20.24 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.24 (4) ~ (e2 = e1) % 136.14/20.25 (5) ~ (e3 = e2) % 136.14/20.25 (6) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.14/20.25 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.14/20.25 (7) all_57_2 = e2 % 136.14/20.25 (8) ~ (e3 = e1) % 136.14/20.25 (9) all_57_6 = e2 % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | BETA: splitting (2) gives: % 136.14/20.25 | % 136.14/20.25 | Case 1: % 136.14/20.25 | | % 136.14/20.25 | | (10) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = % 136.14/20.25 | | e1) % 136.14/20.25 | | % 136.14/20.25 | | REF_CLOSE: (1), (3), (4), (7), (10) are inconsistent by sub-proof #496. % 136.14/20.25 | | % 136.14/20.25 | Case 2: % 136.14/20.25 | | % 136.14/20.25 | | (11) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = % 136.14/20.25 | | e1) % 136.14/20.25 | | % 136.14/20.25 | | BETA: splitting (11) gives: % 136.14/20.25 | | % 136.14/20.25 | | Case 1: % 136.14/20.25 | | | % 136.14/20.25 | | | (12) all_57_6 = e1 & op(e1, e3) = e1 % 136.14/20.25 | | | % 136.14/20.25 | | | ALPHA: (12) implies: % 136.14/20.25 | | | (13) all_57_6 = e1 % 136.14/20.25 | | | % 136.14/20.25 | | | COMBINE_EQS: (9), (13) imply: % 136.14/20.25 | | | (14) e2 = e1 % 136.14/20.25 | | | % 136.14/20.25 | | | REDUCE: (4), (14) imply: % 136.14/20.25 | | | (15) $false % 136.14/20.25 | | | % 136.14/20.25 | | | CLOSE: (15) is inconsistent. % 136.14/20.25 | | | % 136.14/20.25 | | Case 2: % 136.14/20.25 | | | % 136.14/20.25 | | | (16) all_57_12 = e1 & op(e0, e3) = e1 % 136.14/20.25 | | | % 136.14/20.25 | | | ALPHA: (16) implies: % 136.14/20.25 | | | (17) all_57_12 = e1 % 136.14/20.25 | | | % 136.14/20.25 | | | BETA: splitting (6) gives: % 136.14/20.25 | | | % 136.14/20.25 | | | Case 1: % 136.14/20.25 | | | | % 136.14/20.25 | | | | (18) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) % 136.14/20.25 | | | | = e3) % 136.14/20.25 | | | | % 136.14/20.25 | | | | BETA: splitting (18) gives: % 136.14/20.25 | | | | % 136.14/20.25 | | | | Case 1: % 136.14/20.25 | | | | | % 136.14/20.25 | | | | | (19) all_57_0 = e3 & op(e3, e3) = e3 % 136.14/20.25 | | | | | % 136.14/20.25 | | | | | ALPHA: (19) implies: % 136.14/20.25 | | | | | (20) op(e3, e3) = e3 % 136.14/20.25 | | | | | % 136.14/20.25 | | | | | REF_CLOSE: (1), (3), (5), (20) are inconsistent by sub-proof #778. % 136.14/20.25 | | | | | % 136.14/20.25 | | | | Case 2: % 136.14/20.25 | | | | | % 136.14/20.25 | | | | | (21) all_57_2 = e3 & op(e2, e3) = e3 % 136.14/20.25 | | | | | % 136.14/20.25 | | | | | REF_CLOSE: (5), (7), (21) are inconsistent by sub-proof #590. % 136.14/20.25 | | | | | % 136.14/20.25 | | | | End of split % 136.14/20.25 | | | | % 136.14/20.25 | | | Case 2: % 136.14/20.25 | | | | % 136.14/20.25 | | | | (22) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) % 136.14/20.25 | | | | = e3) % 136.14/20.25 | | | | % 136.14/20.25 | | | | BETA: splitting (22) gives: % 136.14/20.25 | | | | % 136.14/20.25 | | | | Case 1: % 136.14/20.25 | | | | | % 136.14/20.25 | | | | | (23) all_57_6 = e3 & op(e1, e3) = e3 % 136.14/20.25 | | | | | % 136.14/20.25 | | | | | ALPHA: (23) implies: % 136.14/20.25 | | | | | (24) all_57_6 = e3 % 136.14/20.25 | | | | | % 136.14/20.25 | | | | | REF_CLOSE: (5), (9), (24) are inconsistent by sub-proof #592. % 136.14/20.25 | | | | | % 136.14/20.25 | | | | Case 2: % 136.14/20.25 | | | | | % 136.14/20.25 | | | | | (25) all_57_12 = e3 & op(e0, e3) = e3 % 136.14/20.25 | | | | | % 136.14/20.25 | | | | | REF_CLOSE: (8), (17), (25) are inconsistent by sub-proof #394. % 136.14/20.25 | | | | | % 136.14/20.25 | | | | End of split % 136.14/20.25 | | | | % 136.14/20.25 | | | End of split % 136.14/20.25 | | | % 136.14/20.25 | | End of split % 136.14/20.25 | | % 136.14/20.25 | End of split % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #394 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) all_57_12 = e3 & op(e0, e3) = e3 % 136.14/20.25 (2) all_57_12 = e1 % 136.14/20.25 (3) ~ (e3 = e1) % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | ALPHA: (1) implies: % 136.14/20.25 | (4) all_57_12 = e3 % 136.14/20.25 | % 136.14/20.25 | COMBINE_EQS: (2), (4) imply: % 136.14/20.25 | (5) e3 = e1 % 136.14/20.25 | % 136.14/20.25 | REDUCE: (3), (5) imply: % 136.14/20.25 | (6) $false % 136.14/20.25 | % 136.14/20.25 | CLOSE: (6) is inconsistent. % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #395 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) ~ (all_52_4 = e0) % 136.14/20.25 (2) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.25 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 136.14/20.25 (3) ~ (e2 = e0) % 136.14/20.25 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.25 (5) op(e0, e2) = all_52_7 % 136.14/20.25 (6) ~ (all_52_6 = e0) % 136.14/20.25 (7) op(e1, e2) = all_52_6 % 136.14/20.25 (8) ~ (all_52_7 = e0) % 136.14/20.25 (9) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) % 136.14/20.25 (10) ~ (all_52_4 = e2) % 136.14/20.25 (11) op(e3, e2) = all_52_4 % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | BETA: splitting (9) gives: % 136.14/20.25 | % 136.14/20.25 | Case 1: % 136.14/20.25 | | % 136.14/20.25 | | (12) all_57_1 = e2 & op(e3, e2) = e2 % 136.14/20.25 | | % 136.14/20.25 | | REF_CLOSE: (4), (10), (11), (12) are inconsistent by sub-proof #396. % 136.14/20.25 | | % 136.14/20.25 | Case 2: % 136.14/20.25 | | % 136.14/20.25 | | (13) all_57_3 = e2 & op(e2, e2) = e2 % 136.14/20.25 | | % 136.14/20.25 | | ALPHA: (13) implies: % 136.14/20.25 | | (14) all_57_3 = e2 % 136.14/20.25 | | % 136.14/20.25 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (14) are % 136.14/20.25 | | inconsistent by sub-proof #503. % 136.14/20.25 | | % 136.14/20.25 | End of split % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #396 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) all_57_1 = e2 & op(e3, e2) = e2 % 136.14/20.25 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.25 (3) op(e3, e2) = all_52_4 % 136.14/20.25 (4) ~ (all_52_4 = e2) % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | ALPHA: (1) implies: % 136.14/20.25 | (5) op(e3, e2) = e2 % 136.14/20.25 | % 136.14/20.25 | GROUND_INST: instantiating (2) with all_52_4, e2, e2, e3, simplifying with % 136.14/20.25 | (3), (5) gives: % 136.14/20.25 | (6) all_52_4 = e2 % 136.14/20.25 | % 136.14/20.25 | REDUCE: (4), (6) imply: % 136.14/20.25 | (7) $false % 136.14/20.25 | % 136.14/20.25 | CLOSE: (7) is inconsistent. % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #397 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) all_57_14 = e2 & op(e0, e1) = e2 % 136.14/20.25 (2) all_57_14 = e3 % 136.14/20.25 (3) ~ (e3 = e2) % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | ALPHA: (1) implies: % 136.14/20.25 | (4) all_57_14 = e2 % 136.14/20.25 | % 136.14/20.25 | COMBINE_EQS: (2), (4) imply: % 136.14/20.25 | (5) e3 = e2 % 136.14/20.25 | % 136.14/20.25 | REDUCE: (3), (5) imply: % 136.14/20.25 | (6) $false % 136.14/20.25 | % 136.14/20.25 | CLOSE: (6) is inconsistent. % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #398 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) ~ (e2 = e0) % 136.14/20.25 (2) ~ (e3 = e0) % 136.14/20.25 (3) all_57_15 = e2 % 136.14/20.25 (4) all_57_13 = e2 % 136.14/20.25 (5) all_57_14 = e3 % 136.14/20.25 (6) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.25 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = % 136.14/20.25 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.25 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.25 (7) ~ (e1 = e0) % 136.14/20.25 (8) all_57_12 = e1 % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | BETA: splitting (6) gives: % 136.14/20.25 | % 136.14/20.25 | Case 1: % 136.14/20.25 | | % 136.14/20.25 | | (9) all_57_15 = e0 & op(e0, e0) = e0 % 136.14/20.25 | | % 136.14/20.25 | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #437. % 136.14/20.25 | | % 136.14/20.25 | Case 2: % 136.14/20.25 | | % 136.14/20.25 | | (10) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = % 136.14/20.25 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 & % 136.14/20.25 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) | % 136.14/20.25 | | (all_57_14 = e0 & op(e0, e1) = e0)) % 136.14/20.25 | | % 136.14/20.25 | | ALPHA: (10) implies: % 136.14/20.25 | | (11) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 136.14/20.25 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 136.14/20.25 | | % 136.14/20.25 | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (11) are inconsistent by sub-proof % 136.14/20.25 | | #399. % 136.14/20.25 | | % 136.14/20.25 | End of split % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #399 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) ~ (e2 = e0) % 136.14/20.25 (2) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) | % 136.14/20.25 (all_57_14 = e0 & op(e0, e1) = e0) % 136.14/20.25 (3) ~ (e3 = e0) % 136.14/20.25 (4) all_57_13 = e2 % 136.14/20.25 (5) all_57_14 = e3 % 136.14/20.25 (6) ~ (e1 = e0) % 136.14/20.25 (7) all_57_12 = e1 % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | BETA: splitting (2) gives: % 136.14/20.25 | % 136.14/20.25 | Case 1: % 136.14/20.25 | | % 136.14/20.25 | | (8) all_57_12 = e0 & op(e0, e3) = e0 % 136.14/20.25 | | % 136.14/20.25 | | ALPHA: (8) implies: % 136.14/20.25 | | (9) all_57_12 = e0 % 136.14/20.25 | | % 136.14/20.25 | | REF_CLOSE: (6), (7), (9) are inconsistent by sub-proof #581. % 136.14/20.25 | | % 136.14/20.25 | Case 2: % 136.14/20.25 | | % 136.14/20.25 | | (10) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = % 136.14/20.25 | | e0) % 136.14/20.25 | | % 136.14/20.25 | | BETA: splitting (10) gives: % 136.14/20.25 | | % 136.14/20.25 | | Case 1: % 136.14/20.25 | | | % 136.14/20.25 | | | (11) all_57_13 = e0 & op(e0, e2) = e0 % 136.14/20.25 | | | % 136.14/20.25 | | | REF_CLOSE: (1), (4), (11) are inconsistent by sub-proof #411. % 136.14/20.25 | | | % 136.14/20.25 | | Case 2: % 136.14/20.25 | | | % 136.14/20.25 | | | (12) all_57_14 = e0 & op(e0, e1) = e0 % 136.14/20.25 | | | % 136.14/20.25 | | | ALPHA: (12) implies: % 136.14/20.25 | | | (13) all_57_14 = e0 % 136.14/20.25 | | | % 136.14/20.25 | | | REF_CLOSE: (3), (5), (13) are inconsistent by sub-proof #400. % 136.14/20.25 | | | % 136.14/20.25 | | End of split % 136.14/20.25 | | % 136.14/20.25 | End of split % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #400 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) all_57_14 = e3 % 136.14/20.25 (2) all_57_14 = e0 % 136.14/20.25 (3) ~ (e3 = e0) % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | COMBINE_EQS: (1), (2) imply: % 136.14/20.25 | (4) e3 = e0 % 136.14/20.25 | % 136.14/20.25 | SIMP: (4) implies: % 136.14/20.25 | (5) e3 = e0 % 136.14/20.25 | % 136.14/20.25 | REDUCE: (3), (5) imply: % 136.14/20.25 | (6) $false % 136.14/20.25 | % 136.14/20.25 | CLOSE: (6) is inconsistent. % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #401 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) ~ (e2 = e0) % 136.14/20.25 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 136.14/20.25 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.25 (3) ~ (e2 = e1) % 136.14/20.25 (4) ~ (e3 = e0) % 136.14/20.25 (5) ~ (e3 = e2) % 136.14/20.25 (6) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) | % 136.14/20.25 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.25 (7) all_57_13 = e2 % 136.14/20.25 (8) all_57_14 = e2 % 136.14/20.25 (9) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.25 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = % 136.14/20.25 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.25 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.25 (10) ~ (e3 = e1) % 136.14/20.25 (11) ~ (e1 = e0) % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | BETA: splitting (2) gives: % 136.14/20.25 | % 136.14/20.25 | Case 1: % 136.14/20.25 | | % 136.14/20.25 | | (12) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = % 136.14/20.25 | | e3) % 136.14/20.25 | | % 136.14/20.25 | | BETA: splitting (12) gives: % 136.14/20.25 | | % 136.14/20.25 | | Case 1: % 136.14/20.25 | | | % 136.14/20.25 | | | (13) all_57_12 = e3 & op(e0, e3) = e3 % 136.14/20.25 | | | % 136.14/20.25 | | | ALPHA: (13) implies: % 136.14/20.25 | | | (14) all_57_12 = e3 % 136.14/20.25 | | | % 136.14/20.25 | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (14) are % 136.14/20.25 | | | inconsistent by sub-proof #409. % 136.14/20.25 | | | % 136.14/20.25 | | Case 2: % 136.14/20.25 | | | % 136.14/20.25 | | | (15) all_57_13 = e3 & op(e0, e2) = e3 % 136.14/20.25 | | | % 136.14/20.25 | | | ALPHA: (15) implies: % 136.14/20.25 | | | (16) all_57_13 = e3 % 136.14/20.25 | | | % 136.14/20.25 | | | REF_CLOSE: (5), (7), (16) are inconsistent by sub-proof #408. % 136.14/20.25 | | | % 136.14/20.25 | | End of split % 136.14/20.25 | | % 136.14/20.25 | Case 2: % 136.14/20.25 | | % 136.14/20.25 | | (17) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = % 136.14/20.25 | | e3) % 136.14/20.25 | | % 136.14/20.25 | | BETA: splitting (17) gives: % 136.14/20.25 | | % 136.14/20.25 | | Case 1: % 136.14/20.25 | | | % 136.14/20.25 | | | (18) all_57_14 = e3 & op(e0, e1) = e3 % 136.14/20.25 | | | % 136.14/20.25 | | | ALPHA: (18) implies: % 136.14/20.25 | | | (19) all_57_14 = e3 % 136.14/20.25 | | | % 136.14/20.25 | | | REF_CLOSE: (5), (8), (19) are inconsistent by sub-proof #407. % 136.14/20.25 | | | % 136.14/20.25 | | Case 2: % 136.14/20.25 | | | % 136.14/20.25 | | | (20) all_57_15 = e3 & op(e0, e0) = e3 % 136.14/20.25 | | | % 136.14/20.25 | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (20) are % 136.14/20.25 | | | inconsistent by sub-proof #402. % 136.14/20.25 | | | % 136.14/20.25 | | End of split % 136.14/20.25 | | % 136.14/20.25 | End of split % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #402 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) ~ (e2 = e0) % 136.14/20.25 (2) ~ (e2 = e1) % 136.14/20.25 (3) ~ (e3 = e0) % 136.14/20.25 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) | % 136.14/20.25 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.25 (5) all_57_13 = e2 % 136.14/20.25 (6) all_57_14 = e2 % 136.14/20.25 (7) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.25 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = % 136.14/20.25 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.25 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.25 (8) ~ (e3 = e1) % 136.14/20.25 (9) ~ (e1 = e0) % 136.14/20.25 (10) all_57_15 = e3 & op(e0, e0) = e3 % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | ALPHA: (10) implies: % 136.14/20.25 | (11) all_57_15 = e3 % 136.14/20.25 | % 136.14/20.25 | BETA: splitting (7) gives: % 136.14/20.25 | % 136.14/20.25 | Case 1: % 136.14/20.25 | | % 136.14/20.25 | | (12) all_57_15 = e0 & op(e0, e0) = e0 % 136.14/20.25 | | % 136.14/20.25 | | REF_CLOSE: (3), (11), (12) are inconsistent by sub-proof #406. % 136.14/20.25 | | % 136.14/20.25 | Case 2: % 136.14/20.25 | | % 136.14/20.25 | | (13) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = % 136.14/20.25 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 & % 136.14/20.25 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) | % 136.14/20.25 | | (all_57_14 = e0 & op(e0, e1) = e0)) % 136.14/20.25 | | % 136.14/20.25 | | ALPHA: (13) implies: % 136.14/20.25 | | (14) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 136.14/20.25 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 136.14/20.25 | | % 136.14/20.25 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (11), (14) are inconsistent by % 136.14/20.25 | | sub-proof #403. % 136.14/20.25 | | % 136.14/20.25 | End of split % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #403 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) ~ (e2 = e0) % 136.14/20.25 (2) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) | % 136.14/20.25 (all_57_14 = e0 & op(e0, e1) = e0) % 136.14/20.25 (3) ~ (e2 = e1) % 136.14/20.25 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) | % 136.14/20.25 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.25 (5) all_57_15 = e3 % 136.14/20.25 (6) all_57_13 = e2 % 136.14/20.25 (7) all_57_14 = e2 % 136.14/20.25 (8) ~ (e3 = e1) % 136.14/20.25 (9) ~ (e1 = e0) % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | BETA: splitting (2) gives: % 136.14/20.25 | % 136.14/20.25 | Case 1: % 136.14/20.25 | | % 136.14/20.25 | | (10) all_57_12 = e0 & op(e0, e3) = e0 % 136.14/20.25 | | % 136.14/20.25 | | ALPHA: (10) implies: % 136.14/20.25 | | (11) all_57_12 = e0 % 136.14/20.25 | | % 136.14/20.25 | | BETA: splitting (4) gives: % 136.14/20.25 | | % 136.14/20.25 | | Case 1: % 136.14/20.25 | | | % 136.14/20.25 | | | (12) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) % 136.14/20.25 | | | = e1) % 136.14/20.25 | | | % 136.14/20.25 | | | BETA: splitting (12) gives: % 136.14/20.25 | | | % 136.14/20.25 | | | Case 1: % 136.14/20.25 | | | | % 136.14/20.25 | | | | (13) all_57_12 = e1 & op(e0, e3) = e1 % 136.14/20.25 | | | | % 136.14/20.25 | | | | REF_CLOSE: (9), (11), (13) are inconsistent by sub-proof #405. % 136.14/20.25 | | | | % 136.14/20.25 | | | Case 2: % 136.14/20.25 | | | | % 136.14/20.25 | | | | (14) all_57_13 = e1 & op(e0, e2) = e1 % 136.14/20.25 | | | | % 136.14/20.25 | | | | ALPHA: (14) implies: % 136.14/20.25 | | | | (15) all_57_13 = e1 % 136.14/20.25 | | | | % 136.14/20.25 | | | | REF_CLOSE: (3), (6), (15) are inconsistent by sub-proof #567. % 136.14/20.25 | | | | % 136.14/20.25 | | | End of split % 136.14/20.25 | | | % 136.14/20.25 | | Case 2: % 136.14/20.25 | | | % 136.14/20.25 | | | (16) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) % 136.14/20.25 | | | = e1) % 136.14/20.25 | | | % 136.14/20.25 | | | BETA: splitting (16) gives: % 136.14/20.25 | | | % 136.14/20.25 | | | Case 1: % 136.14/20.25 | | | | % 136.14/20.25 | | | | (17) all_57_14 = e1 & op(e0, e1) = e1 % 136.14/20.25 | | | | % 136.14/20.25 | | | | ALPHA: (17) implies: % 136.14/20.25 | | | | (18) all_57_14 = e1 % 136.14/20.25 | | | | % 136.14/20.25 | | | | REF_CLOSE: (3), (7), (18) are inconsistent by sub-proof #560. % 136.14/20.25 | | | | % 136.14/20.25 | | | Case 2: % 136.14/20.25 | | | | % 136.14/20.25 | | | | (19) all_57_15 = e1 & op(e0, e0) = e1 % 136.14/20.25 | | | | % 136.14/20.25 | | | | ALPHA: (19) implies: % 136.14/20.25 | | | | (20) all_57_15 = e1 % 136.14/20.25 | | | | % 136.14/20.25 | | | | COMBINE_EQS: (5), (20) imply: % 136.14/20.25 | | | | (21) e3 = e1 % 136.14/20.25 | | | | % 136.14/20.25 | | | | REDUCE: (8), (21) imply: % 136.14/20.25 | | | | (22) $false % 136.14/20.25 | | | | % 136.14/20.25 | | | | CLOSE: (22) is inconsistent. % 136.14/20.25 | | | | % 136.14/20.25 | | | End of split % 136.14/20.25 | | | % 136.14/20.25 | | End of split % 136.14/20.25 | | % 136.14/20.25 | Case 2: % 136.14/20.25 | | % 136.14/20.25 | | (23) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = % 136.14/20.25 | | e0) % 136.14/20.25 | | % 136.14/20.25 | | BETA: splitting (23) gives: % 136.14/20.25 | | % 136.14/20.25 | | Case 1: % 136.14/20.25 | | | % 136.14/20.25 | | | (24) all_57_13 = e0 & op(e0, e2) = e0 % 136.14/20.25 | | | % 136.14/20.25 | | | ALPHA: (24) implies: % 136.14/20.25 | | | (25) all_57_13 = e0 % 136.14/20.25 | | | % 136.14/20.25 | | | REF_CLOSE: (1), (6), (25) are inconsistent by sub-proof #404. % 136.14/20.25 | | | % 136.14/20.25 | | Case 2: % 136.14/20.25 | | | % 136.14/20.25 | | | (26) all_57_14 = e0 & op(e0, e1) = e0 % 136.14/20.25 | | | % 136.14/20.25 | | | REF_CLOSE: (1), (7), (26) are inconsistent by sub-proof #580. % 136.14/20.25 | | | % 136.14/20.25 | | End of split % 136.14/20.25 | | % 136.14/20.25 | End of split % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #404 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) all_57_13 = e2 % 136.14/20.25 (2) all_57_13 = e0 % 136.14/20.25 (3) ~ (e2 = e0) % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | COMBINE_EQS: (1), (2) imply: % 136.14/20.25 | (4) e2 = e0 % 136.14/20.25 | % 136.14/20.25 | SIMP: (4) implies: % 136.14/20.25 | (5) e2 = e0 % 136.14/20.25 | % 136.14/20.25 | REDUCE: (3), (5) imply: % 136.14/20.25 | (6) $false % 136.14/20.25 | % 136.14/20.25 | CLOSE: (6) is inconsistent. % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #405 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) all_57_12 = e1 & op(e0, e3) = e1 % 136.14/20.25 (2) all_57_12 = e0 % 136.14/20.25 (3) ~ (e1 = e0) % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | ALPHA: (1) implies: % 136.14/20.25 | (4) all_57_12 = e1 % 136.14/20.25 | % 136.14/20.25 | COMBINE_EQS: (2), (4) imply: % 136.14/20.25 | (5) e1 = e0 % 136.14/20.25 | % 136.14/20.25 | REDUCE: (3), (5) imply: % 136.14/20.25 | (6) $false % 136.14/20.25 | % 136.14/20.25 | CLOSE: (6) is inconsistent. % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #406 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) all_57_15 = e0 & op(e0, e0) = e0 % 136.14/20.25 (2) all_57_15 = e3 % 136.14/20.25 (3) ~ (e3 = e0) % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | ALPHA: (1) implies: % 136.14/20.25 | (4) all_57_15 = e0 % 136.14/20.25 | % 136.14/20.25 | COMBINE_EQS: (2), (4) imply: % 136.14/20.25 | (5) e3 = e0 % 136.14/20.25 | % 136.14/20.25 | SIMP: (5) implies: % 136.14/20.25 | (6) e3 = e0 % 136.14/20.25 | % 136.14/20.25 | REDUCE: (3), (6) imply: % 136.14/20.25 | (7) $false % 136.14/20.25 | % 136.14/20.25 | CLOSE: (7) is inconsistent. % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #407 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) all_57_14 = e3 % 136.14/20.25 (2) all_57_14 = e2 % 136.14/20.25 (3) ~ (e3 = e2) % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | COMBINE_EQS: (1), (2) imply: % 136.14/20.25 | (4) e3 = e2 % 136.14/20.25 | % 136.14/20.25 | SIMP: (4) implies: % 136.14/20.25 | (5) e3 = e2 % 136.14/20.25 | % 136.14/20.25 | REDUCE: (3), (5) imply: % 136.14/20.25 | (6) $false % 136.14/20.25 | % 136.14/20.25 | CLOSE: (6) is inconsistent. % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #408 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) all_57_13 = e3 % 136.14/20.25 (2) all_57_13 = e2 % 136.14/20.25 (3) ~ (e3 = e2) % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | COMBINE_EQS: (1), (2) imply: % 136.14/20.25 | (4) e3 = e2 % 136.14/20.25 | % 136.14/20.25 | SIMP: (4) implies: % 136.14/20.25 | (5) e3 = e2 % 136.14/20.25 | % 136.14/20.25 | REDUCE: (3), (5) imply: % 136.14/20.25 | (6) $false % 136.14/20.25 | % 136.14/20.25 | CLOSE: (6) is inconsistent. % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #409 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) ~ (e2 = e0) % 136.14/20.25 (2) ~ (e2 = e1) % 136.14/20.25 (3) ~ (e3 = e0) % 136.14/20.25 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) | % 136.14/20.25 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.25 (5) all_57_13 = e2 % 136.14/20.25 (6) all_57_12 = e3 % 136.14/20.25 (7) all_57_14 = e2 % 136.14/20.25 (8) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.25 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = % 136.14/20.25 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.25 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.25 (9) ~ (e3 = e1) % 136.14/20.25 (10) ~ (e1 = e0) % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | BETA: splitting (4) gives: % 136.14/20.25 | % 136.14/20.25 | Case 1: % 136.14/20.25 | | % 136.14/20.25 | | (11) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = % 136.14/20.25 | | e1) % 136.14/20.25 | | % 136.14/20.25 | | BETA: splitting (11) gives: % 136.14/20.25 | | % 136.14/20.25 | | Case 1: % 136.14/20.25 | | | % 136.14/20.25 | | | (12) all_57_12 = e1 & op(e0, e3) = e1 % 136.14/20.25 | | | % 136.14/20.25 | | | REF_CLOSE: (6), (9), (12) are inconsistent by sub-proof #490. % 136.14/20.25 | | | % 136.14/20.25 | | Case 2: % 136.14/20.25 | | | % 136.14/20.25 | | | (13) all_57_13 = e1 & op(e0, e2) = e1 % 136.14/20.25 | | | % 136.14/20.25 | | | ALPHA: (13) implies: % 136.14/20.25 | | | (14) all_57_13 = e1 % 136.14/20.25 | | | % 136.14/20.25 | | | REF_CLOSE: (2), (5), (14) are inconsistent by sub-proof #567. % 136.14/20.25 | | | % 136.14/20.25 | | End of split % 136.14/20.25 | | % 136.14/20.25 | Case 2: % 136.14/20.25 | | % 136.14/20.25 | | (15) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 136.14/20.25 | | e1) % 136.14/20.25 | | % 136.14/20.25 | | BETA: splitting (15) gives: % 136.14/20.25 | | % 136.14/20.25 | | Case 1: % 136.14/20.25 | | | % 136.14/20.25 | | | (16) all_57_14 = e1 & op(e0, e1) = e1 % 136.14/20.25 | | | % 136.14/20.25 | | | ALPHA: (16) implies: % 136.14/20.25 | | | (17) all_57_14 = e1 % 136.14/20.25 | | | % 136.14/20.25 | | | REF_CLOSE: (2), (7), (17) are inconsistent by sub-proof #560. % 136.14/20.25 | | | % 136.14/20.25 | | Case 2: % 136.14/20.25 | | | % 136.14/20.25 | | | (18) all_57_15 = e1 & op(e0, e0) = e1 % 136.14/20.25 | | | % 136.14/20.25 | | | ALPHA: (18) implies: % 136.14/20.25 | | | (19) all_57_15 = e1 % 136.14/20.25 | | | % 136.14/20.25 | | | BETA: splitting (8) gives: % 136.14/20.25 | | | % 136.14/20.25 | | | Case 1: % 136.14/20.25 | | | | % 136.14/20.25 | | | | (20) all_57_15 = e0 & op(e0, e0) = e0 % 136.14/20.25 | | | | % 136.14/20.25 | | | | REF_CLOSE: (10), (19), (20) are inconsistent by sub-proof #412. % 136.14/20.25 | | | | % 136.14/20.25 | | | Case 2: % 136.14/20.25 | | | | % 136.14/20.25 | | | | (21) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, % 136.14/20.25 | | | | e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & % 136.14/20.25 | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, % 136.14/20.25 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 136.14/20.25 | | | | % 136.14/20.25 | | | | ALPHA: (21) implies: % 136.14/20.25 | | | | (22) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, % 136.14/20.25 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 136.14/20.25 | | | | % 136.14/20.25 | | | | REF_CLOSE: (1), (3), (5), (6), (7), (22) are inconsistent by sub-proof % 136.14/20.25 | | | | #410. % 136.14/20.25 | | | | % 136.14/20.25 | | | End of split % 136.14/20.25 | | | % 136.14/20.25 | | End of split % 136.14/20.25 | | % 136.14/20.25 | End of split % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #410 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) ~ (e2 = e0) % 136.14/20.25 (2) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) | % 136.14/20.25 (all_57_14 = e0 & op(e0, e1) = e0) % 136.14/20.25 (3) ~ (e3 = e0) % 136.14/20.25 (4) all_57_13 = e2 % 136.14/20.25 (5) all_57_12 = e3 % 136.14/20.25 (6) all_57_14 = e2 % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | BETA: splitting (2) gives: % 136.14/20.25 | % 136.14/20.25 | Case 1: % 136.14/20.25 | | % 136.14/20.25 | | (7) all_57_12 = e0 & op(e0, e3) = e0 % 136.14/20.25 | | % 136.14/20.25 | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #436. % 136.14/20.25 | | % 136.14/20.25 | Case 2: % 136.14/20.25 | | % 136.14/20.25 | | (8) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = % 136.14/20.25 | | e0) % 136.14/20.25 | | % 136.14/20.25 | | BETA: splitting (8) gives: % 136.14/20.25 | | % 136.14/20.25 | | Case 1: % 136.14/20.25 | | | % 136.14/20.25 | | | (9) all_57_13 = e0 & op(e0, e2) = e0 % 136.14/20.25 | | | % 136.14/20.25 | | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #411. % 136.14/20.25 | | | % 136.14/20.25 | | Case 2: % 136.14/20.25 | | | % 136.14/20.25 | | | (10) all_57_14 = e0 & op(e0, e1) = e0 % 136.14/20.25 | | | % 136.14/20.25 | | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #580. % 136.14/20.25 | | | % 136.14/20.25 | | End of split % 136.14/20.25 | | % 136.14/20.25 | End of split % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #411 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) all_57_13 = e0 & op(e0, e2) = e0 % 136.14/20.25 (2) all_57_13 = e2 % 136.14/20.25 (3) ~ (e2 = e0) % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | ALPHA: (1) implies: % 136.14/20.25 | (4) all_57_13 = e0 % 136.14/20.25 | % 136.14/20.25 | COMBINE_EQS: (2), (4) imply: % 136.14/20.25 | (5) e2 = e0 % 136.14/20.25 | % 136.14/20.25 | REDUCE: (3), (5) imply: % 136.14/20.25 | (6) $false % 136.14/20.25 | % 136.14/20.25 | CLOSE: (6) is inconsistent. % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #412 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) all_57_15 = e0 & op(e0, e0) = e0 % 136.14/20.25 (2) all_57_15 = e1 % 136.14/20.25 (3) ~ (e1 = e0) % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | ALPHA: (1) implies: % 136.14/20.25 | (4) all_57_15 = e0 % 136.14/20.25 | % 136.14/20.25 | COMBINE_EQS: (2), (4) imply: % 136.14/20.25 | (5) e1 = e0 % 136.14/20.25 | % 136.14/20.25 | SIMP: (5) implies: % 136.14/20.25 | (6) e1 = e0 % 136.14/20.25 | % 136.14/20.25 | REDUCE: (3), (6) imply: % 136.14/20.25 | (7) $false % 136.14/20.25 | % 136.14/20.25 | CLOSE: (7) is inconsistent. % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #413 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.25 (2) op(e3, e2) = e3 % 136.14/20.25 (3) op(e3, e2) = e1 % 136.14/20.25 (4) ~ (e3 = e1) % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | GROUND_INST: instantiating (1) with e1, e3, e2, e3, simplifying with (2), (3) % 136.14/20.25 | gives: % 136.14/20.25 | (5) e3 = e1 % 136.14/20.25 | % 136.14/20.25 | REDUCE: (4), (5) imply: % 136.14/20.25 | (6) $false % 136.14/20.25 | % 136.14/20.25 | CLOSE: (6) is inconsistent. % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #414 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) all_57_10 = e2 % 136.14/20.25 (2) all_57_10 = e1 % 136.14/20.25 (3) ~ (e2 = e1) % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | COMBINE_EQS: (1), (2) imply: % 136.14/20.25 | (4) e2 = e1 % 136.14/20.25 | % 136.14/20.25 | SIMP: (4) implies: % 136.14/20.25 | (5) e2 = e1 % 136.14/20.25 | % 136.14/20.25 | REDUCE: (3), (5) imply: % 136.14/20.25 | (6) $false % 136.14/20.25 | % 136.14/20.25 | CLOSE: (6) is inconsistent. % 136.14/20.25 | % 136.14/20.25 End of proof % 136.14/20.25 % 136.14/20.25 Sub-proof #415 shows that the following formulas are inconsistent: % 136.14/20.25 ---------------------------------------------------------------- % 136.14/20.25 (1) op(e2, e2) = e0 % 136.14/20.25 (2) ~ (all_16_0 = e1) % 136.14/20.25 (3) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) % 136.14/20.25 (4) op(e2, e3) = all_16_0 % 136.14/20.25 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.25 (6) ~ (e1 = e0) % 136.14/20.25 % 136.14/20.25 Begin of proof % 136.14/20.25 | % 136.14/20.25 | BETA: splitting (3) gives: % 136.14/20.25 | % 136.14/20.25 | Case 1: % 136.14/20.25 | | % 136.14/20.25 | | (7) all_57_2 = e1 & op(e2, e3) = e1 % 136.14/20.25 | | % 136.14/20.25 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #425. % 136.14/20.25 | | % 136.14/20.25 | Case 2: % 136.14/20.25 | | % 136.14/20.25 | | (8) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.25 | | % 136.14/20.25 | | ALPHA: (8) implies: % 136.14/20.26 | | (9) op(e2, e2) = e1 % 136.14/20.26 | | % 136.14/20.26 | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #675. % 136.14/20.26 | | % 136.14/20.26 | End of split % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #416 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) all_57_6 = e0 % 136.14/20.26 (2) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 136.14/20.26 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 136.14/20.26 (3) ~ (e2 = e1) % 136.14/20.26 (4) all_57_0 = e2 % 136.14/20.26 (5) all_57_2 = e3 % 136.14/20.26 (6) ~ (e3 = e1) % 136.14/20.26 (7) ~ (e1 = e0) % 136.14/20.26 (8) all_57_12 = e2 % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | BETA: splitting (2) gives: % 136.14/20.26 | % 136.14/20.26 | Case 1: % 136.14/20.26 | | % 136.14/20.26 | | (9) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) % 136.14/20.26 | | % 136.14/20.26 | | BETA: splitting (9) gives: % 136.14/20.26 | | % 136.14/20.26 | | Case 1: % 136.14/20.26 | | | % 136.14/20.26 | | | (10) all_57_0 = e1 & op(e3, e3) = e1 % 136.14/20.26 | | | % 136.14/20.26 | | | ALPHA: (10) implies: % 136.14/20.26 | | | (11) all_57_0 = e1 % 136.14/20.26 | | | % 136.14/20.26 | | | COMBINE_EQS: (4), (11) imply: % 136.14/20.26 | | | (12) e2 = e1 % 136.14/20.26 | | | % 136.14/20.26 | | | REDUCE: (3), (12) imply: % 136.14/20.26 | | | (13) $false % 136.14/20.26 | | | % 136.14/20.26 | | | CLOSE: (13) is inconsistent. % 136.14/20.26 | | | % 136.14/20.26 | | Case 2: % 136.14/20.26 | | | % 136.14/20.26 | | | (14) all_57_2 = e1 & op(e2, e3) = e1 % 136.14/20.26 | | | % 136.14/20.26 | | | REF_CLOSE: (5), (6), (14) are inconsistent by sub-proof #453. % 136.14/20.26 | | | % 136.14/20.26 | | End of split % 136.14/20.26 | | % 136.14/20.26 | Case 2: % 136.14/20.26 | | % 136.14/20.26 | | (15) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = % 136.14/20.26 | | e1) % 136.14/20.26 | | % 136.14/20.26 | | REF_CLOSE: (1), (3), (7), (8), (15) are inconsistent by sub-proof #417. % 136.14/20.26 | | % 136.14/20.26 | End of split % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #417 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) all_57_6 = e0 % 136.14/20.26 (2) ~ (e2 = e1) % 136.14/20.26 (3) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 136.14/20.26 (4) ~ (e1 = e0) % 136.14/20.26 (5) all_57_12 = e2 % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | BETA: splitting (3) gives: % 136.14/20.26 | % 136.14/20.26 | Case 1: % 136.14/20.26 | | % 136.14/20.26 | | (6) all_57_6 = e1 & op(e1, e3) = e1 % 136.14/20.26 | | % 136.14/20.26 | | ALPHA: (6) implies: % 136.14/20.26 | | (7) all_57_6 = e1 % 136.14/20.26 | | % 136.14/20.26 | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #493. % 136.14/20.26 | | % 136.14/20.26 | Case 2: % 136.14/20.26 | | % 136.14/20.26 | | (8) all_57_12 = e1 & op(e0, e3) = e1 % 136.14/20.26 | | % 136.14/20.26 | | ALPHA: (8) implies: % 136.14/20.26 | | (9) all_57_12 = e1 % 136.14/20.26 | | % 136.14/20.26 | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #644. % 136.14/20.26 | | % 136.14/20.26 | End of split % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #418 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) all_57_5 = e2 % 136.14/20.26 (2) all_57_5 = e1 % 136.14/20.26 (3) ~ (e2 = e1) % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | COMBINE_EQS: (1), (2) imply: % 136.14/20.26 | (4) e2 = e1 % 136.14/20.26 | % 136.14/20.26 | SIMP: (4) implies: % 136.14/20.26 | (5) e2 = e1 % 136.14/20.26 | % 136.14/20.26 | REDUCE: (3), (5) imply: % 136.14/20.26 | (6) $false % 136.14/20.26 | % 136.14/20.26 | CLOSE: (6) is inconsistent. % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #419 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) all_57_4 = e1 & op(e3, e1) = e1 % 136.14/20.26 (2) all_57_4 = e0 % 136.14/20.26 (3) ~ (e1 = e0) % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | ALPHA: (1) implies: % 136.14/20.26 | (4) all_57_4 = e1 % 136.14/20.26 | % 136.14/20.26 | COMBINE_EQS: (2), (4) imply: % 136.14/20.26 | (5) e1 = e0 % 136.14/20.26 | % 136.14/20.26 | SIMP: (5) implies: % 136.14/20.26 | (6) e1 = e0 % 136.14/20.26 | % 136.14/20.26 | REDUCE: (3), (6) imply: % 136.14/20.26 | (7) $false % 136.14/20.26 | % 136.14/20.26 | CLOSE: (7) is inconsistent. % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #420 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.26 (2) ~ (e3 = e0) % 136.14/20.26 (3) ~ (all_52_9 = e3) % 136.14/20.26 (4) op(e2, e1) = all_52_9 % 136.14/20.26 (5) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) % 136.14/20.26 (6) op(e3, e1) = all_52_8 % 136.14/20.26 (7) op(e3, e1) = e0 % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | BETA: splitting (5) gives: % 136.14/20.26 | % 136.14/20.26 | Case 1: % 136.14/20.26 | | % 136.14/20.26 | | (8) all_57_4 = e3 & op(e3, e1) = e3 % 136.14/20.26 | | % 136.14/20.26 | | ALPHA: (8) implies: % 136.14/20.26 | | (9) op(e3, e1) = e3 % 136.14/20.26 | | % 136.14/20.26 | | REF_CLOSE: (1), (2), (6), (7), (9) are inconsistent by sub-proof #600. % 136.14/20.26 | | % 136.14/20.26 | Case 2: % 136.14/20.26 | | % 136.14/20.26 | | (10) all_57_5 = e3 & op(e2, e1) = e3 % 136.14/20.26 | | % 136.14/20.26 | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #547. % 136.14/20.26 | | % 136.14/20.26 | End of split % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #421 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) % 136.14/20.26 (2) ~ (all_52_4 = e0) % 136.14/20.26 (3) op(e3, e3) = e2 % 136.14/20.26 (4) ~ (e2 = e0) % 136.14/20.26 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.26 (6) op(e3, e2) = all_52_4 % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | BETA: splitting (1) gives: % 136.14/20.26 | % 136.14/20.26 | Case 1: % 136.14/20.26 | | % 136.14/20.26 | | (7) all_57_0 = e0 & op(e3, e3) = e0 % 136.14/20.26 | | % 136.14/20.26 | | ALPHA: (7) implies: % 136.14/20.26 | | (8) op(e3, e3) = e0 % 136.14/20.26 | | % 136.14/20.26 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #495. % 136.14/20.26 | | % 136.14/20.26 | Case 2: % 136.14/20.26 | | % 136.14/20.26 | | (9) all_57_1 = e0 & op(e3, e2) = e0 % 136.14/20.26 | | % 136.14/20.26 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #693. % 136.14/20.26 | | % 136.14/20.26 | End of split % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #422 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) all_54_12 = all_52_3 % 136.14/20.26 (2) ~ (all_52_2 = all_52_3) % 136.14/20.26 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.26 (4) ~ (all_52_3 = e3) % 136.14/20.26 (5) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 136.14/20.26 (6) all_57_6 = e1 & op(e1, e3) = e1 % 136.14/20.26 (7) ~ (all_52_3 = e2) % 136.14/20.26 (8) op(e1, e3) = all_52_2 % 136.14/20.26 (9) ~ (all_52_3 = e0) % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | ALPHA: (6) implies: % 136.14/20.26 | (10) op(e1, e3) = e1 % 136.14/20.26 | % 136.14/20.26 | BETA: splitting (5) gives: % 136.14/20.26 | % 136.14/20.26 | Case 1: % 136.14/20.26 | | % 136.14/20.26 | | (11) all_54_12 = e3 % 136.14/20.26 | | % 136.14/20.26 | | REF_CLOSE: (1), (4), (11) are inconsistent by sub-proof #424. % 136.14/20.26 | | % 136.14/20.26 | Case 2: % 136.14/20.26 | | % 136.14/20.26 | | (12) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0 % 136.14/20.26 | | % 136.14/20.26 | | BETA: splitting (12) gives: % 136.14/20.26 | | % 136.14/20.26 | | Case 1: % 136.14/20.26 | | | % 136.14/20.26 | | | (13) all_54_12 = e2 % 136.14/20.26 | | | % 136.14/20.26 | | | REF_CLOSE: (1), (7), (13) are inconsistent by sub-proof #423. % 136.14/20.26 | | | % 136.14/20.26 | | Case 2: % 136.14/20.26 | | | % 136.14/20.26 | | | (14) all_54_12 = e1 | all_54_12 = e0 % 136.14/20.26 | | | % 136.14/20.26 | | | BETA: splitting (14) gives: % 136.14/20.26 | | | % 136.14/20.26 | | | Case 1: % 136.14/20.26 | | | | % 136.14/20.26 | | | | (15) all_54_12 = e1 % 136.14/20.26 | | | | % 136.14/20.26 | | | | COMBINE_EQS: (1), (15) imply: % 136.14/20.26 | | | | (16) all_52_3 = e1 % 136.14/20.26 | | | | % 136.14/20.26 | | | | SIMP: (16) implies: % 136.14/20.26 | | | | (17) all_52_3 = e1 % 136.14/20.26 | | | | % 136.14/20.26 | | | | REDUCE: (2), (17) imply: % 136.14/20.26 | | | | (18) ~ (all_52_2 = e1) % 136.14/20.26 | | | | % 136.14/20.26 | | | | REF_CLOSE: (3), (8), (10), (18) are inconsistent by sub-proof #725. % 136.14/20.26 | | | | % 136.14/20.26 | | | Case 2: % 136.14/20.26 | | | | % 136.14/20.26 | | | | (19) all_54_12 = e0 % 136.14/20.26 | | | | % 136.14/20.26 | | | | COMBINE_EQS: (1), (19) imply: % 136.14/20.26 | | | | (20) all_52_3 = e0 % 136.14/20.26 | | | | % 136.14/20.26 | | | | SIMP: (20) implies: % 136.14/20.26 | | | | (21) all_52_3 = e0 % 136.14/20.26 | | | | % 136.14/20.26 | | | | REDUCE: (9), (21) imply: % 136.14/20.26 | | | | (22) $false % 136.14/20.26 | | | | % 136.14/20.26 | | | | CLOSE: (22) is inconsistent. % 136.14/20.26 | | | | % 136.14/20.26 | | | End of split % 136.14/20.26 | | | % 136.14/20.26 | | End of split % 136.14/20.26 | | % 136.14/20.26 | End of split % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #423 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) all_54_12 = all_52_3 % 136.14/20.26 (2) all_54_12 = e2 % 136.14/20.26 (3) ~ (all_52_3 = e2) % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | COMBINE_EQS: (1), (2) imply: % 136.14/20.26 | (4) all_52_3 = e2 % 136.14/20.26 | % 136.14/20.26 | SIMP: (4) implies: % 136.14/20.26 | (5) all_52_3 = e2 % 136.14/20.26 | % 136.14/20.26 | REDUCE: (3), (5) imply: % 136.14/20.26 | (6) $false % 136.14/20.26 | % 136.14/20.26 | CLOSE: (6) is inconsistent. % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #424 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) all_54_12 = all_52_3 % 136.14/20.26 (2) all_54_12 = e3 % 136.14/20.26 (3) ~ (all_52_3 = e3) % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | COMBINE_EQS: (1), (2) imply: % 136.14/20.26 | (4) all_52_3 = e3 % 136.14/20.26 | % 136.14/20.26 | SIMP: (4) implies: % 136.14/20.26 | (5) all_52_3 = e3 % 136.14/20.26 | % 136.14/20.26 | REDUCE: (3), (5) imply: % 136.14/20.26 | (6) $false % 136.14/20.26 | % 136.14/20.26 | CLOSE: (6) is inconsistent. % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #425 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) all_57_2 = e1 & op(e2, e3) = e1 % 136.14/20.26 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.26 (3) op(e2, e3) = all_16_0 % 136.14/20.26 (4) ~ (all_16_0 = e1) % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | ALPHA: (1) implies: % 136.14/20.26 | (5) op(e2, e3) = e1 % 136.14/20.26 | % 136.14/20.26 | GROUND_INST: instantiating (2) with e1, all_16_0, e3, e2, simplifying with % 136.14/20.26 | (3), (5) gives: % 136.14/20.26 | (6) all_16_0 = e1 % 136.14/20.26 | % 136.14/20.26 | REDUCE: (4), (6) imply: % 136.14/20.26 | (7) $false % 136.14/20.26 | % 136.14/20.26 | CLOSE: (7) is inconsistent. % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #426 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) op(e3, e3) = e2 % 136.14/20.26 (2) ~ (e2 = e0) % 136.14/20.26 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.26 (4) ~ (e3 = e0) % 136.14/20.26 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) % 136.14/20.26 (6) all_57_2 = e3 % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | BETA: splitting (5) gives: % 136.14/20.26 | % 136.14/20.26 | Case 1: % 136.14/20.26 | | % 136.14/20.26 | | (7) all_57_0 = e0 & op(e3, e3) = e0 % 136.14/20.26 | | % 136.14/20.26 | | ALPHA: (7) implies: % 136.14/20.26 | | (8) op(e3, e3) = e0 % 136.14/20.26 | | % 136.14/20.26 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #495. % 136.14/20.26 | | % 136.14/20.26 | Case 2: % 136.14/20.26 | | % 136.14/20.26 | | (9) all_57_2 = e0 & op(e2, e3) = e0 % 136.14/20.26 | | % 136.14/20.26 | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #521. % 136.14/20.26 | | % 136.14/20.26 | End of split % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #427 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) op(e0, e0) = all_4_2 % 136.14/20.26 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.26 (3) ~ (all_4_2 = e2) % 136.14/20.26 (4) op(e0, e0) = e2 % 136.14/20.26 (5) op(e0, e0) = all_56_31 % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | GROUND_INST: instantiating (2) with all_4_2, all_56_31, e0, e0, simplifying % 136.14/20.26 | with (1), (5) gives: % 136.14/20.26 | (6) all_56_31 = all_4_2 % 136.14/20.26 | % 136.14/20.26 | GROUND_INST: instantiating (2) with e2, all_56_31, e0, e0, simplifying with % 136.14/20.26 | (4), (5) gives: % 136.14/20.26 | (7) all_56_31 = e2 % 136.14/20.26 | % 136.14/20.26 | COMBINE_EQS: (6), (7) imply: % 136.14/20.26 | (8) all_4_2 = e2 % 136.14/20.26 | % 136.14/20.26 | REDUCE: (3), (8) imply: % 136.14/20.26 | (9) $false % 136.14/20.26 | % 136.14/20.26 | CLOSE: (9) is inconsistent. % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #428 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) op(e1, e0) = e2 % 136.14/20.26 (2) op(e0, e1) = e2 % 136.14/20.26 (3) ~ (e2 = e0) % 136.14/20.26 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.26 (5) ~ (e2 = e1) % 136.14/20.26 (6) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.14/20.26 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 136.14/20.26 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.14/20.26 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 136.14/20.26 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.14/20.26 e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 136.14/20.26 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.14/20.26 = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.26 $i(all_56_21) & $i(all_56_29)) % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | BETA: splitting (6) gives: % 136.14/20.26 | % 136.14/20.26 | Case 1: % 136.14/20.26 | | % 136.14/20.26 | | (7) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 % 136.14/20.26 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 % 136.14/20.26 | | & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.14/20.26 | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) % 136.14/20.26 | | % 136.14/20.26 | | ALPHA: (7) implies: % 136.14/20.26 | | (8) op(e1, e0) = e1 % 136.14/20.26 | | % 136.14/20.26 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #720. % 136.14/20.26 | | % 136.14/20.26 | Case 2: % 136.14/20.26 | | % 136.14/20.26 | | (9) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.14/20.26 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 136.14/20.26 | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 136.14/20.26 | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.26 | | $i(all_56_21) & $i(all_56_29) % 136.14/20.26 | | % 136.14/20.26 | | ALPHA: (9) implies: % 136.14/20.26 | | (10) op(e0, e1) = e0 % 136.14/20.26 | | % 136.14/20.26 | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #660. % 136.14/20.26 | | % 136.14/20.26 | End of split % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #429 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) ~ (all_52_2 = e2) % 136.14/20.26 (2) ~ (all_52_2 = e1) % 136.14/20.26 (3) ~ (all_52_2 = e0) % 136.14/20.26 (4) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 136.14/20.26 (5) all_54_8 = all_52_2 % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | BETA: splitting (4) gives: % 136.14/20.26 | % 136.14/20.26 | Case 1: % 136.14/20.26 | | % 136.14/20.26 | | (6) all_54_8 = e2 % 136.14/20.26 | | % 136.14/20.26 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #430. % 136.14/20.26 | | % 136.14/20.26 | Case 2: % 136.14/20.26 | | % 136.14/20.26 | | (7) all_54_8 = e1 | all_54_8 = e0 % 136.14/20.26 | | % 136.14/20.26 | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #474. % 136.14/20.26 | | % 136.14/20.26 | End of split % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #430 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) all_54_8 = all_52_2 % 136.14/20.26 (2) all_54_8 = e2 % 136.14/20.26 (3) ~ (all_52_2 = e2) % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | COMBINE_EQS: (1), (2) imply: % 136.14/20.26 | (4) all_52_2 = e2 % 136.14/20.26 | % 136.14/20.26 | SIMP: (4) implies: % 136.14/20.26 | (5) all_52_2 = e2 % 136.14/20.26 | % 136.14/20.26 | REDUCE: (3), (5) imply: % 136.14/20.26 | (6) $false % 136.14/20.26 | % 136.14/20.26 | CLOSE: (6) is inconsistent. % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #431 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) ~ (all_44_1 = e2) & op(e3, e3) = all_44_1 & $i(all_44_1) % 136.14/20.26 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.26 (3) op(e3, e3) = e2 % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | ALPHA: (1) implies: % 136.14/20.26 | (4) ~ (all_44_1 = e2) % 136.14/20.26 | (5) op(e3, e3) = all_44_1 % 136.14/20.26 | % 136.14/20.26 | GROUND_INST: instantiating (2) with e2, all_44_1, e3, e3, simplifying with % 136.14/20.26 | (3), (5) gives: % 136.14/20.26 | (6) all_44_1 = e2 % 136.14/20.26 | % 136.14/20.26 | REDUCE: (4), (6) imply: % 136.14/20.26 | (7) $false % 136.14/20.26 | % 136.14/20.26 | CLOSE: (7) is inconsistent. % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #432 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.26 (2) op(e3, e0) = all_44_0 % 136.14/20.26 (3) op(e3, e0) = e1 % 136.14/20.26 (4) ~ (all_44_0 = e1) % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | GROUND_INST: instantiating (1) with e1, all_44_0, e0, e3, simplifying with % 136.14/20.26 | (2), (3) gives: % 136.14/20.26 | (5) all_44_0 = e1 % 136.14/20.26 | % 136.14/20.26 | REDUCE: (4), (5) imply: % 136.14/20.26 | (6) $false % 136.14/20.26 | % 136.14/20.26 | CLOSE: (6) is inconsistent. % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #433 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) ~ (e2 = e0) % 136.14/20.26 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 136.14/20.26 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.26 (3) ~ (all_52_7 = e3) % 136.14/20.26 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.26 (5) ~ (e2 = e1) % 136.14/20.26 (6) ~ (e3 = e0) % 136.14/20.26 (7) ~ (e3 = e2) % 136.14/20.26 (8) op(e0, e2) = all_52_7 % 136.14/20.26 (9) all_57_15 = e2 % 136.14/20.26 (10) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.26 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = % 136.14/20.26 e1) % 136.14/20.26 (11) all_57_14 = e2 % 136.14/20.26 (12) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.26 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.14/20.26 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.26 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.26 (13) ~ (e3 = e1) % 136.14/20.26 (14) ~ (e1 = e0) % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | BETA: splitting (2) gives: % 136.14/20.26 | % 136.14/20.26 | Case 1: % 136.14/20.26 | | % 136.14/20.26 | | (15) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = % 136.14/20.26 | | e3) % 136.14/20.26 | | % 136.14/20.26 | | BETA: splitting (15) gives: % 136.14/20.26 | | % 136.14/20.26 | | Case 1: % 136.14/20.26 | | | % 136.14/20.26 | | | (16) all_57_12 = e3 & op(e0, e3) = e3 % 136.14/20.26 | | | % 136.14/20.26 | | | ALPHA: (16) implies: % 136.14/20.26 | | | (17) all_57_12 = e3 % 136.14/20.26 | | | % 136.14/20.26 | | | REF_CLOSE: (1), (5), (6), (9), (10), (11), (12), (13), (14), (17) are % 136.14/20.26 | | | inconsistent by sub-proof #434. % 136.14/20.26 | | | % 136.14/20.26 | | Case 2: % 136.14/20.26 | | | % 136.14/20.26 | | | (18) all_57_13 = e3 & op(e0, e2) = e3 % 136.14/20.26 | | | % 136.14/20.26 | | | REF_CLOSE: (3), (4), (8), (18) are inconsistent by sub-proof #556. % 136.14/20.26 | | | % 136.14/20.26 | | End of split % 136.14/20.26 | | % 136.14/20.26 | Case 2: % 136.14/20.26 | | % 136.14/20.26 | | (19) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = % 136.14/20.26 | | e3) % 136.14/20.26 | | % 136.14/20.26 | | BETA: splitting (19) gives: % 136.14/20.26 | | % 136.14/20.26 | | Case 1: % 136.14/20.26 | | | % 136.14/20.26 | | | (20) all_57_14 = e3 & op(e0, e1) = e3 % 136.14/20.26 | | | % 136.14/20.26 | | | ALPHA: (20) implies: % 136.14/20.26 | | | (21) all_57_14 = e3 % 136.14/20.26 | | | % 136.14/20.26 | | | COMBINE_EQS: (11), (21) imply: % 136.14/20.26 | | | (22) e3 = e2 % 136.14/20.26 | | | % 136.14/20.26 | | | REDUCE: (7), (22) imply: % 136.14/20.26 | | | (23) $false % 136.14/20.26 | | | % 136.14/20.26 | | | CLOSE: (23) is inconsistent. % 136.14/20.26 | | | % 136.14/20.26 | | Case 2: % 136.14/20.26 | | | % 136.14/20.26 | | | (24) all_57_15 = e3 & op(e0, e0) = e3 % 136.14/20.26 | | | % 136.14/20.26 | | | ALPHA: (24) implies: % 136.14/20.26 | | | (25) all_57_15 = e3 % 136.14/20.26 | | | % 136.14/20.26 | | | COMBINE_EQS: (9), (25) imply: % 136.14/20.26 | | | (26) e3 = e2 % 136.14/20.26 | | | % 136.14/20.26 | | | REDUCE: (7), (26) imply: % 136.14/20.26 | | | (27) $false % 136.14/20.26 | | | % 136.14/20.26 | | | CLOSE: (27) is inconsistent. % 136.14/20.26 | | | % 136.14/20.26 | | End of split % 136.14/20.26 | | % 136.14/20.26 | End of split % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #434 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) ~ (e2 = e0) % 136.14/20.26 (2) ~ (e2 = e1) % 136.14/20.26 (3) ~ (e3 = e0) % 136.14/20.26 (4) all_57_15 = e2 % 136.14/20.26 (5) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) | % 136.14/20.26 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.26 (6) all_57_12 = e3 % 136.14/20.26 (7) all_57_14 = e2 % 136.14/20.26 (8) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.26 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = % 136.14/20.26 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.26 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.26 (9) ~ (e3 = e1) % 136.14/20.26 (10) ~ (e1 = e0) % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | BETA: splitting (8) gives: % 136.14/20.26 | % 136.14/20.26 | Case 1: % 136.14/20.26 | | % 136.14/20.26 | | (11) all_57_15 = e0 & op(e0, e0) = e0 % 136.14/20.26 | | % 136.14/20.26 | | REF_CLOSE: (1), (4), (11) are inconsistent by sub-proof #437. % 136.14/20.26 | | % 136.14/20.26 | Case 2: % 136.14/20.26 | | % 136.14/20.26 | | (12) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = % 136.14/20.26 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 & % 136.14/20.26 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) | % 136.14/20.26 | | (all_57_14 = e0 & op(e0, e1) = e0)) % 136.14/20.26 | | % 136.14/20.26 | | ALPHA: (12) implies: % 136.14/20.26 | | (13) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 136.14/20.26 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 136.14/20.26 | | % 136.14/20.26 | | BETA: splitting (13) gives: % 136.14/20.26 | | % 136.14/20.26 | | Case 1: % 136.14/20.26 | | | % 136.14/20.26 | | | (14) all_57_12 = e0 & op(e0, e3) = e0 % 136.14/20.26 | | | % 136.14/20.26 | | | REF_CLOSE: (3), (6), (14) are inconsistent by sub-proof #436. % 136.14/20.26 | | | % 136.14/20.26 | | Case 2: % 136.14/20.26 | | | % 136.14/20.26 | | | (15) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) % 136.14/20.26 | | | = e0) % 136.14/20.26 | | | % 136.14/20.26 | | | BETA: splitting (15) gives: % 136.14/20.26 | | | % 136.14/20.26 | | | Case 1: % 136.14/20.26 | | | | % 136.14/20.26 | | | | (16) all_57_13 = e0 & op(e0, e2) = e0 % 136.14/20.26 | | | | % 136.14/20.26 | | | | ALPHA: (16) implies: % 136.14/20.26 | | | | (17) all_57_13 = e0 % 136.14/20.26 | | | | % 136.14/20.26 | | | | BETA: splitting (5) gives: % 136.14/20.26 | | | | % 136.14/20.26 | | | | Case 1: % 136.14/20.26 | | | | | % 136.14/20.26 | | | | | (18) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, % 136.14/20.26 | | | | | e2) = e1) % 136.14/20.26 | | | | | % 136.14/20.26 | | | | | BETA: splitting (18) gives: % 136.14/20.26 | | | | | % 136.14/20.26 | | | | | Case 1: % 136.14/20.26 | | | | | | % 136.14/20.26 | | | | | | (19) all_57_12 = e1 & op(e0, e3) = e1 % 136.14/20.26 | | | | | | % 136.14/20.26 | | | | | | REF_CLOSE: (6), (9), (19) are inconsistent by sub-proof #490. % 136.14/20.26 | | | | | | % 136.14/20.26 | | | | | Case 2: % 136.14/20.26 | | | | | | % 136.14/20.26 | | | | | | (20) all_57_13 = e1 & op(e0, e2) = e1 % 136.14/20.26 | | | | | | % 136.14/20.26 | | | | | | ALPHA: (20) implies: % 136.14/20.26 | | | | | | (21) all_57_13 = e1 % 136.14/20.26 | | | | | | % 136.14/20.26 | | | | | | REF_CLOSE: (10), (17), (21) are inconsistent by sub-proof #681. % 136.14/20.26 | | | | | | % 136.14/20.26 | | | | | End of split % 136.14/20.26 | | | | | % 136.14/20.26 | | | | Case 2: % 136.14/20.26 | | | | | % 136.14/20.26 | | | | | (22) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, % 136.14/20.26 | | | | | e0) = e1) % 136.14/20.26 | | | | | % 136.14/20.26 | | | | | BETA: splitting (22) gives: % 136.14/20.26 | | | | | % 136.14/20.26 | | | | | Case 1: % 136.14/20.26 | | | | | | % 136.14/20.26 | | | | | | (23) all_57_14 = e1 & op(e0, e1) = e1 % 136.14/20.26 | | | | | | % 136.14/20.26 | | | | | | ALPHA: (23) implies: % 136.14/20.26 | | | | | | (24) all_57_14 = e1 % 136.14/20.26 | | | | | | % 136.14/20.26 | | | | | | REF_CLOSE: (2), (7), (24) are inconsistent by sub-proof #560. % 136.14/20.26 | | | | | | % 136.14/20.26 | | | | | Case 2: % 136.14/20.26 | | | | | | % 136.14/20.26 | | | | | | (25) all_57_15 = e1 & op(e0, e0) = e1 % 136.14/20.26 | | | | | | % 136.14/20.26 | | | | | | REF_CLOSE: (2), (4), (25) are inconsistent by sub-proof #435. % 136.14/20.26 | | | | | | % 136.14/20.26 | | | | | End of split % 136.14/20.26 | | | | | % 136.14/20.26 | | | | End of split % 136.14/20.26 | | | | % 136.14/20.26 | | | Case 2: % 136.14/20.26 | | | | % 136.14/20.26 | | | | (26) all_57_14 = e0 & op(e0, e1) = e0 % 136.14/20.26 | | | | % 136.14/20.26 | | | | REF_CLOSE: (1), (7), (26) are inconsistent by sub-proof #580. % 136.14/20.26 | | | | % 136.14/20.26 | | | End of split % 136.14/20.26 | | | % 136.14/20.26 | | End of split % 136.14/20.26 | | % 136.14/20.26 | End of split % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #435 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) all_57_15 = e1 & op(e0, e0) = e1 % 136.14/20.26 (2) all_57_15 = e2 % 136.14/20.26 (3) ~ (e2 = e1) % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | ALPHA: (1) implies: % 136.14/20.26 | (4) all_57_15 = e1 % 136.14/20.26 | % 136.14/20.26 | COMBINE_EQS: (2), (4) imply: % 136.14/20.26 | (5) e2 = e1 % 136.14/20.26 | % 136.14/20.26 | SIMP: (5) implies: % 136.14/20.26 | (6) e2 = e1 % 136.14/20.26 | % 136.14/20.26 | REDUCE: (3), (6) imply: % 136.14/20.26 | (7) $false % 136.14/20.26 | % 136.14/20.26 | CLOSE: (7) is inconsistent. % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #436 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) all_57_12 = e0 & op(e0, e3) = e0 % 136.14/20.26 (2) all_57_12 = e3 % 136.14/20.26 (3) ~ (e3 = e0) % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | ALPHA: (1) implies: % 136.14/20.26 | (4) all_57_12 = e0 % 136.14/20.26 | % 136.14/20.26 | COMBINE_EQS: (2), (4) imply: % 136.14/20.26 | (5) e3 = e0 % 136.14/20.26 | % 136.14/20.26 | REDUCE: (3), (5) imply: % 136.14/20.26 | (6) $false % 136.14/20.26 | % 136.14/20.26 | CLOSE: (6) is inconsistent. % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #437 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) all_57_15 = e0 & op(e0, e0) = e0 % 136.14/20.26 (2) all_57_15 = e2 % 136.14/20.26 (3) ~ (e2 = e0) % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | ALPHA: (1) implies: % 136.14/20.26 | (4) all_57_15 = e0 % 136.14/20.26 | % 136.14/20.26 | COMBINE_EQS: (2), (4) imply: % 136.14/20.26 | (5) e2 = e0 % 136.14/20.26 | % 136.14/20.26 | SIMP: (5) implies: % 136.14/20.26 | (6) e2 = e0 % 136.14/20.26 | % 136.14/20.26 | REDUCE: (3), (6) imply: % 136.14/20.26 | (7) $false % 136.14/20.26 | % 136.14/20.26 | CLOSE: (7) is inconsistent. % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #438 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) all_57_4 = e3 & op(e3, e1) = e3 % 136.14/20.26 (2) all_57_4 = e1 % 136.14/20.26 (3) ~ (e3 = e1) % 136.14/20.26 % 136.14/20.26 Begin of proof % 136.14/20.26 | % 136.14/20.26 | ALPHA: (1) implies: % 136.14/20.26 | (4) all_57_4 = e3 % 136.14/20.26 | % 136.14/20.26 | COMBINE_EQS: (2), (4) imply: % 136.14/20.26 | (5) e3 = e1 % 136.14/20.26 | % 136.14/20.26 | REDUCE: (3), (5) imply: % 136.14/20.26 | (6) $false % 136.14/20.26 | % 136.14/20.26 | CLOSE: (6) is inconsistent. % 136.14/20.26 | % 136.14/20.26 End of proof % 136.14/20.26 % 136.14/20.26 Sub-proof #439 shows that the following formulas are inconsistent: % 136.14/20.26 ---------------------------------------------------------------- % 136.14/20.26 (1) op(e1, e0) = e2 % 136.14/20.26 (2) op(e0, e0) = e3 % 136.14/20.26 (3) ~ (e2 = e0) % 136.14/20.26 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.26 (5) ~ (e2 = e1) % 136.14/20.26 (6) ~ (e3 = e0) % 136.14/20.27 (7) all_57_9 = e3 % 136.14/20.27 (8) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.27 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = % 136.14/20.27 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.27 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.27 (9) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.14/20.27 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.14/20.27 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.14/20.27 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.14/20.27 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) % 136.14/20.27 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.14/20.27 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 136.14/20.27 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 136.14/20.27 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & % 136.14/20.27 all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ % 136.14/20.27 (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = % 136.14/20.27 e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 136.14/20.27 all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 % 136.14/20.27 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.27 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, % 136.14/20.27 e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.14/20.27 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.14/20.27 $i(all_56_29)) % 136.14/20.27 (10) all_57_11 = e2 % 136.14/20.27 (11) ~ (e3 = e1) % 136.14/20.27 (12) ~ (e1 = e0) % 136.14/20.27 (13) op(e0, e0) = all_56_31 % 136.14/20.27 (14) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) | % 136.14/20.27 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.27 % 136.14/20.27 Begin of proof % 136.14/20.27 | % 136.14/20.27 | BETA: splitting (14) gives: % 136.14/20.27 | % 136.14/20.27 | Case 1: % 136.14/20.27 | | % 136.14/20.27 | | (15) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = % 136.14/20.27 | | e1) % 136.14/20.27 | | % 136.14/20.27 | | BETA: splitting (15) gives: % 136.14/20.27 | | % 136.14/20.27 | | Case 1: % 136.14/20.27 | | | % 136.14/20.27 | | | (16) all_57_9 = e1 & op(e3, e0) = e1 % 136.14/20.27 | | | % 136.14/20.27 | | | ALPHA: (16) implies: % 136.14/20.27 | | | (17) all_57_9 = e1 % 136.14/20.27 | | | % 136.14/20.27 | | | REF_CLOSE: (7), (11), (17) are inconsistent by sub-proof #690. % 136.14/20.27 | | | % 136.14/20.27 | | Case 2: % 136.14/20.27 | | | % 136.14/20.27 | | | (18) all_57_10 = e1 & op(e2, e0) = e1 % 136.14/20.27 | | | % 136.14/20.27 | | | ALPHA: (18) implies: % 136.14/20.27 | | | (19) all_57_10 = e1 % 136.14/20.27 | | | % 136.14/20.27 | | | BETA: splitting (8) gives: % 136.14/20.27 | | | % 136.14/20.27 | | | Case 1: % 136.14/20.27 | | | | % 136.14/20.27 | | | | (20) all_57_15 = e0 & op(e0, e0) = e0 % 136.14/20.27 | | | | % 136.14/20.27 | | | | ALPHA: (20) implies: % 136.14/20.27 | | | | (21) op(e0, e0) = e0 % 136.14/20.27 | | | | % 136.14/20.27 | | | | REF_CLOSE: (3), (4), (6), (9), (12), (13), (21) are inconsistent by % 136.14/20.27 | | | | sub-proof #710. % 136.14/20.27 | | | | % 136.14/20.27 | | | Case 2: % 136.14/20.27 | | | | % 136.14/20.27 | | | | (22) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, % 136.14/20.27 | | | | e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & % 136.14/20.27 | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, % 136.14/20.27 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 136.14/20.27 | | | | % 136.14/20.27 | | | | REF_CLOSE: (3), (6), (7), (10), (12), (19), (22) are inconsistent by % 136.14/20.27 | | | | sub-proof #637. % 136.14/20.27 | | | | % 136.14/20.27 | | | End of split % 136.14/20.27 | | | % 136.14/20.27 | | End of split % 136.14/20.27 | | % 136.14/20.27 | Case 2: % 136.14/20.27 | | % 136.14/20.27 | | (23) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = % 136.14/20.27 | | e1) % 136.14/20.27 | | % 136.14/20.27 | | REF_CLOSE: (1), (2), (4), (5), (11), (23) are inconsistent by sub-proof % 136.14/20.27 | | #557. % 136.14/20.27 | | % 136.14/20.27 | End of split % 136.14/20.27 | % 136.14/20.27 End of proof % 136.14/20.27 % 136.14/20.27 Sub-proof #440 shows that the following formulas are inconsistent: % 136.14/20.27 ---------------------------------------------------------------- % 136.14/20.27 (1) op(e2, e0) = all_52_13 % 136.14/20.27 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.27 (3) ~ (all_52_13 = e2) % 136.14/20.27 (4) op(e3, e0) = all_52_12 % 136.14/20.27 (5) ~ (all_52_12 = e2) % 136.14/20.27 (6) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 136.14/20.27 % 136.14/20.27 Begin of proof % 136.14/20.27 | % 136.14/20.27 | BETA: splitting (6) gives: % 136.14/20.27 | % 136.14/20.27 | Case 1: % 136.14/20.27 | | % 136.14/20.27 | | (7) all_57_9 = e2 & op(e3, e0) = e2 % 136.14/20.27 | | % 136.14/20.27 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #460. % 136.14/20.27 | | % 136.14/20.27 | Case 2: % 136.14/20.27 | | % 136.14/20.27 | | (8) all_57_10 = e2 & op(e2, e0) = e2 % 136.14/20.27 | | % 136.14/20.27 | | ALPHA: (8) implies: % 136.14/20.27 | | (9) op(e2, e0) = e2 % 136.14/20.27 | | % 136.14/20.27 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #768. % 136.14/20.27 | | % 136.14/20.27 | End of split % 136.14/20.27 | % 136.14/20.27 End of proof % 136.14/20.27 % 136.14/20.27 Sub-proof #441 shows that the following formulas are inconsistent: % 136.14/20.27 ---------------------------------------------------------------- % 136.14/20.27 (1) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) % 136.14/20.27 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.27 (3) ~ (all_52_9 = e2) % 136.14/20.27 (4) op(e2, e1) = all_52_9 % 136.14/20.27 (5) ~ (all_52_8 = e2) % 136.14/20.27 (6) op(e3, e1) = all_52_8 % 136.14/20.27 % 136.14/20.27 Begin of proof % 136.14/20.27 | % 136.14/20.27 | BETA: splitting (1) gives: % 136.14/20.27 | % 136.14/20.27 | Case 1: % 136.14/20.27 | | % 136.14/20.27 | | (7) all_57_4 = e2 & op(e3, e1) = e2 % 136.14/20.27 | | % 136.14/20.27 | | REF_CLOSE: (2), (5), (6), (7) are inconsistent by sub-proof #442. % 136.14/20.27 | | % 136.14/20.27 | Case 2: % 136.14/20.27 | | % 136.14/20.27 | | (8) all_57_5 = e2 & op(e2, e1) = e2 % 136.14/20.27 | | % 136.14/20.27 | | ALPHA: (8) implies: % 136.14/20.27 | | (9) op(e2, e1) = e2 % 136.14/20.27 | | % 136.14/20.27 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #770. % 136.14/20.27 | | % 136.14/20.27 | End of split % 136.14/20.27 | % 136.14/20.27 End of proof % 136.14/20.27 % 136.14/20.27 Sub-proof #442 shows that the following formulas are inconsistent: % 136.14/20.27 ---------------------------------------------------------------- % 136.14/20.27 (1) all_57_4 = e2 & op(e3, e1) = e2 % 136.14/20.27 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.27 (3) op(e3, e1) = all_52_8 % 136.14/20.27 (4) ~ (all_52_8 = e2) % 136.14/20.27 % 136.14/20.27 Begin of proof % 136.14/20.27 | % 136.14/20.27 | ALPHA: (1) implies: % 136.14/20.27 | (5) op(e3, e1) = e2 % 136.14/20.27 | % 136.14/20.27 | GROUND_INST: instantiating (2) with all_52_8, e2, e1, e3, simplifying with % 136.14/20.27 | (3), (5) gives: % 136.14/20.27 | (6) all_52_8 = e2 % 136.14/20.27 | % 136.14/20.27 | REDUCE: (4), (6) imply: % 136.14/20.27 | (7) $false % 136.14/20.27 | % 136.14/20.27 | CLOSE: (7) is inconsistent. % 136.14/20.27 | % 136.14/20.27 End of proof % 136.14/20.27 % 136.14/20.27 Sub-proof #443 shows that the following formulas are inconsistent: % 136.14/20.27 ---------------------------------------------------------------- % 136.14/20.27 (1) op(e3, e3) = e2 % 136.14/20.27 (2) ~ (e2 = e0) % 136.14/20.27 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.27 (4) ~ (all_52_1 = e2) % 136.14/20.27 (5) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.14/20.27 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.14/20.27 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.14/20.27 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.14/20.27 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 136.14/20.27 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 136.14/20.27 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 136.14/20.27 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.14/20.27 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.27 $i(all_56_17) & $i(all_56_25)) % 136.14/20.27 (6) op(e2, e3) = all_52_1 % 136.14/20.27 % 136.14/20.27 Begin of proof % 136.14/20.27 | % 136.14/20.27 | BETA: splitting (5) gives: % 136.14/20.27 | % 136.14/20.27 | Case 1: % 136.14/20.27 | | % 136.14/20.27 | | (7) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.14/20.27 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.14/20.27 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.14/20.27 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.14/20.27 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.14/20.27 | | % 136.14/20.27 | | ALPHA: (7) implies: % 136.14/20.27 | | (8) op(e3, e3) = e0 % 136.14/20.27 | | % 136.14/20.27 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #495. % 136.14/20.27 | | % 136.14/20.27 | Case 2: % 136.14/20.27 | | % 136.14/20.27 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.14/20.27 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.27 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.14/20.27 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) % 136.14/20.27 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.14/20.27 | | % 136.14/20.27 | | ALPHA: (9) implies: % 136.14/20.27 | | (10) op(e2, e3) = e2 % 136.14/20.27 | | % 136.14/20.27 | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #779. % 136.14/20.27 | | % 136.14/20.27 | End of split % 136.14/20.27 | % 136.14/20.27 End of proof % 136.14/20.27 % 136.14/20.27 Sub-proof #444 shows that the following formulas are inconsistent: % 136.14/20.27 ---------------------------------------------------------------- % 136.14/20.27 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 136.14/20.27 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 136.14/20.27 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.14/20.27 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.14/20.27 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.14/20.27 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.27 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 136.14/20.27 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.14/20.27 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.27 $i(all_56_21) & $i(all_56_29)) % 136.14/20.27 (2) op(e3, e3) = e2 % 136.14/20.27 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.27 (4) ~ (e2 = e1) % 136.14/20.27 (5) op(e2, e2) = e2 % 136.14/20.27 % 136.14/20.27 Begin of proof % 136.14/20.27 | % 136.14/20.27 | BETA: splitting (1) gives: % 136.14/20.27 | % 136.14/20.27 | Case 1: % 136.14/20.27 | | % 136.14/20.27 | | (6) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.14/20.27 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.14/20.27 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.14/20.27 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.14/20.27 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.14/20.27 | | % 136.14/20.27 | | ALPHA: (6) implies: % 136.14/20.27 | | (7) ~ (all_56_11 = e2) % 136.14/20.27 | | (8) op(e2, e2) = all_56_11 % 136.14/20.27 | | % 136.14/20.27 | | REF_CLOSE: (3), (5), (7), (8) are inconsistent by sub-proof #531. % 136.14/20.27 | | % 136.14/20.27 | Case 2: % 136.14/20.27 | | % 136.14/20.27 | | (9) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.14/20.27 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 136.14/20.27 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.14/20.27 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.14/20.27 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.14/20.27 | | % 136.14/20.27 | | ALPHA: (9) implies: % 136.14/20.27 | | (10) op(e3, e3) = e1 % 136.14/20.27 | | % 136.14/20.27 | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #743. % 136.14/20.27 | | % 136.14/20.27 | End of split % 136.14/20.27 | % 136.14/20.27 End of proof % 136.14/20.27 % 136.14/20.27 Sub-proof #445 shows that the following formulas are inconsistent: % 136.14/20.27 ---------------------------------------------------------------- % 136.14/20.27 (1) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 136.14/20.27 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 136.14/20.27 (2) ~ (all_52_4 = e0) % 136.14/20.27 (3) ~ (e2 = e0) % 136.14/20.27 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.27 (5) ~ (e2 = e1) % 136.14/20.27 (6) ~ (e3 = e0) % 136.14/20.27 (7) ~ (e3 = e2) % 136.14/20.27 (8) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) % 136.14/20.27 (9) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 136.14/20.27 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) % 136.14/20.27 (10) op(e2, e0) = e0 % 136.14/20.27 (11) op(e3, e2) = all_52_4 % 136.14/20.27 (12) all_57_10 = e0 % 136.14/20.27 (13) ~ (e3 = e1) % 136.14/20.27 (14) ~ (e1 = e0) % 136.14/20.27 (15) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.27 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.14/20.27 % 136.14/20.27 Begin of proof % 136.14/20.27 | % 136.14/20.27 | BETA: splitting (8) gives: % 136.14/20.27 | % 136.14/20.27 | Case 1: % 136.14/20.27 | | % 136.14/20.27 | | (16) all_57_1 = e0 & op(e3, e2) = e0 % 136.14/20.27 | | % 136.14/20.27 | | REF_CLOSE: (2), (4), (11), (16) are inconsistent by sub-proof #693. % 136.14/20.27 | | % 136.14/20.27 | Case 2: % 136.14/20.27 | | % 136.14/20.27 | | (17) all_57_3 = e0 & op(e2, e2) = e0 % 136.14/20.27 | | % 136.14/20.27 | | ALPHA: (17) implies: % 136.14/20.27 | | (18) all_57_3 = e0 % 136.14/20.27 | | (19) op(e2, e2) = e0 % 136.14/20.27 | | % 136.14/20.27 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (12), (13), (14), (15), % 136.14/20.27 | | (18), (19) are inconsistent by sub-proof #446. % 136.14/20.27 | | % 136.14/20.27 | End of split % 136.14/20.27 | % 136.14/20.27 End of proof % 136.14/20.27 % 136.14/20.27 Sub-proof #446 shows that the following formulas are inconsistent: % 136.14/20.27 ---------------------------------------------------------------- % 136.14/20.27 (1) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 136.14/20.27 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 136.14/20.27 (2) op(e2, e2) = e0 % 136.14/20.27 (3) ~ (e2 = e0) % 136.14/20.27 (4) all_57_3 = e0 % 136.14/20.27 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.27 (6) ~ (e2 = e1) % 136.14/20.27 (7) ~ (e3 = e0) % 136.14/20.27 (8) ~ (e3 = e2) % 136.14/20.27 (9) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 136.14/20.27 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) % 136.14/20.27 (10) op(e2, e0) = e0 % 136.14/20.27 (11) all_57_10 = e0 % 136.14/20.27 (12) ~ (e3 = e1) % 136.14/20.27 (13) ~ (e1 = e0) % 136.14/20.27 (14) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.27 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.14/20.27 % 136.14/20.27 Begin of proof % 136.14/20.27 | % 136.14/20.27 | BETA: splitting (9) gives: % 136.14/20.27 | % 136.14/20.27 | Case 1: % 136.14/20.27 | | % 136.14/20.27 | | (15) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = % 136.14/20.27 | | e3) % 136.14/20.27 | | % 136.14/20.27 | | BETA: splitting (15) gives: % 136.14/20.27 | | % 136.14/20.27 | | Case 1: % 136.14/20.27 | | | % 136.14/20.27 | | | (16) all_57_2 = e3 & op(e2, e3) = e3 % 136.14/20.27 | | | % 136.14/20.27 | | | ALPHA: (16) implies: % 136.14/20.27 | | | (17) all_57_2 = e3 % 136.14/20.27 | | | % 136.14/20.27 | | | BETA: splitting (1) gives: % 136.14/20.27 | | | % 136.14/20.27 | | | Case 1: % 136.14/20.27 | | | | % 136.14/20.27 | | | | (18) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) % 136.14/20.27 | | | | = e2) % 136.14/20.27 | | | | % 136.14/20.27 | | | | BETA: splitting (18) gives: % 136.14/20.27 | | | | % 136.14/20.27 | | | | Case 1: % 136.14/20.27 | | | | | % 136.14/20.27 | | | | | (19) all_57_2 = e2 & op(e2, e3) = e2 % 136.14/20.27 | | | | | % 136.14/20.27 | | | | | REF_CLOSE: (8), (17), (19) are inconsistent by sub-proof #454. % 136.14/20.27 | | | | | % 136.14/20.27 | | | | Case 2: % 136.14/20.27 | | | | | % 136.14/20.27 | | | | | (20) all_57_3 = e2 & op(e2, e2) = e2 % 136.14/20.27 | | | | | % 136.14/20.27 | | | | | ALPHA: (20) implies: % 136.14/20.27 | | | | | (21) all_57_3 = e2 % 136.14/20.27 | | | | | % 136.14/20.27 | | | | | REF_CLOSE: (3), (4), (21) are inconsistent by sub-proof #679. % 136.14/20.27 | | | | | % 136.14/20.27 | | | | End of split % 136.14/20.27 | | | | % 136.14/20.27 | | | Case 2: % 136.14/20.27 | | | | % 136.14/20.27 | | | | (22) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) % 136.14/20.27 | | | | = e2) % 136.14/20.27 | | | | % 136.14/20.27 | | | | BETA: splitting (22) gives: % 136.14/20.27 | | | | % 136.14/20.27 | | | | Case 1: % 136.14/20.27 | | | | | % 136.14/20.27 | | | | | (23) all_57_5 = e2 & op(e2, e1) = e2 % 136.14/20.27 | | | | | % 136.14/20.27 | | | | | ALPHA: (23) implies: % 136.14/20.27 | | | | | (24) all_57_5 = e2 % 136.14/20.27 | | | | | % 136.14/20.27 | | | | | REF_CLOSE: (2), (5), (6), (10), (12), (13), (14), (17), (24) are % 136.14/20.27 | | | | | inconsistent by sub-proof #452. % 136.14/20.27 | | | | | % 136.14/20.27 | | | | Case 2: % 136.14/20.27 | | | | | % 136.14/20.27 | | | | | (25) all_57_10 = e2 & op(e2, e0) = e2 % 136.14/20.27 | | | | | % 136.14/20.27 | | | | | ALPHA: (25) implies: % 136.14/20.27 | | | | | (26) op(e2, e0) = e2 % 136.14/20.27 | | | | | % 136.14/20.27 | | | | | REF_CLOSE: (3), (5), (10), (26) are inconsistent by sub-proof #451. % 136.14/20.27 | | | | | % 136.14/20.27 | | | | End of split % 136.14/20.27 | | | | % 136.14/20.27 | | | End of split % 136.14/20.27 | | | % 136.14/20.27 | | Case 2: % 136.14/20.27 | | | % 136.14/20.27 | | | (27) all_57_3 = e3 & op(e2, e2) = e3 % 136.14/20.27 | | | % 136.14/20.27 | | | ALPHA: (27) implies: % 136.14/20.27 | | | (28) op(e2, e2) = e3 % 136.14/20.27 | | | % 136.14/20.27 | | | REF_CLOSE: (2), (5), (7), (28) are inconsistent by sub-proof #641. % 136.14/20.27 | | | % 136.14/20.27 | | End of split % 136.14/20.27 | | % 136.14/20.27 | Case 2: % 136.14/20.27 | | % 136.14/20.27 | | (29) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = % 136.14/20.27 | | e3) % 136.14/20.27 | | % 136.14/20.27 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14), % 136.14/20.27 | | (29) are inconsistent by sub-proof #447. % 136.14/20.27 | | % 136.14/20.27 | End of split % 136.14/20.27 | % 136.14/20.27 End of proof % 136.14/20.27 % 136.14/20.27 Sub-proof #447 shows that the following formulas are inconsistent: % 136.14/20.27 ---------------------------------------------------------------- % 136.14/20.27 (1) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) % 136.14/20.27 (2) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 136.14/20.27 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 136.14/20.27 (3) ~ (e2 = e0) % 136.14/20.27 (4) all_57_3 = e0 % 136.14/20.27 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.27 (6) ~ (e2 = e1) % 136.14/20.27 (7) ~ (e3 = e0) % 136.14/20.27 (8) ~ (e3 = e2) % 136.14/20.27 (9) op(e2, e0) = e0 % 136.14/20.27 (10) all_57_10 = e0 % 136.14/20.27 (11) ~ (e3 = e1) % 136.14/20.27 (12) ~ (e1 = e0) % 136.14/20.27 (13) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.27 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.14/20.27 % 136.14/20.27 Begin of proof % 136.14/20.27 | % 136.14/20.27 | BETA: splitting (1) gives: % 136.14/20.27 | % 136.14/20.27 | Case 1: % 136.14/20.27 | | % 136.14/20.27 | | (14) all_57_5 = e3 & op(e2, e1) = e3 % 136.14/20.27 | | % 136.14/20.27 | | ALPHA: (14) implies: % 136.14/20.27 | | (15) all_57_5 = e3 % 136.14/20.27 | | % 136.14/20.27 | | BETA: splitting (13) gives: % 136.14/20.27 | | % 136.14/20.27 | | Case 1: % 136.14/20.27 | | | % 136.14/20.27 | | | (16) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = % 136.14/20.27 | | | e1) % 136.14/20.27 | | | % 136.14/20.27 | | | BETA: splitting (16) gives: % 136.14/20.27 | | | % 136.14/20.27 | | | Case 1: % 136.14/20.27 | | | | % 136.14/20.27 | | | | (17) all_57_2 = e1 & op(e2, e3) = e1 % 136.14/20.27 | | | | % 136.14/20.27 | | | | ALPHA: (17) implies: % 136.14/20.27 | | | | (18) op(e2, e3) = e1 % 136.14/20.27 | | | | % 136.14/20.27 | | | | BETA: splitting (2) gives: % 136.14/20.27 | | | | % 136.14/20.27 | | | | Case 1: % 136.14/20.27 | | | | | % 136.14/20.27 | | | | | (19) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, % 136.14/20.27 | | | | | e2) = e2) % 136.14/20.27 | | | | | % 136.14/20.27 | | | | | BETA: splitting (19) gives: % 136.14/20.27 | | | | | % 136.14/20.27 | | | | | Case 1: % 136.14/20.27 | | | | | | % 136.14/20.27 | | | | | | (20) all_57_2 = e2 & op(e2, e3) = e2 % 136.14/20.27 | | | | | | % 136.14/20.27 | | | | | | ALPHA: (20) implies: % 136.14/20.27 | | | | | | (21) op(e2, e3) = e2 % 136.14/20.27 | | | | | | % 136.14/20.27 | | | | | | REF_CLOSE: (5), (6), (18), (21) are inconsistent by sub-proof #450. % 136.14/20.27 | | | | | | % 136.14/20.27 | | | | | Case 2: % 136.14/20.27 | | | | | | % 136.14/20.27 | | | | | | (22) all_57_3 = e2 & op(e2, e2) = e2 % 136.14/20.27 | | | | | | % 136.14/20.27 | | | | | | ALPHA: (22) implies: % 136.14/20.27 | | | | | | (23) all_57_3 = e2 % 136.14/20.27 | | | | | | % 136.14/20.27 | | | | | | REF_CLOSE: (3), (4), (23) are inconsistent by sub-proof #679. % 136.14/20.27 | | | | | | % 136.14/20.27 | | | | | End of split % 136.14/20.27 | | | | | % 136.14/20.27 | | | | Case 2: % 136.14/20.27 | | | | | % 136.14/20.27 | | | | | (24) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, % 136.14/20.27 | | | | | e0) = e2) % 136.14/20.27 | | | | | % 136.14/20.27 | | | | | BETA: splitting (24) gives: % 136.14/20.27 | | | | | % 136.14/20.27 | | | | | Case 1: % 136.14/20.27 | | | | | | % 136.14/20.27 | | | | | | (25) all_57_5 = e2 & op(e2, e1) = e2 % 136.14/20.27 | | | | | | % 136.14/20.27 | | | | | | ALPHA: (25) implies: % 136.14/20.27 | | | | | | (26) all_57_5 = e2 % 136.14/20.27 | | | | | | % 136.14/20.27 | | | | | | REF_CLOSE: (8), (15), (26) are inconsistent by sub-proof #501. % 136.14/20.27 | | | | | | % 136.14/20.27 | | | | | Case 2: % 136.14/20.27 | | | | | | % 136.14/20.27 | | | | | | (27) all_57_10 = e2 & op(e2, e0) = e2 % 136.14/20.27 | | | | | | % 136.14/20.27 | | | | | | ALPHA: (27) implies: % 136.14/20.27 | | | | | | (28) op(e2, e0) = e2 % 136.14/20.27 | | | | | | % 136.14/20.27 | | | | | | REF_CLOSE: (3), (5), (9), (28) are inconsistent by sub-proof #451. % 136.14/20.27 | | | | | | % 136.14/20.27 | | | | | End of split % 136.14/20.27 | | | | | % 136.14/20.27 | | | | End of split % 136.14/20.27 | | | | % 136.14/20.27 | | | Case 2: % 136.14/20.27 | | | | % 136.14/20.27 | | | | (29) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.27 | | | | % 136.14/20.27 | | | | REF_CLOSE: (4), (12), (29) are inconsistent by sub-proof #449. % 136.14/20.27 | | | | % 136.14/20.27 | | | End of split % 136.14/20.27 | | | % 136.14/20.27 | | Case 2: % 136.14/20.27 | | | % 136.14/20.27 | | | (30) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = % 136.14/20.27 | | | e1) % 136.14/20.27 | | | % 136.14/20.27 | | | BETA: splitting (30) gives: % 136.14/20.27 | | | % 136.14/20.27 | | | Case 1: % 136.14/20.27 | | | | % 136.14/20.27 | | | | (31) all_57_5 = e1 & op(e2, e1) = e1 % 136.14/20.27 | | | | % 136.14/20.27 | | | | REF_CLOSE: (11), (15), (31) are inconsistent by sub-proof #673. % 136.14/20.27 | | | | % 136.14/20.27 | | | Case 2: % 136.14/20.27 | | | | % 136.14/20.27 | | | | (32) all_57_10 = e1 & op(e2, e0) = e1 % 136.14/20.27 | | | | % 136.14/20.27 | | | | ALPHA: (32) implies: % 136.14/20.27 | | | | (33) op(e2, e0) = e1 % 136.14/20.27 | | | | % 136.14/20.27 | | | | REF_CLOSE: (5), (9), (12), (33) are inconsistent by sub-proof #695. % 136.14/20.27 | | | | % 136.14/20.27 | | | End of split % 136.14/20.27 | | | % 136.14/20.27 | | End of split % 136.14/20.27 | | % 136.14/20.27 | Case 2: % 136.14/20.27 | | % 136.14/20.27 | | (34) all_57_10 = e3 & op(e2, e0) = e3 % 136.14/20.27 | | % 136.14/20.27 | | ALPHA: (34) implies: % 136.14/20.27 | | (35) all_57_10 = e3 % 136.14/20.27 | | % 136.14/20.27 | | REF_CLOSE: (7), (10), (35) are inconsistent by sub-proof #448. % 136.14/20.27 | | % 136.14/20.27 | End of split % 136.14/20.27 | % 136.14/20.27 End of proof % 136.14/20.27 % 136.14/20.27 Sub-proof #448 shows that the following formulas are inconsistent: % 136.14/20.27 ---------------------------------------------------------------- % 136.14/20.27 (1) all_57_10 = e3 % 136.14/20.27 (2) all_57_10 = e0 % 136.14/20.27 (3) ~ (e3 = e0) % 136.14/20.27 % 136.14/20.27 Begin of proof % 136.14/20.27 | % 136.14/20.27 | COMBINE_EQS: (1), (2) imply: % 136.14/20.27 | (4) e3 = e0 % 136.14/20.27 | % 136.14/20.27 | SIMP: (4) implies: % 136.14/20.27 | (5) e3 = e0 % 136.14/20.27 | % 136.14/20.27 | REDUCE: (3), (5) imply: % 136.14/20.27 | (6) $false % 136.14/20.27 | % 136.14/20.27 | CLOSE: (6) is inconsistent. % 136.14/20.27 | % 136.14/20.27 End of proof % 136.14/20.27 % 136.14/20.27 Sub-proof #449 shows that the following formulas are inconsistent: % 136.14/20.27 ---------------------------------------------------------------- % 136.14/20.27 (1) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.27 (2) all_57_3 = e0 % 136.14/20.27 (3) ~ (e1 = e0) % 136.14/20.27 % 136.14/20.27 Begin of proof % 136.14/20.27 | % 136.14/20.27 | ALPHA: (1) implies: % 136.14/20.27 | (4) all_57_3 = e1 % 136.14/20.27 | % 136.14/20.27 | COMBINE_EQS: (2), (4) imply: % 136.14/20.27 | (5) e1 = e0 % 136.14/20.27 | % 136.14/20.27 | REDUCE: (3), (5) imply: % 136.14/20.27 | (6) $false % 136.14/20.27 | % 136.14/20.27 | CLOSE: (6) is inconsistent. % 136.14/20.27 | % 136.14/20.27 End of proof % 136.14/20.27 % 136.14/20.27 Sub-proof #450 shows that the following formulas are inconsistent: % 136.14/20.27 ---------------------------------------------------------------- % 136.14/20.27 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.27 (2) op(e2, e3) = e2 % 136.14/20.27 (3) op(e2, e3) = e1 % 136.14/20.27 (4) ~ (e2 = e1) % 136.14/20.27 % 136.14/20.27 Begin of proof % 136.14/20.27 | % 136.14/20.27 | GROUND_INST: instantiating (1) with e1, e2, e3, e2, simplifying with (2), (3) % 136.14/20.27 | gives: % 136.14/20.27 | (5) e2 = e1 % 136.14/20.27 | % 136.14/20.27 | REDUCE: (4), (5) imply: % 136.14/20.27 | (6) $false % 136.14/20.27 | % 136.14/20.27 | CLOSE: (6) is inconsistent. % 136.14/20.27 | % 136.14/20.27 End of proof % 136.14/20.27 % 136.14/20.27 Sub-proof #451 shows that the following formulas are inconsistent: % 136.14/20.27 ---------------------------------------------------------------- % 136.14/20.27 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.27 (2) op(e2, e0) = e2 % 136.14/20.27 (3) op(e2, e0) = e0 % 136.14/20.27 (4) ~ (e2 = e0) % 136.14/20.27 % 136.14/20.27 Begin of proof % 136.14/20.27 | % 136.14/20.27 | GROUND_INST: instantiating (1) with e0, e2, e0, e2, simplifying with (2), (3) % 136.14/20.27 | gives: % 136.14/20.27 | (5) e2 = e0 % 136.14/20.27 | % 136.14/20.27 | REDUCE: (4), (5) imply: % 136.14/20.27 | (6) $false % 136.14/20.27 | % 136.14/20.27 | CLOSE: (6) is inconsistent. % 136.14/20.27 | % 136.14/20.27 End of proof % 136.14/20.27 % 136.14/20.27 Sub-proof #452 shows that the following formulas are inconsistent: % 136.14/20.27 ---------------------------------------------------------------- % 136.14/20.27 (1) op(e2, e2) = e0 % 136.14/20.27 (2) all_57_5 = e2 % 136.14/20.27 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.27 (4) ~ (e2 = e1) % 136.14/20.27 (5) op(e2, e0) = e0 % 136.14/20.27 (6) all_57_2 = e3 % 136.14/20.27 (7) ~ (e3 = e1) % 136.14/20.27 (8) ~ (e1 = e0) % 136.14/20.27 (9) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.27 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.14/20.27 % 136.14/20.27 Begin of proof % 136.14/20.27 | % 136.14/20.27 | BETA: splitting (9) gives: % 136.14/20.27 | % 136.14/20.27 | Case 1: % 136.14/20.27 | | % 136.14/20.27 | | (10) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = % 136.14/20.27 | | e1) % 136.14/20.27 | | % 136.14/20.27 | | BETA: splitting (10) gives: % 136.14/20.27 | | % 136.14/20.27 | | Case 1: % 136.14/20.27 | | | % 136.14/20.27 | | | (11) all_57_2 = e1 & op(e2, e3) = e1 % 136.14/20.27 | | | % 136.14/20.27 | | | REF_CLOSE: (6), (7), (11) are inconsistent by sub-proof #453. % 136.14/20.27 | | | % 136.14/20.27 | | Case 2: % 136.14/20.27 | | | % 136.14/20.28 | | | (12) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.28 | | | % 136.14/20.28 | | | ALPHA: (12) implies: % 136.14/20.28 | | | (13) op(e2, e2) = e1 % 136.14/20.28 | | | % 136.14/20.28 | | | REF_CLOSE: (1), (3), (8), (13) are inconsistent by sub-proof #675. % 136.14/20.28 | | | % 136.14/20.28 | | End of split % 136.14/20.28 | | % 136.14/20.28 | Case 2: % 136.14/20.28 | | % 136.14/20.28 | | (14) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = % 136.14/20.28 | | e1) % 136.14/20.28 | | % 136.14/20.28 | | BETA: splitting (14) gives: % 136.14/20.28 | | % 136.14/20.28 | | Case 1: % 136.14/20.28 | | | % 136.14/20.28 | | | (15) all_57_5 = e1 & op(e2, e1) = e1 % 136.14/20.28 | | | % 136.14/20.28 | | | REF_CLOSE: (2), (4), (15) are inconsistent by sub-proof #500. % 136.14/20.28 | | | % 136.14/20.28 | | Case 2: % 136.14/20.28 | | | % 136.14/20.28 | | | (16) all_57_10 = e1 & op(e2, e0) = e1 % 136.14/20.28 | | | % 136.14/20.28 | | | ALPHA: (16) implies: % 136.14/20.28 | | | (17) op(e2, e0) = e1 % 136.14/20.28 | | | % 136.14/20.28 | | | REF_CLOSE: (3), (5), (8), (17) are inconsistent by sub-proof #695. % 136.14/20.28 | | | % 136.14/20.28 | | End of split % 136.14/20.28 | | % 136.14/20.28 | End of split % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #453 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.28 (1) all_57_2 = e1 & op(e2, e3) = e1 % 136.14/20.28 (2) all_57_2 = e3 % 136.14/20.28 (3) ~ (e3 = e1) % 136.14/20.28 % 136.14/20.28 Begin of proof % 136.14/20.28 | % 136.14/20.28 | ALPHA: (1) implies: % 136.14/20.28 | (4) all_57_2 = e1 % 136.14/20.28 | % 136.14/20.28 | COMBINE_EQS: (2), (4) imply: % 136.14/20.28 | (5) e3 = e1 % 136.14/20.28 | % 136.14/20.28 | REDUCE: (3), (5) imply: % 136.14/20.28 | (6) $false % 136.14/20.28 | % 136.14/20.28 | CLOSE: (6) is inconsistent. % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #454 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.28 (1) all_57_2 = e2 & op(e2, e3) = e2 % 136.14/20.28 (2) all_57_2 = e3 % 136.14/20.28 (3) ~ (e3 = e2) % 136.14/20.28 % 136.14/20.28 Begin of proof % 136.14/20.28 | % 136.14/20.28 | ALPHA: (1) implies: % 136.14/20.28 | (4) all_57_2 = e2 % 136.14/20.28 | % 136.14/20.28 | COMBINE_EQS: (2), (4) imply: % 136.14/20.28 | (5) e3 = e2 % 136.14/20.28 | % 136.14/20.28 | REDUCE: (3), (5) imply: % 136.14/20.28 | (6) $false % 136.14/20.28 | % 136.14/20.28 | CLOSE: (6) is inconsistent. % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #455 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.28 (1) all_57_5 = e0 & op(e2, e1) = e0 % 136.14/20.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.28 (3) op(e2, e1) = all_52_9 % 136.14/20.28 (4) ~ (all_52_9 = e0) % 136.14/20.28 % 136.14/20.28 Begin of proof % 136.14/20.28 | % 136.14/20.28 | ALPHA: (1) implies: % 136.14/20.28 | (5) op(e2, e1) = e0 % 136.14/20.28 | % 136.14/20.28 | GROUND_INST: instantiating (2) with all_52_9, e0, e1, e2, simplifying with % 136.14/20.28 | (3), (5) gives: % 136.14/20.28 | (6) all_52_9 = e0 % 136.14/20.28 | % 136.14/20.28 | REDUCE: (4), (6) imply: % 136.14/20.28 | (7) $false % 136.14/20.28 | % 136.14/20.28 | CLOSE: (7) is inconsistent. % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #456 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.28 (1) all_57_2 = e0 % 136.14/20.28 (2) op(e2, e2) = e0 % 136.14/20.28 (3) all_57_5 = e2 % 136.14/20.28 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.28 (5) ~ (e2 = e1) % 136.14/20.28 (6) ~ (e3 = e0) % 136.14/20.28 (7) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 136.14/20.28 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) % 136.14/20.28 (8) ~ (all_52_9 = e3) % 136.14/20.28 (9) op(e2, e1) = all_52_9 % 136.14/20.28 (10) ~ (e3 = e1) % 136.14/20.28 (11) ~ (e1 = e0) % 136.14/20.28 (12) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.28 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.14/20.28 % 136.14/20.28 Begin of proof % 136.14/20.28 | % 136.14/20.28 | BETA: splitting (7) gives: % 136.14/20.28 | % 136.14/20.28 | Case 1: % 136.14/20.28 | | % 136.14/20.28 | | (13) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = % 136.14/20.28 | | e3) % 136.14/20.28 | | % 136.14/20.28 | | REF_CLOSE: (1), (2), (4), (6), (13) are inconsistent by sub-proof #502. % 136.14/20.28 | | % 136.14/20.28 | Case 2: % 136.14/20.28 | | % 136.14/20.28 | | (14) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = % 136.14/20.28 | | e3) % 136.14/20.28 | | % 136.14/20.28 | | BETA: splitting (14) gives: % 136.14/20.28 | | % 136.14/20.28 | | Case 1: % 136.14/20.28 | | | % 136.14/20.28 | | | (15) all_57_5 = e3 & op(e2, e1) = e3 % 136.14/20.28 | | | % 136.14/20.28 | | | REF_CLOSE: (4), (8), (9), (15) are inconsistent by sub-proof #547. % 136.14/20.28 | | | % 136.14/20.28 | | Case 2: % 136.14/20.28 | | | % 136.14/20.28 | | | (16) all_57_10 = e3 & op(e2, e0) = e3 % 136.14/20.28 | | | % 136.14/20.28 | | | ALPHA: (16) implies: % 136.14/20.28 | | | (17) all_57_10 = e3 % 136.14/20.28 | | | % 136.14/20.28 | | | REF_CLOSE: (1), (2), (3), (4), (5), (10), (11), (12), (17) are % 136.14/20.28 | | | inconsistent by sub-proof #499. % 136.14/20.28 | | | % 136.14/20.28 | | End of split % 136.14/20.28 | | % 136.14/20.28 | End of split % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #457 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.28 (1) op(e2, e2) = e0 % 136.14/20.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.28 (3) ~ (e3 = e0) % 136.14/20.28 (4) ~ (all_10_2 = e0) % 136.14/20.28 (5) op(e3, e3) = all_10_2 % 136.14/20.28 (6) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.14/20.28 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.14/20.28 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.14/20.28 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.14/20.28 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 136.14/20.28 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 136.14/20.28 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 136.14/20.28 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.14/20.28 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.28 $i(all_56_17) & $i(all_56_25)) % 136.14/20.28 % 136.14/20.28 Begin of proof % 136.14/20.28 | % 136.14/20.28 | BETA: splitting (6) gives: % 136.14/20.28 | % 136.14/20.28 | Case 1: % 136.14/20.28 | | % 136.14/20.28 | | (7) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.14/20.28 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.14/20.28 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.14/20.28 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.14/20.28 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.14/20.28 | | % 136.14/20.28 | | ALPHA: (7) implies: % 136.14/20.28 | | (8) op(e3, e3) = e0 % 136.14/20.28 | | % 136.14/20.28 | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #534. % 136.14/20.28 | | % 136.14/20.28 | Case 2: % 136.14/20.28 | | % 136.14/20.28 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.14/20.28 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.28 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.14/20.28 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) % 136.14/20.28 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.14/20.28 | | % 136.14/20.28 | | ALPHA: (9) implies: % 136.14/20.28 | | (10) op(e2, e2) = e3 % 136.14/20.28 | | % 136.14/20.28 | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #641. % 136.14/20.28 | | % 136.14/20.28 | End of split % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #458 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.28 (1) ~ (e2 = e0) % 136.14/20.28 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) | % 136.14/20.28 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.28 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.28 (4) ~ (e2 = e1) % 136.14/20.28 (5) ~ (e3 = e0) % 136.14/20.28 (6) ~ (e3 = e2) % 136.14/20.28 (7) op(e0, e1) = all_52_11 % 136.14/20.28 (8) ~ (all_52_11 = e3) % 136.14/20.28 (9) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) | % 136.14/20.28 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.28 (10) op(e0, e0) = e2 % 136.14/20.28 (11) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.28 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.14/20.28 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.28 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.28 (12) ~ (e3 = e1) % 136.14/20.28 (13) ~ (e1 = e0) % 136.14/20.28 (14) all_57_12 = e2 % 136.14/20.28 % 136.14/20.28 Begin of proof % 136.14/20.28 | % 136.14/20.28 | BETA: splitting (2) gives: % 136.14/20.28 | % 136.14/20.28 | Case 1: % 136.14/20.28 | | % 136.14/20.28 | | (15) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = % 136.14/20.28 | | e3) % 136.14/20.28 | | % 136.14/20.28 | | BETA: splitting (15) gives: % 136.14/20.28 | | % 136.14/20.28 | | Case 1: % 136.14/20.28 | | | % 136.14/20.28 | | | (16) all_57_12 = e3 & op(e0, e3) = e3 % 136.14/20.28 | | | % 136.14/20.28 | | | ALPHA: (16) implies: % 136.14/20.28 | | | (17) all_57_12 = e3 % 136.14/20.28 | | | % 136.14/20.28 | | | REF_CLOSE: (6), (14), (17) are inconsistent by sub-proof #518. % 136.14/20.28 | | | % 136.14/20.28 | | Case 2: % 136.14/20.28 | | | % 136.14/20.28 | | | (18) all_57_13 = e3 & op(e0, e2) = e3 % 136.14/20.28 | | | % 136.14/20.28 | | | ALPHA: (18) implies: % 136.14/20.28 | | | (19) all_57_13 = e3 % 136.14/20.28 | | | % 136.14/20.28 | | | REF_CLOSE: (1), (3), (4), (5), (9), (10), (11), (12), (13), (14), (19) are % 136.14/20.28 | | | inconsistent by sub-proof #482. % 136.14/20.28 | | | % 136.14/20.28 | | End of split % 136.14/20.28 | | % 136.14/20.28 | Case 2: % 136.14/20.28 | | % 136.14/20.28 | | (20) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = % 136.14/20.28 | | e3) % 136.14/20.28 | | % 136.14/20.28 | | REF_CLOSE: (3), (6), (7), (8), (10), (20) are inconsistent by sub-proof % 136.14/20.28 | | #459. % 136.14/20.28 | | % 136.14/20.28 | End of split % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #459 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.28 (1) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.14/20.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.28 (3) ~ (e3 = e2) % 136.14/20.28 (4) op(e0, e1) = all_52_11 % 136.14/20.28 (5) ~ (all_52_11 = e3) % 136.14/20.28 (6) op(e0, e0) = e2 % 136.14/20.28 % 136.14/20.28 Begin of proof % 136.14/20.28 | % 136.14/20.28 | BETA: splitting (1) gives: % 136.14/20.28 | % 136.14/20.28 | Case 1: % 136.14/20.28 | | % 136.14/20.28 | | (7) all_57_14 = e3 & op(e0, e1) = e3 % 136.14/20.28 | | % 136.14/20.28 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #652. % 136.14/20.28 | | % 136.14/20.28 | Case 2: % 136.14/20.28 | | % 136.14/20.28 | | (8) all_57_15 = e3 & op(e0, e0) = e3 % 136.14/20.28 | | % 136.14/20.28 | | ALPHA: (8) implies: % 136.14/20.28 | | (9) op(e0, e0) = e3 % 136.14/20.28 | | % 136.14/20.28 | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #634. % 136.14/20.28 | | % 136.14/20.28 | End of split % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #460 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.28 (1) all_57_9 = e2 & op(e3, e0) = e2 % 136.14/20.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.28 (3) op(e3, e0) = all_52_12 % 136.14/20.28 (4) ~ (all_52_12 = e2) % 136.14/20.28 % 136.14/20.28 Begin of proof % 136.14/20.28 | % 136.14/20.28 | ALPHA: (1) implies: % 136.14/20.28 | (5) op(e3, e0) = e2 % 136.14/20.28 | % 136.14/20.28 | GROUND_INST: instantiating (2) with all_52_12, e2, e0, e3, simplifying with % 136.14/20.28 | (3), (5) gives: % 136.14/20.28 | (6) all_52_12 = e2 % 136.14/20.28 | % 136.14/20.28 | REDUCE: (4), (6) imply: % 136.14/20.28 | (7) $false % 136.14/20.28 | % 136.14/20.28 | CLOSE: (7) is inconsistent. % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #461 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.28 (1) all_57_5 = e0 & op(e2, e1) = e0 % 136.14/20.28 (2) all_57_5 = e1 % 136.14/20.28 (3) ~ (e1 = e0) % 136.14/20.28 % 136.14/20.28 Begin of proof % 136.14/20.28 | % 136.14/20.28 | ALPHA: (1) implies: % 136.14/20.28 | (4) all_57_5 = e0 % 136.14/20.28 | % 136.14/20.28 | COMBINE_EQS: (2), (4) imply: % 136.14/20.28 | (5) e1 = e0 % 136.14/20.28 | % 136.14/20.28 | REDUCE: (3), (5) imply: % 136.14/20.28 | (6) $false % 136.14/20.28 | % 136.14/20.28 | CLOSE: (6) is inconsistent. % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #462 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.28 (1) all_57_4 = e1 & op(e3, e1) = e1 % 136.14/20.28 (2) all_57_4 = e2 % 136.14/20.28 (3) ~ (e2 = e1) % 136.14/20.28 % 136.14/20.28 Begin of proof % 136.14/20.28 | % 136.14/20.28 | ALPHA: (1) implies: % 136.14/20.28 | (4) all_57_4 = e1 % 136.14/20.28 | % 136.14/20.28 | COMBINE_EQS: (2), (4) imply: % 136.14/20.28 | (5) e2 = e1 % 136.14/20.28 | % 136.14/20.28 | REDUCE: (3), (5) imply: % 136.14/20.28 | (6) $false % 136.14/20.28 | % 136.14/20.28 | CLOSE: (6) is inconsistent. % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #463 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.28 (1) ~ (all_52_6 = e3) % 136.14/20.28 (2) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.14/20.28 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 136.14/20.28 (3) ~ (e2 = e0) % 136.14/20.28 (4) all_57_1 = e2 % 136.14/20.28 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.28 (6) ~ (e2 = e1) % 136.14/20.28 (7) ~ (e3 = e0) % 136.14/20.28 (8) ~ (e3 = e2) % 136.14/20.28 (9) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 136.14/20.28 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) % 136.14/20.28 (10) op(e1, e2) = all_52_6 % 136.14/20.28 (11) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.14/20.28 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.14/20.28 (12) ~ (e3 = e1) % 136.14/20.28 (13) ~ (e1 = e0) % 136.14/20.28 (14) all_57_3 = e2 % 136.14/20.28 % 136.14/20.28 Begin of proof % 136.14/20.28 | % 136.14/20.28 | BETA: splitting (9) gives: % 136.14/20.28 | % 136.14/20.28 | Case 1: % 136.14/20.28 | | % 136.14/20.28 | | (15) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = % 136.14/20.28 | | e3) % 136.14/20.28 | | % 136.14/20.28 | | BETA: splitting (15) gives: % 136.14/20.28 | | % 136.14/20.28 | | Case 1: % 136.14/20.28 | | | % 136.14/20.28 | | | (16) all_57_1 = e3 & op(e3, e2) = e3 % 136.14/20.28 | | | % 136.14/20.28 | | | REF_CLOSE: (4), (8), (16) are inconsistent by sub-proof #704. % 136.14/20.28 | | | % 136.14/20.28 | | Case 2: % 136.14/20.28 | | | % 136.14/20.28 | | | (17) all_57_3 = e3 & op(e2, e2) = e3 % 136.14/20.28 | | | % 136.14/20.28 | | | ALPHA: (17) implies: % 136.14/20.28 | | | (18) all_57_3 = e3 % 136.14/20.28 | | | % 136.14/20.28 | | | REF_CLOSE: (8), (14), (18) are inconsistent by sub-proof #762. % 136.14/20.28 | | | % 136.14/20.28 | | End of split % 136.14/20.28 | | % 136.14/20.28 | Case 2: % 136.14/20.28 | | % 136.14/20.28 | | (19) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = % 136.14/20.28 | | e3) % 136.14/20.28 | | % 136.14/20.28 | | BETA: splitting (19) gives: % 136.14/20.28 | | % 136.14/20.28 | | Case 1: % 136.14/20.28 | | | % 136.14/20.28 | | | (20) all_57_7 = e3 & op(e1, e2) = e3 % 136.14/20.28 | | | % 136.14/20.28 | | | ALPHA: (20) implies: % 136.14/20.28 | | | (21) op(e1, e2) = e3 % 136.14/20.28 | | | % 136.14/20.28 | | | REF_CLOSE: (1), (5), (10), (21) are inconsistent by sub-proof #654. % 136.14/20.28 | | | % 136.14/20.28 | | Case 2: % 136.14/20.28 | | | % 136.14/20.28 | | | (22) all_57_13 = e3 & op(e0, e2) = e3 % 136.14/20.28 | | | % 136.14/20.28 | | | ALPHA: (22) implies: % 136.14/20.28 | | | (23) all_57_13 = e3 % 136.14/20.28 | | | % 136.14/20.28 | | | BETA: splitting (2) gives: % 136.14/20.28 | | | % 136.14/20.28 | | | Case 1: % 136.14/20.28 | | | | % 136.14/20.28 | | | | (24) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) % 136.14/20.28 | | | | = e0) % 136.14/20.28 | | | | % 136.14/20.28 | | | | BETA: splitting (24) gives: % 136.14/20.28 | | | | % 136.14/20.28 | | | | Case 1: % 136.14/20.28 | | | | | % 136.14/20.28 | | | | | (25) all_57_1 = e0 & op(e3, e2) = e0 % 136.14/20.28 | | | | | % 136.14/20.28 | | | | | REF_CLOSE: (3), (4), (25) are inconsistent by sub-proof #466. % 136.14/20.28 | | | | | % 136.14/20.28 | | | | Case 2: % 136.14/20.28 | | | | | % 136.14/20.28 | | | | | (26) all_57_3 = e0 & op(e2, e2) = e0 % 136.14/20.28 | | | | | % 136.14/20.28 | | | | | REF_CLOSE: (3), (14), (26) are inconsistent by sub-proof #627. % 136.14/20.28 | | | | | % 136.14/20.28 | | | | End of split % 136.14/20.28 | | | | % 136.14/20.28 | | | Case 2: % 136.14/20.28 | | | | % 136.14/20.28 | | | | (27) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) % 136.14/20.28 | | | | = e0) % 136.14/20.28 | | | | % 136.14/20.28 | | | | BETA: splitting (27) gives: % 136.14/20.28 | | | | % 136.14/20.28 | | | | Case 1: % 136.14/20.28 | | | | | % 136.14/20.28 | | | | | (28) all_57_7 = e0 & op(e1, e2) = e0 % 136.14/20.28 | | | | | % 136.14/20.28 | | | | | ALPHA: (28) implies: % 136.14/20.28 | | | | | (29) all_57_7 = e0 % 136.14/20.28 | | | | | % 136.14/20.28 | | | | | BETA: splitting (11) gives: % 136.14/20.28 | | | | | % 136.14/20.28 | | | | | Case 1: % 136.14/20.28 | | | | | | % 136.14/20.28 | | | | | | (30) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, % 136.14/20.28 | | | | | | e2) = e1) % 136.14/20.28 | | | | | | % 136.14/20.28 | | | | | | BETA: splitting (30) gives: % 136.14/20.28 | | | | | | % 136.14/20.28 | | | | | | Case 1: % 136.14/20.28 | | | | | | | % 136.14/20.28 | | | | | | | (31) all_57_1 = e1 & op(e3, e2) = e1 % 136.14/20.28 | | | | | | | % 136.14/20.28 | | | | | | | REF_CLOSE: (4), (6), (31) are inconsistent by sub-proof #465. % 136.14/20.28 | | | | | | | % 136.14/20.28 | | | | | | Case 2: % 136.14/20.28 | | | | | | | % 136.14/20.28 | | | | | | | (32) all_57_3 = e1 & op(e2, e2) = e1 % 136.14/20.28 | | | | | | | % 136.14/20.28 | | | | | | | ALPHA: (32) implies: % 136.14/20.28 | | | | | | | (33) all_57_3 = e1 % 136.14/20.28 | | | | | | | % 136.14/20.28 | | | | | | | COMBINE_EQS: (14), (33) imply: % 136.14/20.28 | | | | | | | (34) e2 = e1 % 136.14/20.28 | | | | | | | % 136.14/20.28 | | | | | | | REDUCE: (6), (34) imply: % 136.14/20.28 | | | | | | | (35) $false % 136.14/20.28 | | | | | | | % 136.14/20.28 | | | | | | | CLOSE: (35) is inconsistent. % 136.14/20.28 | | | | | | | % 136.14/20.28 | | | | | | End of split % 136.14/20.28 | | | | | | % 136.14/20.28 | | | | | Case 2: % 136.14/20.28 | | | | | | % 136.14/20.28 | | | | | | (36) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, % 136.14/20.28 | | | | | | e2) = e1) % 136.14/20.28 | | | | | | % 136.14/20.28 | | | | | | BETA: splitting (36) gives: % 136.14/20.28 | | | | | | % 136.14/20.28 | | | | | | Case 1: % 136.14/20.28 | | | | | | | % 136.14/20.28 | | | | | | | (37) all_57_7 = e1 & op(e1, e2) = e1 % 136.14/20.28 | | | | | | | % 136.14/20.28 | | | | | | | ALPHA: (37) implies: % 136.14/20.28 | | | | | | | (38) all_57_7 = e1 % 136.14/20.28 | | | | | | | % 136.14/20.28 | | | | | | | REF_CLOSE: (13), (29), (38) are inconsistent by sub-proof #464. % 136.14/20.28 | | | | | | | % 136.14/20.28 | | | | | | Case 2: % 136.14/20.28 | | | | | | | % 136.14/20.28 | | | | | | | (39) all_57_13 = e1 & op(e0, e2) = e1 % 136.14/20.28 | | | | | | | % 136.14/20.28 | | | | | | | REF_CLOSE: (12), (23), (39) are inconsistent by sub-proof #726. % 136.14/20.28 | | | | | | | % 136.14/20.28 | | | | | | End of split % 136.14/20.28 | | | | | | % 136.14/20.28 | | | | | End of split % 136.14/20.28 | | | | | % 136.14/20.28 | | | | Case 2: % 136.14/20.28 | | | | | % 136.14/20.28 | | | | | (40) all_57_13 = e0 & op(e0, e2) = e0 % 136.14/20.28 | | | | | % 136.14/20.28 | | | | | ALPHA: (40) implies: % 136.14/20.28 | | | | | (41) all_57_13 = e0 % 136.14/20.28 | | | | | % 136.14/20.28 | | | | | COMBINE_EQS: (23), (41) imply: % 136.14/20.28 | | | | | (42) e3 = e0 % 136.14/20.28 | | | | | % 136.14/20.28 | | | | | REDUCE: (7), (42) imply: % 136.14/20.28 | | | | | (43) $false % 136.14/20.28 | | | | | % 136.14/20.28 | | | | | CLOSE: (43) is inconsistent. % 136.14/20.28 | | | | | % 136.14/20.28 | | | | End of split % 136.14/20.28 | | | | % 136.14/20.28 | | | End of split % 136.14/20.28 | | | % 136.14/20.28 | | End of split % 136.14/20.28 | | % 136.14/20.28 | End of split % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #464 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.28 (1) all_57_7 = e1 % 136.14/20.28 (2) all_57_7 = e0 % 136.14/20.28 (3) ~ (e1 = e0) % 136.14/20.28 % 136.14/20.28 Begin of proof % 136.14/20.28 | % 136.14/20.28 | COMBINE_EQS: (1), (2) imply: % 136.14/20.28 | (4) e1 = e0 % 136.14/20.28 | % 136.14/20.28 | SIMP: (4) implies: % 136.14/20.28 | (5) e1 = e0 % 136.14/20.28 | % 136.14/20.28 | REDUCE: (3), (5) imply: % 136.14/20.28 | (6) $false % 136.14/20.28 | % 136.14/20.28 | CLOSE: (6) is inconsistent. % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #465 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.28 (1) all_57_1 = e1 & op(e3, e2) = e1 % 136.14/20.28 (2) all_57_1 = e2 % 136.14/20.28 (3) ~ (e2 = e1) % 136.14/20.28 % 136.14/20.28 Begin of proof % 136.14/20.28 | % 136.14/20.28 | ALPHA: (1) implies: % 136.14/20.28 | (4) all_57_1 = e1 % 136.14/20.28 | % 136.14/20.28 | COMBINE_EQS: (2), (4) imply: % 136.14/20.28 | (5) e2 = e1 % 136.14/20.28 | % 136.14/20.28 | REDUCE: (3), (5) imply: % 136.14/20.28 | (6) $false % 136.14/20.28 | % 136.14/20.28 | CLOSE: (6) is inconsistent. % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #466 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.28 (1) all_57_1 = e0 & op(e3, e2) = e0 % 136.14/20.28 (2) all_57_1 = e2 % 136.14/20.28 (3) ~ (e2 = e0) % 136.14/20.28 % 136.14/20.28 Begin of proof % 136.14/20.28 | % 136.14/20.28 | ALPHA: (1) implies: % 136.14/20.28 | (4) all_57_1 = e0 % 136.14/20.28 | % 136.14/20.28 | COMBINE_EQS: (2), (4) imply: % 136.14/20.28 | (5) e2 = e0 % 136.14/20.28 | % 136.14/20.28 | REDUCE: (3), (5) imply: % 136.14/20.28 | (6) $false % 136.14/20.28 | % 136.14/20.28 | CLOSE: (6) is inconsistent. % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #467 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.28 (1) all_56_31 = e2 % 136.14/20.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.28 (3) ~ (e2 = e1) % 136.14/20.28 (4) ~ (e3 = e0) % 136.14/20.28 (5) op(e1, e1) = e3 % 136.14/20.28 (6) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.14/20.28 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 136.14/20.28 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.14/20.28 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 136.14/20.28 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.14/20.28 e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 136.14/20.28 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.14/20.28 = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.28 $i(all_56_21) & $i(all_56_29)) % 136.14/20.28 % 136.14/20.28 Begin of proof % 136.14/20.28 | % 136.14/20.28 | BETA: splitting (6) gives: % 136.14/20.28 | % 136.14/20.28 | Case 1: % 136.14/20.28 | | % 136.14/20.28 | | (7) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 % 136.14/20.28 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 % 136.14/20.28 | | & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.14/20.28 | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) % 136.14/20.28 | | % 136.14/20.28 | | ALPHA: (7) implies: % 136.14/20.28 | | (8) op(e1, e1) = e0 % 136.14/20.28 | | % 136.14/20.28 | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #753. % 136.14/20.28 | | % 136.14/20.28 | Case 2: % 136.14/20.28 | | % 136.14/20.28 | | (9) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.14/20.28 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 136.14/20.28 | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 136.14/20.28 | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.28 | | $i(all_56_21) & $i(all_56_29) % 136.14/20.28 | | % 136.14/20.28 | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #525. % 136.14/20.28 | | % 136.14/20.28 | End of split % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #468 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.28 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.14/20.28 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.14/20.28 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.14/20.28 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.14/20.28 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ % 136.14/20.28 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 136.14/20.28 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = % 136.14/20.28 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.14/20.28 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.14/20.28 $i(all_56_29)) % 136.14/20.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.28 (3) ~ (e2 = e1) % 136.14/20.28 (4) op(e1, e3) = e2 % 136.14/20.28 (5) ~ (all_52_9 = e2) % 136.14/20.28 (6) op(e2, e1) = all_52_9 % 136.14/20.28 (7) op(e1, e3) = all_52_2 % 136.14/20.28 % 136.14/20.28 Begin of proof % 136.14/20.28 | % 136.14/20.28 | BETA: splitting (1) gives: % 136.14/20.28 | % 136.14/20.28 | Case 1: % 136.14/20.28 | | % 136.14/20.28 | | (8) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.14/20.28 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.14/20.28 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.14/20.28 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) % 136.14/20.28 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.14/20.28 | | % 136.14/20.28 | | ALPHA: (8) implies: % 136.14/20.28 | | (9) op(e1, e3) = e1 % 136.14/20.28 | | % 136.14/20.28 | | REF_CLOSE: (2), (3), (4), (7), (9) are inconsistent by sub-proof #517. % 136.14/20.28 | | % 136.14/20.28 | Case 2: % 136.14/20.28 | | % 136.14/20.28 | | (10) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.14/20.28 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = % 136.14/20.28 | | e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.14/20.28 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.14/20.28 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.14/20.28 | | % 136.14/20.28 | | ALPHA: (10) implies: % 136.14/20.28 | | (11) op(e2, e1) = e2 % 136.14/20.28 | | % 136.14/20.28 | | REF_CLOSE: (2), (5), (6), (11) are inconsistent by sub-proof #770. % 136.14/20.28 | | % 136.14/20.28 | End of split % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #469 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.28 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 136.14/20.28 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 136.14/20.28 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.14/20.28 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.14/20.28 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.14/20.28 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.14/20.28 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 136.14/20.28 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.14/20.28 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.14/20.28 $i(all_56_21) & $i(all_56_29)) % 136.14/20.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.28 (3) op(e3, e3) = all_10_2 % 136.14/20.28 (4) ~ (all_10_2 = e2) % 136.14/20.28 (5) op(e3, e1) = all_52_8 % 136.14/20.28 (6) ~ (all_52_8 = e3) % 136.14/20.28 % 136.14/20.28 Begin of proof % 136.14/20.28 | % 136.14/20.28 | BETA: splitting (1) gives: % 136.14/20.28 | % 136.14/20.28 | Case 1: % 136.14/20.28 | | % 136.14/20.28 | | (7) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.14/20.28 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.14/20.28 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.14/20.28 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.14/20.28 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.14/20.28 | | % 136.14/20.28 | | ALPHA: (7) implies: % 136.14/20.28 | | (8) op(e3, e3) = e2 % 136.14/20.28 | | % 136.14/20.28 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #536. % 136.14/20.28 | | % 136.14/20.28 | Case 2: % 136.14/20.28 | | % 136.14/20.28 | | (9) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.14/20.28 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 136.14/20.28 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.14/20.28 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.14/20.28 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.14/20.28 | | % 136.14/20.28 | | ALPHA: (9) implies: % 136.14/20.28 | | (10) op(e3, e1) = e3 % 136.14/20.28 | | % 136.14/20.28 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #705. % 136.14/20.28 | | % 136.14/20.28 | End of split % 136.14/20.28 | % 136.14/20.28 End of proof % 136.14/20.28 % 136.14/20.28 Sub-proof #470 shows that the following formulas are inconsistent: % 136.14/20.28 ---------------------------------------------------------------- % 136.14/20.29 (1) all_54_13 = e1 | all_54_13 = e0 % 136.14/20.29 (2) all_54_13 = all_52_7 % 136.14/20.29 (3) ~ (all_52_7 = e1) % 136.14/20.29 (4) ~ (all_52_7 = e0) % 136.14/20.29 % 136.14/20.29 Begin of proof % 136.14/20.29 | % 136.14/20.29 | BETA: splitting (1) gives: % 136.14/20.29 | % 136.14/20.29 | Case 1: % 136.14/20.29 | | % 136.14/20.29 | | (5) all_54_13 = e1 % 136.14/20.29 | | % 136.14/20.29 | | COMBINE_EQS: (2), (5) imply: % 136.14/20.29 | | (6) all_52_7 = e1 % 136.14/20.29 | | % 136.14/20.29 | | SIMP: (6) implies: % 136.14/20.29 | | (7) all_52_7 = e1 % 136.14/20.29 | | % 136.14/20.29 | | REDUCE: (3), (7) imply: % 136.14/20.29 | | (8) $false % 136.14/20.29 | | % 136.14/20.29 | | CLOSE: (8) is inconsistent. % 136.14/20.29 | | % 136.14/20.29 | Case 2: % 136.14/20.29 | | % 136.14/20.29 | | (9) all_54_13 = e0 % 136.14/20.29 | | % 136.14/20.29 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #471. % 136.14/20.29 | | % 136.14/20.29 | End of split % 136.14/20.29 | % 136.14/20.29 End of proof % 136.14/20.29 % 136.14/20.29 Sub-proof #471 shows that the following formulas are inconsistent: % 136.14/20.29 ---------------------------------------------------------------- % 136.14/20.29 (1) all_54_13 = all_52_7 % 136.14/20.29 (2) all_54_13 = e0 % 136.14/20.29 (3) ~ (all_52_7 = e0) % 136.14/20.29 % 136.14/20.29 Begin of proof % 136.14/20.29 | % 136.14/20.29 | COMBINE_EQS: (1), (2) imply: % 136.14/20.29 | (4) all_52_7 = e0 % 136.14/20.29 | % 136.14/20.29 | SIMP: (4) implies: % 136.14/20.29 | (5) all_52_7 = e0 % 136.14/20.29 | % 136.14/20.29 | REDUCE: (3), (5) imply: % 136.14/20.29 | (6) $false % 136.14/20.29 | % 136.14/20.29 | CLOSE: (6) is inconsistent. % 136.14/20.29 | % 136.14/20.29 End of proof % 136.14/20.29 % 136.14/20.29 Sub-proof #472 shows that the following formulas are inconsistent: % 136.14/20.29 ---------------------------------------------------------------- % 136.14/20.29 (1) all_54_13 = all_52_7 % 136.14/20.29 (2) all_54_13 = e2 % 136.14/20.29 (3) ~ (all_52_7 = e2) % 136.14/20.29 % 136.14/20.29 Begin of proof % 136.14/20.29 | % 136.14/20.29 | COMBINE_EQS: (1), (2) imply: % 136.14/20.29 | (4) all_52_7 = e2 % 136.14/20.29 | % 136.14/20.29 | SIMP: (4) implies: % 136.14/20.29 | (5) all_52_7 = e2 % 136.14/20.29 | % 136.14/20.29 | REDUCE: (3), (5) imply: % 136.14/20.29 | (6) $false % 136.14/20.29 | % 136.14/20.29 | CLOSE: (6) is inconsistent. % 136.14/20.29 | % 136.14/20.29 End of proof % 136.14/20.29 % 136.14/20.29 Sub-proof #473 shows that the following formulas are inconsistent: % 136.14/20.29 ---------------------------------------------------------------- % 136.14/20.29 (1) ~ (all_52_2 = e1) % 136.14/20.29 (2) all_54_8 = all_50_0 % 136.14/20.29 (3) ~ (all_52_2 = e0) % 136.14/20.29 (4) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0 % 136.14/20.29 (5) ~ (all_50_0 = e2) % 136.14/20.29 (6) all_54_8 = all_52_2 % 136.14/20.29 % 136.14/20.29 Begin of proof % 136.14/20.29 | % 136.14/20.29 | BETA: splitting (4) gives: % 136.14/20.29 | % 136.14/20.29 | Case 1: % 136.14/20.29 | | % 136.14/20.29 | | (7) all_54_8 = e2 % 136.14/20.29 | | % 136.14/20.29 | | COMBINE_EQS: (2), (7) imply: % 136.14/20.29 | | (8) all_50_0 = e2 % 136.14/20.29 | | % 136.14/20.29 | | SIMP: (8) implies: % 136.14/20.29 | | (9) all_50_0 = e2 % 136.14/20.29 | | % 136.14/20.29 | | REDUCE: (5), (9) imply: % 136.14/20.29 | | (10) $false % 136.14/20.29 | | % 136.14/20.29 | | CLOSE: (10) is inconsistent. % 136.14/20.29 | | % 136.14/20.29 | Case 2: % 136.14/20.29 | | % 136.14/20.29 | | (11) all_54_8 = e1 | all_54_8 = e0 % 136.14/20.29 | | % 136.14/20.29 | | REF_CLOSE: (1), (3), (6), (11) are inconsistent by sub-proof #474. % 136.14/20.29 | | % 136.14/20.29 | End of split % 136.14/20.29 | % 136.14/20.29 End of proof % 136.14/20.29 % 136.14/20.29 Sub-proof #474 shows that the following formulas are inconsistent: % 136.14/20.29 ---------------------------------------------------------------- % 136.14/20.29 (1) all_54_8 = e1 | all_54_8 = e0 % 136.14/20.29 (2) all_54_8 = all_52_2 % 136.14/20.29 (3) ~ (all_52_2 = e1) % 136.14/20.29 (4) ~ (all_52_2 = e0) % 136.14/20.29 % 136.14/20.29 Begin of proof % 136.14/20.29 | % 136.14/20.29 | BETA: splitting (1) gives: % 136.14/20.29 | % 136.14/20.29 | Case 1: % 136.14/20.29 | | % 136.14/20.29 | | (5) all_54_8 = e1 % 136.14/20.29 | | % 136.14/20.29 | | COMBINE_EQS: (2), (5) imply: % 136.14/20.29 | | (6) all_52_2 = e1 % 136.14/20.29 | | % 136.14/20.29 | | SIMP: (6) implies: % 136.14/20.29 | | (7) all_52_2 = e1 % 136.14/20.29 | | % 136.14/20.29 | | REDUCE: (3), (7) imply: % 136.14/20.29 | | (8) $false % 136.14/20.29 | | % 136.14/20.29 | | CLOSE: (8) is inconsistent. % 136.14/20.29 | | % 136.14/20.29 | Case 2: % 136.14/20.29 | | % 136.14/20.29 | | (9) all_54_8 = e0 % 136.14/20.29 | | % 136.14/20.29 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #475. % 136.14/20.29 | | % 136.14/20.29 | End of split % 136.14/20.29 | % 136.14/20.29 End of proof % 136.14/20.29 % 136.14/20.29 Sub-proof #475 shows that the following formulas are inconsistent: % 136.14/20.29 ---------------------------------------------------------------- % 136.14/20.29 (1) all_54_8 = all_52_2 % 136.14/20.29 (2) all_54_8 = e0 % 136.14/20.29 (3) ~ (all_52_2 = e0) % 136.14/20.29 % 136.14/20.29 Begin of proof % 136.14/20.29 | % 136.14/20.29 | COMBINE_EQS: (1), (2) imply: % 136.14/20.29 | (4) all_52_2 = e0 % 136.14/20.29 | % 136.14/20.29 | SIMP: (4) implies: % 136.14/20.29 | (5) all_52_2 = e0 % 136.14/20.29 | % 136.14/20.29 | REDUCE: (3), (5) imply: % 136.14/20.29 | (6) $false % 136.14/20.29 | % 136.14/20.29 | CLOSE: (6) is inconsistent. % 136.14/20.29 | % 136.14/20.29 End of proof % 136.14/20.29 % 136.14/20.29 Sub-proof #476 shows that the following formulas are inconsistent: % 136.14/20.29 ---------------------------------------------------------------- % 136.14/20.29 (1) op(e1, e1) = all_6_2 % 136.14/20.29 (2) ~ (all_6_2 = e3) % 136.14/20.29 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.29 (4) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0 % 136.14/20.29 (5) all_54_2 = all_52_8 % 136.14/20.29 (6) all_54_10 = all_6_2 % 136.14/20.29 (7) op(e1, e1) = e0 % 136.14/20.29 (8) ~ (all_6_2 = e2) % 136.14/20.29 (9) ~ (all_52_8 = all_6_2) % 136.14/20.29 (10) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 136.14/20.29 (11) ~ (all_52_8 = e2) % 136.14/20.29 (12) ~ (all_52_8 = e1) % 136.14/20.29 % 136.14/20.29 Begin of proof % 136.14/20.29 | % 136.14/20.29 | BETA: splitting (4) gives: % 136.14/20.29 | % 136.14/20.29 | Case 1: % 136.14/20.29 | | % 136.14/20.29 | | (13) all_54_2 = e2 % 136.14/20.29 | | % 136.14/20.29 | | COMBINE_EQS: (5), (13) imply: % 136.14/20.29 | | (14) all_52_8 = e2 % 136.14/20.29 | | % 136.14/20.29 | | REDUCE: (11), (14) imply: % 136.14/20.29 | | (15) $false % 136.14/20.29 | | % 136.14/20.29 | | CLOSE: (15) is inconsistent. % 136.14/20.29 | | % 136.14/20.29 | Case 2: % 136.14/20.29 | | % 136.14/20.29 | | (16) all_54_2 = e1 | all_54_2 = e0 % 136.14/20.29 | | % 136.14/20.29 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (12), (16) are % 136.14/20.29 | | inconsistent by sub-proof #477. % 136.14/20.29 | | % 136.14/20.29 | End of split % 136.14/20.29 | % 136.14/20.29 End of proof % 136.14/20.29 % 136.14/20.29 Sub-proof #477 shows that the following formulas are inconsistent: % 136.14/20.29 ---------------------------------------------------------------- % 136.14/20.29 (1) op(e1, e1) = all_6_2 % 136.14/20.29 (2) ~ (all_6_2 = e3) % 136.14/20.29 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.29 (4) all_54_2 = all_52_8 % 136.14/20.29 (5) all_54_10 = all_6_2 % 136.14/20.29 (6) op(e1, e1) = e0 % 136.14/20.29 (7) ~ (all_6_2 = e2) % 136.14/20.29 (8) ~ (all_52_8 = all_6_2) % 136.14/20.29 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 136.14/20.29 (10) ~ (all_52_8 = e1) % 136.14/20.29 (11) all_54_2 = e1 | all_54_2 = e0 % 136.14/20.29 % 136.14/20.29 Begin of proof % 136.14/20.29 | % 136.14/20.29 | BETA: splitting (11) gives: % 136.14/20.29 | % 136.14/20.29 | Case 1: % 136.14/20.29 | | % 136.14/20.29 | | (12) all_54_2 = e1 % 136.14/20.29 | | % 136.14/20.29 | | COMBINE_EQS: (4), (12) imply: % 136.14/20.29 | | (13) all_52_8 = e1 % 136.14/20.29 | | % 136.14/20.29 | | REDUCE: (10), (13) imply: % 136.14/20.29 | | (14) $false % 136.14/20.29 | | % 136.14/20.29 | | CLOSE: (14) is inconsistent. % 136.14/20.29 | | % 136.14/20.29 | Case 2: % 136.14/20.29 | | % 136.14/20.29 | | (15) all_54_2 = e0 % 136.14/20.29 | | % 136.14/20.29 | | COMBINE_EQS: (4), (15) imply: % 136.14/20.29 | | (16) all_52_8 = e0 % 136.14/20.29 | | % 136.14/20.29 | | REDUCE: (8), (16) imply: % 136.14/20.29 | | (17) ~ (all_6_2 = e0) % 136.14/20.29 | | % 136.14/20.29 | | SIMP: (17) implies: % 136.14/20.29 | | (18) ~ (all_6_2 = e0) % 136.14/20.29 | | % 136.14/20.29 | | BETA: splitting (9) gives: % 136.14/20.29 | | % 136.14/20.29 | | Case 1: % 136.14/20.29 | | | % 136.14/20.29 | | | (19) all_54_10 = e3 % 136.14/20.29 | | | % 136.14/20.29 | | | REF_CLOSE: (2), (5), (19) are inconsistent by sub-proof #742. % 136.14/20.29 | | | % 136.14/20.29 | | Case 2: % 136.14/20.29 | | | % 136.14/20.29 | | | (20) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 136.14/20.29 | | | % 136.14/20.29 | | | BETA: splitting (20) gives: % 136.14/20.29 | | | % 136.14/20.29 | | | Case 1: % 136.14/20.29 | | | | % 136.14/20.29 | | | | (21) all_54_10 = e2 % 136.14/20.29 | | | | % 136.14/20.29 | | | | REF_CLOSE: (5), (7), (21) are inconsistent by sub-proof #741. % 136.14/20.29 | | | | % 136.14/20.29 | | | Case 2: % 136.14/20.29 | | | | % 136.14/20.29 | | | | (22) all_54_10 = e1 | all_54_10 = e0 % 136.14/20.29 | | | | % 136.14/20.29 | | | | BETA: splitting (22) gives: % 136.14/20.29 | | | | % 136.14/20.29 | | | | Case 1: % 136.14/20.29 | | | | | % 136.14/20.29 | | | | | (23) all_54_10 = e1 % 136.14/20.29 | | | | | % 136.14/20.29 | | | | | COMBINE_EQS: (5), (23) imply: % 136.14/20.29 | | | | | (24) all_6_2 = e1 % 136.14/20.29 | | | | | % 136.14/20.29 | | | | | SIMP: (24) implies: % 136.14/20.29 | | | | | (25) all_6_2 = e1 % 136.14/20.29 | | | | | % 136.14/20.29 | | | | | REDUCE: (18), (25) imply: % 136.14/20.29 | | | | | (26) ~ (e1 = e0) % 136.14/20.29 | | | | | % 136.14/20.29 | | | | | REDUCE: (1), (25) imply: % 136.14/20.29 | | | | | (27) op(e1, e1) = e1 % 136.14/20.29 | | | | | % 136.14/20.29 | | | | | REF_CLOSE: (3), (6), (26), (27) are inconsistent by sub-proof #721. % 136.14/20.29 | | | | | % 136.14/20.29 | | | | Case 2: % 136.14/20.29 | | | | | % 136.14/20.29 | | | | | (28) all_54_10 = e0 % 136.14/20.29 | | | | | % 136.14/20.29 | | | | | REF_CLOSE: (5), (18), (28) are inconsistent by sub-proof #506. % 136.14/20.29 | | | | | % 136.14/20.29 | | | | End of split % 136.14/20.29 | | | | % 136.14/20.29 | | | End of split % 136.14/20.29 | | | % 136.14/20.29 | | End of split % 136.14/20.29 | | % 136.14/20.29 | End of split % 136.14/20.29 | % 136.14/20.29 End of proof % 136.14/20.29 % 136.14/20.29 Sub-proof #478 shows that the following formulas are inconsistent: % 136.14/20.29 ---------------------------------------------------------------- % 136.14/20.29 (1) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0 % 136.14/20.29 (2) ~ (all_52_9 = e2) % 136.14/20.29 (3) all_54_6 = all_52_9 % 136.14/20.29 (4) ~ (all_52_9 = e0) % 136.14/20.29 (5) ~ (all_52_9 = e1) % 136.14/20.29 % 136.14/20.29 Begin of proof % 136.14/20.29 | % 136.14/20.29 | BETA: splitting (1) gives: % 136.14/20.29 | % 136.14/20.29 | Case 1: % 136.14/20.29 | | % 136.14/20.29 | | (6) all_54_6 = e2 % 136.14/20.29 | | % 136.14/20.29 | | COMBINE_EQS: (3), (6) imply: % 136.14/20.29 | | (7) all_52_9 = e2 % 136.14/20.29 | | % 136.14/20.29 | | REDUCE: (2), (7) imply: % 136.14/20.29 | | (8) $false % 136.14/20.29 | | % 136.14/20.29 | | CLOSE: (8) is inconsistent. % 136.14/20.29 | | % 136.14/20.29 | Case 2: % 136.14/20.29 | | % 136.14/20.29 | | (9) all_54_6 = e1 | all_54_6 = e0 % 136.14/20.29 | | % 136.14/20.29 | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #479. % 136.14/20.29 | | % 136.14/20.29 | End of split % 136.14/20.29 | % 136.14/20.29 End of proof % 136.14/20.29 % 136.14/20.29 Sub-proof #479 shows that the following formulas are inconsistent: % 136.14/20.29 ---------------------------------------------------------------- % 136.14/20.29 (1) all_54_6 = e1 | all_54_6 = e0 % 136.14/20.29 (2) all_54_6 = all_52_9 % 136.14/20.29 (3) ~ (all_52_9 = e1) % 136.14/20.29 (4) ~ (all_52_9 = e0) % 136.14/20.29 % 136.14/20.29 Begin of proof % 136.14/20.29 | % 136.14/20.29 | BETA: splitting (1) gives: % 136.14/20.29 | % 136.14/20.29 | Case 1: % 136.14/20.29 | | % 136.14/20.29 | | (5) all_54_6 = e1 % 136.14/20.29 | | % 136.14/20.29 | | COMBINE_EQS: (2), (5) imply: % 136.14/20.29 | | (6) all_52_9 = e1 % 136.14/20.29 | | % 136.14/20.29 | | SIMP: (6) implies: % 136.14/20.29 | | (7) all_52_9 = e1 % 136.14/20.29 | | % 136.14/20.29 | | REDUCE: (3), (7) imply: % 136.14/20.29 | | (8) $false % 136.14/20.29 | | % 136.14/20.29 | | CLOSE: (8) is inconsistent. % 136.14/20.29 | | % 136.14/20.29 | Case 2: % 136.14/20.29 | | % 136.14/20.29 | | (9) all_54_6 = e0 % 136.14/20.29 | | % 136.14/20.29 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #480. % 136.14/20.29 | | % 136.14/20.29 | End of split % 136.14/20.29 | % 136.14/20.29 End of proof % 136.14/20.29 % 136.14/20.29 Sub-proof #480 shows that the following formulas are inconsistent: % 136.14/20.29 ---------------------------------------------------------------- % 136.14/20.29 (1) all_54_6 = all_52_9 % 136.14/20.29 (2) all_54_6 = e0 % 136.14/20.29 (3) ~ (all_52_9 = e0) % 136.14/20.29 % 136.14/20.29 Begin of proof % 136.14/20.29 | % 136.14/20.29 | COMBINE_EQS: (1), (2) imply: % 136.14/20.29 | (4) all_52_9 = e0 % 136.14/20.29 | % 136.14/20.29 | SIMP: (4) implies: % 136.14/20.29 | (5) all_52_9 = e0 % 136.14/20.29 | % 136.14/20.29 | REDUCE: (3), (5) imply: % 136.14/20.29 | (6) $false % 136.14/20.29 | % 136.14/20.29 | CLOSE: (6) is inconsistent. % 136.14/20.29 | % 136.14/20.29 End of proof % 136.14/20.29 % 136.14/20.29 Sub-proof #481 shows that the following formulas are inconsistent: % 136.14/20.29 ---------------------------------------------------------------- % 136.14/20.29 (1) all_54_4 = all_52_1 % 136.14/20.29 (2) all_54_4 = e3 % 136.14/20.29 (3) ~ (all_52_1 = e3) % 136.14/20.29 % 136.14/20.29 Begin of proof % 136.14/20.29 | % 136.14/20.29 | COMBINE_EQS: (1), (2) imply: % 136.14/20.29 | (4) all_52_1 = e3 % 136.14/20.29 | % 136.14/20.29 | SIMP: (4) implies: % 136.14/20.29 | (5) all_52_1 = e3 % 136.14/20.29 | % 136.14/20.29 | REDUCE: (3), (5) imply: % 136.14/20.29 | (6) $false % 136.14/20.29 | % 136.14/20.29 | CLOSE: (6) is inconsistent. % 136.14/20.29 | % 136.14/20.29 End of proof % 136.14/20.29 % 136.14/20.29 Sub-proof #482 shows that the following formulas are inconsistent: % 136.14/20.29 ---------------------------------------------------------------- % 136.14/20.29 (1) ~ (e2 = e0) % 136.14/20.29 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.29 (3) ~ (e2 = e1) % 136.14/20.29 (4) all_57_13 = e3 % 136.14/20.29 (5) ~ (e3 = e0) % 136.14/20.29 (6) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) | % 136.14/20.29 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.14/20.29 (7) op(e0, e0) = e2 % 136.14/20.29 (8) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.29 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = % 136.14/20.29 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.14/20.29 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.14/20.29 (9) ~ (e3 = e1) % 136.14/20.29 (10) ~ (e1 = e0) % 136.14/20.29 (11) all_57_12 = e2 % 136.14/20.29 % 136.14/20.29 Begin of proof % 136.14/20.29 | % 136.14/20.29 | BETA: splitting (8) gives: % 136.14/20.29 | % 136.14/20.29 | Case 1: % 136.14/20.29 | | % 136.14/20.29 | | (12) all_57_15 = e0 & op(e0, e0) = e0 % 136.14/20.29 | | % 136.14/20.29 | | ALPHA: (12) implies: % 136.14/20.29 | | (13) op(e0, e0) = e0 % 136.14/20.29 | | % 136.14/20.29 | | REF_CLOSE: (1), (2), (7), (13) are inconsistent by sub-proof #714. % 136.14/20.29 | | % 136.14/20.29 | Case 2: % 136.14/20.29 | | % 136.14/20.29 | | (14) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = % 136.14/20.29 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 & % 136.14/20.29 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) | % 136.14/20.29 | | (all_57_14 = e0 & op(e0, e1) = e0)) % 136.14/20.29 | | % 136.14/20.29 | | ALPHA: (14) implies: % 136.14/20.29 | | (15) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 136.14/20.29 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 136.14/20.29 | | % 136.14/20.29 | | BETA: splitting (6) gives: % 136.14/20.29 | | % 136.14/20.29 | | Case 1: % 136.14/20.29 | | | % 136.14/20.29 | | | (16) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) % 136.14/20.29 | | | = e1) % 136.14/20.29 | | | % 136.14/20.29 | | | BETA: splitting (16) gives: % 136.14/20.29 | | | % 136.14/20.29 | | | Case 1: % 136.14/20.29 | | | | % 136.14/20.29 | | | | (17) all_57_12 = e1 & op(e0, e3) = e1 % 136.14/20.29 | | | | % 136.14/20.29 | | | | REF_CLOSE: (3), (11), (17) are inconsistent by sub-proof #516. % 136.14/20.29 | | | | % 136.14/20.29 | | | Case 2: % 136.14/20.29 | | | | % 136.14/20.29 | | | | (18) all_57_13 = e1 & op(e0, e2) = e1 % 136.14/20.29 | | | | % 136.14/20.29 | | | | REF_CLOSE: (4), (9), (18) are inconsistent by sub-proof #726. % 136.14/20.29 | | | | % 136.14/20.29 | | | End of split % 136.14/20.29 | | | % 136.14/20.29 | | Case 2: % 136.14/20.29 | | | % 136.14/20.29 | | | (19) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) % 136.14/20.29 | | | = e1) % 136.14/20.29 | | | % 136.14/20.29 | | | BETA: splitting (19) gives: % 136.14/20.29 | | | % 136.14/20.29 | | | Case 1: % 136.14/20.29 | | | | % 136.14/20.29 | | | | (20) all_57_14 = e1 & op(e0, e1) = e1 % 136.14/20.29 | | | | % 136.14/20.29 | | | | ALPHA: (20) implies: % 136.14/20.29 | | | | (21) all_57_14 = e1 % 136.14/20.29 | | | | % 136.14/20.29 | | | | BETA: splitting (15) gives: % 136.14/20.29 | | | | % 136.14/20.29 | | | | Case 1: % 136.14/20.29 | | | | | % 136.14/20.29 | | | | | (22) all_57_12 = e0 & op(e0, e3) = e0 % 136.14/20.29 | | | | | % 136.14/20.29 | | | | | ALPHA: (22) implies: % 136.14/20.29 | | | | | (23) all_57_12 = e0 % 136.14/20.29 | | | | | % 136.14/20.29 | | | | | REF_CLOSE: (1), (11), (23) are inconsistent by sub-proof #682. % 136.14/20.29 | | | | | % 136.14/20.29 | | | | Case 2: % 136.14/20.29 | | | | | % 136.14/20.29 | | | | | (24) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 136.14/20.29 | | | | | e1) = e0) % 136.14/20.29 | | | | | % 136.14/20.29 | | | | | BETA: splitting (24) gives: % 136.14/20.29 | | | | | % 136.14/20.29 | | | | | Case 1: % 136.14/20.29 | | | | | | % 136.14/20.29 | | | | | | (25) all_57_13 = e0 & op(e0, e2) = e0 % 136.14/20.29 | | | | | | % 136.14/20.29 | | | | | | ALPHA: (25) implies: % 136.14/20.29 | | | | | | (26) all_57_13 = e0 % 136.14/20.29 | | | | | | % 136.14/20.29 | | | | | | REF_CLOSE: (4), (5), (26) are inconsistent by sub-proof #484. % 136.14/20.29 | | | | | | % 136.14/20.29 | | | | | Case 2: % 136.14/20.29 | | | | | | % 136.14/20.29 | | | | | | (27) all_57_14 = e0 & op(e0, e1) = e0 % 136.14/20.29 | | | | | | % 136.14/20.29 | | | | | | REF_CLOSE: (10), (21), (27) are inconsistent by sub-proof #483. % 136.14/20.29 | | | | | | % 136.14/20.29 | | | | | End of split % 136.14/20.29 | | | | | % 136.14/20.29 | | | | End of split % 136.14/20.29 | | | | % 136.14/20.29 | | | Case 2: % 136.14/20.29 | | | | % 136.14/20.29 | | | | (28) all_57_15 = e1 & op(e0, e0) = e1 % 136.14/20.29 | | | | % 136.14/20.29 | | | | ALPHA: (28) implies: % 136.14/20.29 | | | | (29) op(e0, e0) = e1 % 136.14/20.29 | | | | % 136.14/20.29 | | | | REF_CLOSE: (2), (3), (7), (29) are inconsistent by sub-proof #636. % 136.14/20.29 | | | | % 136.14/20.29 | | | End of split % 136.14/20.29 | | | % 136.14/20.29 | | End of split % 136.14/20.29 | | % 136.14/20.29 | End of split % 136.14/20.29 | % 136.14/20.29 End of proof % 136.14/20.29 % 136.14/20.29 Sub-proof #483 shows that the following formulas are inconsistent: % 136.14/20.29 ---------------------------------------------------------------- % 136.14/20.29 (1) all_57_14 = e0 & op(e0, e1) = e0 % 136.14/20.29 (2) all_57_14 = e1 % 136.14/20.29 (3) ~ (e1 = e0) % 136.14/20.29 % 136.14/20.29 Begin of proof % 136.14/20.29 | % 136.14/20.29 | ALPHA: (1) implies: % 136.14/20.29 | (4) all_57_14 = e0 % 136.14/20.29 | % 136.14/20.29 | COMBINE_EQS: (2), (4) imply: % 136.14/20.29 | (5) e1 = e0 % 136.14/20.29 | % 136.14/20.29 | REDUCE: (3), (5) imply: % 136.14/20.29 | (6) $false % 136.14/20.29 | % 136.14/20.29 | CLOSE: (6) is inconsistent. % 136.14/20.29 | % 136.14/20.29 End of proof % 136.14/20.29 % 136.14/20.29 Sub-proof #484 shows that the following formulas are inconsistent: % 136.14/20.29 ---------------------------------------------------------------- % 136.14/20.29 (1) all_57_13 = e3 % 136.14/20.29 (2) all_57_13 = e0 % 136.14/20.29 (3) ~ (e3 = e0) % 136.14/20.29 % 136.14/20.29 Begin of proof % 136.14/20.29 | % 136.14/20.29 | COMBINE_EQS: (1), (2) imply: % 136.14/20.29 | (4) e3 = e0 % 136.14/20.29 | % 136.14/20.29 | SIMP: (4) implies: % 136.14/20.29 | (5) e3 = e0 % 136.14/20.29 | % 136.14/20.29 | REDUCE: (3), (5) imply: % 136.14/20.29 | (6) $false % 136.14/20.29 | % 136.14/20.29 | CLOSE: (6) is inconsistent. % 136.14/20.29 | % 136.14/20.29 End of proof % 136.14/20.29 % 136.14/20.29 Sub-proof #485 shows that the following formulas are inconsistent: % 136.14/20.29 ---------------------------------------------------------------- % 136.14/20.29 (1) op(e1, e1) = all_6_2 % 136.14/20.29 (2) all_57_6 = e0 % 136.14/20.29 (3) ~ (all_52_4 = e0) % 136.14/20.29 (4) op(e2, e2) = e0 % 136.14/20.29 (5) ~ (e2 = e0) % 136.14/20.29 (6) op(e3, e3) = e1 % 136.14/20.29 (7) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.14/20.29 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.14/20.29 (8) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 136.14/20.29 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 136.14/20.29 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.14/20.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.14/20.29 (10) ~ (e2 = e1) % 136.14/20.29 (11) ~ (e3 = e0) % 136.14/20.29 (12) ~ (all_52_2 = e1) % 136.14/20.29 (13) ~ (e3 = e2) % 136.14/20.29 (14) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 136.14/20.29 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) % 136.14/20.29 (15) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.14/20.29 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.14/20.29 (16) ~ (all_52_1 = e1) % 136.14/20.29 (17) all_57_2 = e2 % 136.14/20.29 (18) op(e1, e1) = e0 % 136.14/20.29 (19) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 136.14/20.29 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 136.47/20.29 (20) ~ (all_52_8 = all_6_2) % 136.47/20.29 (21) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) | % 136.47/20.29 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3) % 136.47/20.29 (22) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.47/20.29 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) % 136.47/20.29 (23) all_57_12 = e3 % 136.47/20.29 (24) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.47/20.29 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.47/20.29 (25) op(e1, e3) = all_52_2 % 136.47/20.29 (26) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 136.47/20.29 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 136.47/20.29 (27) op(e3, e2) = all_52_4 % 136.47/20.29 (28) ~ (all_40_0 = e3) % 136.47/20.29 (29) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 136.47/20.29 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 136.47/20.29 (30) op(e0, e0) = e2 % 136.47/20.29 (31) op(e2, e3) = all_52_1 % 136.47/20.29 (32) op(e3, e1) = all_52_8 % 136.47/20.29 (33) ~ (e3 = e1) % 136.47/20.29 (34) ~ (e1 = e0) % 136.47/20.29 (35) all_57_7 = e2 % 136.47/20.29 (36) ~ (all_52_4 = e1) % 136.47/20.29 (37) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) | % 136.47/20.29 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) % 136.47/20.29 (38) op(e0, e1) = all_40_0 % 136.47/20.29 (39) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.47/20.29 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.47/20.29 (40) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.47/20.29 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.47/20.29 % 136.47/20.29 Begin of proof % 136.47/20.29 | % 136.47/20.29 | BETA: splitting (22) gives: % 136.47/20.29 | % 136.47/20.29 | Case 1: % 136.47/20.29 | | % 136.47/20.29 | | (41) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = % 136.47/20.29 | | e1) % 136.47/20.29 | | % 136.47/20.29 | | REF_CLOSE: (4), (9), (27), (34), (36), (41) are inconsistent by sub-proof % 136.47/20.29 | | #564. % 136.47/20.29 | | % 136.47/20.29 | Case 2: % 136.47/20.29 | | % 136.47/20.29 | | (42) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = % 136.47/20.29 | | e1) % 136.47/20.29 | | % 136.47/20.29 | | BETA: splitting (42) gives: % 136.47/20.29 | | % 136.47/20.29 | | Case 1: % 136.47/20.29 | | | % 136.47/20.29 | | | (43) all_57_7 = e1 & op(e1, e2) = e1 % 136.47/20.29 | | | % 136.47/20.29 | | | REF_CLOSE: (10), (35), (43) are inconsistent by sub-proof #727. % 136.47/20.29 | | | % 136.47/20.29 | | Case 2: % 136.47/20.29 | | | % 136.47/20.29 | | | (44) all_57_13 = e1 & op(e0, e2) = e1 % 136.47/20.29 | | | % 136.47/20.29 | | | ALPHA: (44) implies: % 136.47/20.29 | | | (45) all_57_13 = e1 % 136.47/20.29 | | | % 136.47/20.29 | | | BETA: splitting (29) gives: % 136.47/20.29 | | | % 136.47/20.29 | | | Case 1: % 136.47/20.29 | | | | % 136.47/20.29 | | | | (46) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) % 136.47/20.29 | | | | = e1) % 136.47/20.29 | | | | % 136.47/20.29 | | | | BETA: splitting (46) gives: % 136.47/20.29 | | | | % 136.47/20.29 | | | | Case 1: % 136.47/20.29 | | | | | % 136.47/20.29 | | | | | (47) all_57_6 = e1 & op(e1, e3) = e1 % 136.47/20.29 | | | | | % 136.47/20.29 | | | | | ALPHA: (47) implies: % 136.47/20.29 | | | | | (48) op(e1, e3) = e1 % 136.47/20.29 | | | | | % 136.47/20.29 | | | | | REF_CLOSE: (9), (12), (25), (48) are inconsistent by sub-proof #725. % 136.47/20.29 | | | | | % 136.47/20.29 | | | | Case 2: % 136.47/20.29 | | | | | % 136.47/20.29 | | | | | (49) all_57_7 = e1 & op(e1, e2) = e1 % 136.47/20.29 | | | | | % 136.47/20.29 | | | | | REF_CLOSE: (10), (35), (49) are inconsistent by sub-proof #727. % 136.47/20.29 | | | | | % 136.47/20.29 | | | | End of split % 136.47/20.29 | | | | % 136.47/20.29 | | | Case 2: % 136.47/20.29 | | | | % 136.47/20.29 | | | | (50) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) % 136.47/20.29 | | | | = e1) % 136.47/20.29 | | | | % 136.47/20.29 | | | | BETA: splitting (50) gives: % 136.47/20.29 | | | | % 136.47/20.29 | | | | Case 1: % 136.47/20.29 | | | | | % 136.47/20.29 | | | | | (51) all_57_8 = e1 & op(e1, e1) = e1 % 136.47/20.29 | | | | | % 136.47/20.29 | | | | | ALPHA: (51) implies: % 136.47/20.29 | | | | | (52) op(e1, e1) = e1 % 136.47/20.29 | | | | | % 136.47/20.29 | | | | | REF_CLOSE: (9), (18), (34), (52) are inconsistent by sub-proof #721. % 136.47/20.29 | | | | | % 136.47/20.29 | | | | Case 2: % 136.47/20.29 | | | | | % 136.47/20.29 | | | | | (53) all_57_11 = e1 & op(e1, e0) = e1 % 136.47/20.29 | | | | | % 136.47/20.29 | | | | | ALPHA: (53) implies: % 136.47/20.29 | | | | | (54) all_57_11 = e1 % 136.47/20.29 | | | | | % 136.47/20.29 | | | | | BETA: splitting (14) gives: % 136.47/20.29 | | | | | % 136.47/20.29 | | | | | Case 1: % 136.47/20.29 | | | | | | % 136.47/20.29 | | | | | | (55) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, % 136.47/20.29 | | | | | | e2) = e3) % 136.47/20.29 | | | | | | % 136.47/20.29 | | | | | | BETA: splitting (55) gives: % 136.47/20.29 | | | | | | % 136.47/20.29 | | | | | | Case 1: % 136.47/20.29 | | | | | | | % 136.47/20.29 | | | | | | | (56) all_57_1 = e3 & op(e3, e2) = e3 % 136.47/20.29 | | | | | | | % 136.47/20.29 | | | | | | | ALPHA: (56) implies: % 136.47/20.29 | | | | | | | (57) all_57_1 = e3 % 136.47/20.29 | | | | | | | % 136.47/20.29 | | | | | | | BETA: splitting (19) gives: % 136.47/20.29 | | | | | | | % 136.47/20.29 | | | | | | | Case 1: % 136.47/20.29 | | | | | | | | % 136.47/20.29 | | | | | | | | (58) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & % 136.47/20.29 | | | | | | | | op(e3, e2) = e2) % 136.47/20.29 | | | | | | | | % 136.47/20.29 | | | | | | | | BETA: splitting (58) gives: % 136.47/20.29 | | | | | | | | % 136.47/20.29 | | | | | | | | Case 1: % 136.47/20.29 | | | | | | | | | % 136.47/20.29 | | | | | | | | | (59) all_57_0 = e2 & op(e3, e3) = e2 % 136.47/20.29 | | | | | | | | | % 136.47/20.29 | | | | | | | | | ALPHA: (59) implies: % 136.47/20.29 | | | | | | | | | (60) op(e3, e3) = e2 % 136.47/20.29 | | | | | | | | | % 136.47/20.29 | | | | | | | | | REF_CLOSE: (5), (8), (9), (10), (11), (17), (23), (24), (33), % 136.47/20.29 | | | | | | | | | (34), (60) are inconsistent by sub-proof #489. % 136.47/20.29 | | | | | | | | | % 136.47/20.29 | | | | | | | | Case 2: % 136.47/20.29 | | | | | | | | | % 136.47/20.29 | | | | | | | | | (61) all_57_1 = e2 & op(e3, e2) = e2 % 136.47/20.29 | | | | | | | | | % 136.47/20.29 | | | | | | | | | REF_CLOSE: (13), (57), (61) are inconsistent by sub-proof % 136.47/20.29 | | | | | | | | | #563. % 136.47/20.29 | | | | | | | | | % 136.47/20.29 | | | | | | | | End of split % 136.47/20.29 | | | | | | | | % 136.47/20.29 | | | | | | | Case 2: % 136.47/20.29 | | | | | | | | % 136.47/20.29 | | | | | | | | (62) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & % 136.47/20.29 | | | | | | | | op(e3, e0) = e2) % 136.47/20.29 | | | | | | | | % 136.47/20.29 | | | | | | | | BETA: splitting (62) gives: % 136.47/20.29 | | | | | | | | % 136.47/20.29 | | | | | | | | Case 1: % 136.47/20.29 | | | | | | | | | % 136.47/20.29 | | | | | | | | | (63) all_57_4 = e2 & op(e3, e1) = e2 % 136.47/20.29 | | | | | | | | | % 136.47/20.29 | | | | | | | | | ALPHA: (63) implies: % 136.47/20.29 | | | | | | | | | (64) all_57_4 = e2 % 136.47/20.29 | | | | | | | | | % 136.47/20.29 | | | | | | | | | BETA: splitting (7) gives: % 136.47/20.29 | | | | | | | | | % 136.47/20.29 | | | | | | | | | Case 1: % 136.47/20.29 | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | (65) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & % 136.47/20.29 | | | | | | | | | | op(e3, e2) = e0) % 136.47/20.29 | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | REF_CLOSE: (3), (6), (9), (27), (34), (65) are inconsistent % 136.47/20.29 | | | | | | | | | | by sub-proof #692. % 136.47/20.29 | | | | | | | | | | % 136.47/20.29 | | | | | | | | | Case 2: % 136.47/20.29 | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | (66) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & % 136.47/20.29 | | | | | | | | | | op(e3, e0) = e0) % 136.47/20.29 | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | BETA: splitting (66) gives: % 136.47/20.29 | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | Case 1: % 136.47/20.29 | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | (67) all_57_4 = e0 & op(e3, e1) = e0 % 136.47/20.29 | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | ALPHA: (67) implies: % 136.47/20.29 | | | | | | | | | | | (68) op(e3, e1) = e0 % 136.47/20.29 | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | REF_CLOSE: (1), (9), (18), (20), (32), (68) are inconsistent % 136.47/20.29 | | | | | | | | | | | by sub-proof #619. % 136.47/20.29 | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | Case 2: % 136.47/20.29 | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | (69) all_57_9 = e0 & op(e3, e0) = e0 % 136.47/20.29 | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | ALPHA: (69) implies: % 136.47/20.29 | | | | | | | | | | | (70) all_57_9 = e0 % 136.47/20.29 | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | BETA: splitting (21) gives: % 136.47/20.29 | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | Case 1: % 136.47/20.29 | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | (71) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = % 136.47/20.29 | | | | | | | | | | | | e3 & op(e2, e0) = e3) % 136.47/20.29 | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | BETA: splitting (71) gives: % 136.47/20.29 | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | Case 1: % 136.47/20.29 | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | (72) all_57_9 = e3 & op(e3, e0) = e3 % 136.47/20.29 | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | REF_CLOSE: (11), (70), (72) are inconsistent by sub-proof % 136.47/20.29 | | | | | | | | | | | | | #614. % 136.47/20.29 | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | Case 2: % 136.47/20.29 | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | (73) all_57_10 = e3 & op(e2, e0) = e3 % 136.47/20.29 | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | ALPHA: (73) implies: % 136.47/20.29 | | | | | | | | | | | | | (74) all_57_10 = e3 % 136.47/20.29 | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | BETA: splitting (37) gives: % 136.47/20.29 | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | Case 1: % 136.47/20.29 | | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | | (75) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 % 136.47/20.29 | | | | | | | | | | | | | | & op(e2, e1) = e3) % 136.47/20.29 | | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | | BETA: splitting (75) gives: % 136.47/20.29 | | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | | Case 1: % 136.47/20.29 | | | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | | | (76) all_57_4 = e3 & op(e3, e1) = e3 % 136.47/20.29 | | | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | | | REF_CLOSE: (13), (64), (76) are inconsistent by sub-proof % 136.47/20.29 | | | | | | | | | | | | | | | #734. % 136.47/20.29 | | | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | | Case 2: % 136.47/20.29 | | | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | | | (77) all_57_5 = e3 & op(e2, e1) = e3 % 136.47/20.29 | | | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | | | ALPHA: (77) implies: % 136.47/20.29 | | | | | | | | | | | | | | | (78) all_57_5 = e3 % 136.47/20.29 | | | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | | | BETA: splitting (26) gives: % 136.47/20.29 | | | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | | | Case 1: % 136.47/20.29 | | | | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | | | | (79) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 % 136.47/20.29 | | | | | | | | | | | | | | | | & op(e1, e2) = e3) % 136.47/20.29 | | | | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 136.47/20.29 | | | | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | | | | Case 1: % 136.47/20.29 | | | | | | | | | | | | | | | | | % 136.47/20.29 | | | | | | | | | | | | | | | | | (80) all_57_6 = e3 & op(e1, e3) = e3 % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | | ALPHA: (80) implies: % 136.47/20.30 | | | | | | | | | | | | | | | | | (81) all_57_6 = e3 % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (81) imply: % 136.47/20.30 | | | | | | | | | | | | | | | | | (82) e3 = e0 % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | | REDUCE: (11), (82) imply: % 136.47/20.30 | | | | | | | | | | | | | | | | | (83) $false % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | | CLOSE: (83) is inconsistent. % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | Case 2: % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | | (84) all_57_7 = e3 & op(e1, e2) = e3 % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | | ALPHA: (84) implies: % 136.47/20.30 | | | | | | | | | | | | | | | | | (85) all_57_7 = e3 % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (85) imply: % 136.47/20.30 | | | | | | | | | | | | | | | | | (86) e3 = e2 % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | | SIMP: (86) implies: % 136.47/20.30 | | | | | | | | | | | | | | | | | (87) e3 = e2 % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (87) imply: % 136.47/20.30 | | | | | | | | | | | | | | | | | (88) all_57_10 = e2 % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (10), (11), (13), % 136.47/20.30 | | | | | | | | | | | | | | | | | (16), (19), (27), (31), (33), (34), (39), (40), % 136.47/20.30 | | | | | | | | | | | | | | | | | (64), (78), (88) are inconsistent by sub-proof % 136.47/20.30 | | | | | | | | | | | | | | | | | #666. % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | End of split % 136.47/20.30 | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | Case 2: % 136.47/20.30 | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | (89) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = % 136.47/20.30 | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3) % 136.47/20.30 | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | BETA: splitting (89) gives: % 136.47/20.30 | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | Case 1: % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | | (90) all_57_8 = e3 & op(e1, e1) = e3 % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | | ALPHA: (90) implies: % 136.47/20.30 | | | | | | | | | | | | | | | | | (91) op(e1, e1) = e3 % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (18), (91) are inconsistent by % 136.47/20.30 | | | | | | | | | | | | | | | | | sub-proof #753. % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | Case 2: % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | | (92) all_57_11 = e3 & op(e1, e0) = e3 % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (9), (11), (13), (15), (17), (23), (33), % 136.47/20.30 | | | | | | | | | | | | | | | | | (54), (92) are inconsistent by sub-proof #488. % 136.47/20.30 | | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | | End of split % 136.47/20.30 | | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | End of split % 136.47/20.30 | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | End of split % 136.47/20.30 | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | Case 2: % 136.47/20.30 | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | (93) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = % 136.47/20.30 | | | | | | | | | | | | | | e3 & op(e0, e1) = e3) % 136.47/20.30 | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | BETA: splitting (93) gives: % 136.47/20.30 | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | Case 1: % 136.47/20.30 | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | (94) all_57_8 = e3 & op(e1, e1) = e3 % 136.47/20.30 | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | ALPHA: (94) implies: % 136.47/20.30 | | | | | | | | | | | | | | | (95) op(e1, e1) = e3 % 136.47/20.30 | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (18), (95) are inconsistent by % 136.47/20.30 | | | | | | | | | | | | | | | sub-proof #753. % 136.47/20.30 | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | Case 2: % 136.47/20.30 | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | (96) all_57_14 = e3 & op(e0, e1) = e3 % 136.47/20.30 | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | ALPHA: (96) implies: % 136.47/20.30 | | | | | | | | | | | | | | | (97) op(e0, e1) = e3 % 136.47/20.30 | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | | REF_CLOSE: (9), (28), (38), (97) are inconsistent by % 136.47/20.30 | | | | | | | | | | | | | | | sub-proof #529. % 136.47/20.30 | | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | | End of split % 136.47/20.30 | | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | End of split % 136.47/20.30 | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | End of split % 136.47/20.30 | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | Case 2: % 136.47/20.30 | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | (98) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = % 136.47/20.30 | | | | | | | | | | | | e3 & op(e0, e0) = e3) % 136.47/20.30 | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | BETA: splitting (98) gives: % 136.47/20.30 | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | Case 1: % 136.47/20.30 | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | (99) all_57_11 = e3 & op(e1, e0) = e3 % 136.47/20.30 | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | REF_CLOSE: (2), (6), (9), (11), (13), (15), (17), (23), (33), % 136.47/20.30 | | | | | | | | | | | | | (54), (99) are inconsistent by sub-proof #488. % 136.47/20.30 | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | Case 2: % 136.47/20.30 | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | (100) all_57_15 = e3 & op(e0, e0) = e3 % 136.47/20.30 | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | ALPHA: (100) implies: % 136.47/20.30 | | | | | | | | | | | | | (101) op(e0, e0) = e3 % 136.47/20.30 | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | | REF_CLOSE: (9), (13), (30), (101) are inconsistent by % 136.47/20.30 | | | | | | | | | | | | | sub-proof #634. % 136.47/20.30 | | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | | End of split % 136.47/20.30 | | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | | End of split % 136.47/20.30 | | | | | | | | | | | % 136.47/20.30 | | | | | | | | | | End of split % 136.47/20.30 | | | | | | | | | | % 136.47/20.30 | | | | | | | | | End of split % 136.47/20.30 | | | | | | | | | % 136.47/20.30 | | | | | | | | Case 2: % 136.47/20.30 | | | | | | | | | % 136.47/20.30 | | | | | | | | | (102) all_57_9 = e2 & op(e3, e0) = e2 % 136.47/20.30 | | | | | | | | | % 136.47/20.30 | | | | | | | | | ALPHA: (102) implies: % 136.47/20.30 | | | | | | | | | (103) all_57_9 = e2 % 136.47/20.30 | | | | | | | | | % 136.47/20.30 | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (9), (18), (20), (27), % 136.47/20.30 | | | | | | | | | (32), (34), (103) are inconsistent by sub-proof % 136.47/20.30 | | | | | | | | | #487. % 136.47/20.30 | | | | | | | | | % 136.47/20.30 | | | | | | | | End of split % 136.47/20.30 | | | | | | | | % 136.47/20.30 | | | | | | | End of split % 136.47/20.30 | | | | | | | % 136.47/20.30 | | | | | | Case 2: % 136.47/20.30 | | | | | | | % 136.47/20.30 | | | | | | | (104) all_57_3 = e3 & op(e2, e2) = e3 % 136.47/20.30 | | | | | | | % 136.47/20.30 | | | | | | | ALPHA: (104) implies: % 136.47/20.30 | | | | | | | (105) op(e2, e2) = e3 % 136.47/20.30 | | | | | | | % 136.47/20.30 | | | | | | | REF_CLOSE: (4), (9), (11), (105) are inconsistent by sub-proof % 136.47/20.30 | | | | | | | #641. % 136.47/20.30 | | | | | | | % 136.47/20.30 | | | | | | End of split % 136.47/20.30 | | | | | | % 136.47/20.30 | | | | | Case 2: % 136.47/20.30 | | | | | | % 136.47/20.30 | | | | | | (106) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & % 136.47/20.30 | | | | | | op(e0, e2) = e3) % 136.47/20.30 | | | | | | % 136.47/20.30 | | | | | | BETA: splitting (106) gives: % 136.47/20.30 | | | | | | % 136.47/20.30 | | | | | | Case 1: % 136.47/20.30 | | | | | | | % 136.47/20.30 | | | | | | | (107) all_57_7 = e3 & op(e1, e2) = e3 % 136.47/20.30 | | | | | | | % 136.47/20.30 | | | | | | | ALPHA: (107) implies: % 136.47/20.30 | | | | | | | (108) all_57_7 = e3 % 136.47/20.30 | | | | | | | % 136.47/20.30 | | | | | | | REF_CLOSE: (13), (35), (108) are inconsistent by sub-proof #486. % 136.47/20.30 | | | | | | | % 136.47/20.30 | | | | | | Case 2: % 136.47/20.30 | | | | | | | % 136.47/20.30 | | | | | | | (109) all_57_13 = e3 & op(e0, e2) = e3 % 136.47/20.30 | | | | | | | % 136.47/20.30 | | | | | | | ALPHA: (109) implies: % 136.47/20.30 | | | | | | | (110) all_57_13 = e3 % 136.47/20.30 | | | | | | | % 136.47/20.30 | | | | | | | COMBINE_EQS: (45), (110) imply: % 136.47/20.30 | | | | | | | (111) e3 = e1 % 136.47/20.30 | | | | | | | % 136.47/20.30 | | | | | | | SIMP: (111) implies: % 136.47/20.30 | | | | | | | (112) e3 = e1 % 136.47/20.30 | | | | | | | % 136.47/20.30 | | | | | | | COMBINE_EQS: (23), (112) imply: % 136.47/20.30 | | | | | | | (113) all_57_12 = e1 % 136.47/20.30 | | | | | | | % 136.47/20.30 | | | | | | | REF_CLOSE: (2), (6), (9), (11), (13), (15), (17), (33), (113) are % 136.47/20.30 | | | | | | | inconsistent by sub-proof #587. % 136.47/20.30 | | | | | | | % 136.47/20.30 | | | | | | End of split % 136.47/20.30 | | | | | | % 136.47/20.30 | | | | | End of split % 136.47/20.30 | | | | | % 136.47/20.30 | | | | End of split % 136.47/20.30 | | | | % 136.47/20.30 | | | End of split % 136.47/20.30 | | | % 136.47/20.30 | | End of split % 136.47/20.30 | | % 136.47/20.30 | End of split % 136.47/20.30 | % 136.47/20.30 End of proof % 136.47/20.30 % 136.47/20.30 Sub-proof #486 shows that the following formulas are inconsistent: % 136.47/20.30 ---------------------------------------------------------------- % 136.47/20.30 (1) all_57_7 = e3 % 136.47/20.30 (2) all_57_7 = e2 % 136.47/20.30 (3) ~ (e3 = e2) % 136.47/20.30 % 136.47/20.30 Begin of proof % 136.47/20.30 | % 136.47/20.30 | COMBINE_EQS: (1), (2) imply: % 136.47/20.30 | (4) e3 = e2 % 136.47/20.30 | % 136.47/20.30 | SIMP: (4) implies: % 136.47/20.30 | (5) e3 = e2 % 136.47/20.30 | % 136.47/20.30 | REDUCE: (3), (5) imply: % 136.47/20.30 | (6) $false % 136.47/20.30 | % 136.47/20.30 | CLOSE: (6) is inconsistent. % 136.47/20.30 | % 136.47/20.30 End of proof % 136.47/20.30 % 136.47/20.30 Sub-proof #487 shows that the following formulas are inconsistent: % 136.47/20.30 ---------------------------------------------------------------- % 136.47/20.30 (1) op(e1, e1) = all_6_2 % 136.47/20.30 (2) ~ (all_52_4 = e0) % 136.47/20.30 (3) ~ (e2 = e0) % 136.47/20.30 (4) op(e3, e3) = e1 % 136.47/20.30 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.47/20.30 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.47/20.30 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.30 (7) all_57_9 = e2 % 136.47/20.30 (8) op(e1, e1) = e0 % 136.47/20.30 (9) ~ (all_52_8 = all_6_2) % 136.47/20.30 (10) op(e3, e2) = all_52_4 % 136.47/20.30 (11) op(e3, e1) = all_52_8 % 136.47/20.30 (12) ~ (e1 = e0) % 136.47/20.30 % 136.47/20.30 Begin of proof % 136.47/20.30 | % 136.47/20.30 | BETA: splitting (5) gives: % 136.47/20.30 | % 136.47/20.30 | Case 1: % 136.47/20.30 | | % 136.47/20.30 | | (13) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = % 136.47/20.30 | | e0) % 136.47/20.30 | | % 136.47/20.30 | | REF_CLOSE: (2), (4), (6), (10), (12), (13) are inconsistent by sub-proof % 136.47/20.30 | | #692. % 136.47/20.30 | | % 136.47/20.30 | Case 2: % 136.47/20.30 | | % 136.47/20.30 | | (14) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = % 136.47/20.30 | | e0) % 136.47/20.30 | | % 136.47/20.30 | | BETA: splitting (14) gives: % 136.47/20.30 | | % 136.47/20.30 | | Case 1: % 136.47/20.30 | | | % 136.47/20.30 | | | (15) all_57_4 = e0 & op(e3, e1) = e0 % 136.47/20.30 | | | % 136.47/20.30 | | | ALPHA: (15) implies: % 136.47/20.30 | | | (16) op(e3, e1) = e0 % 136.47/20.30 | | | % 136.47/20.30 | | | REF_CLOSE: (1), (6), (8), (9), (11), (16) are inconsistent by sub-proof % 136.47/20.30 | | | #619. % 136.47/20.30 | | | % 136.47/20.30 | | Case 2: % 136.47/20.30 | | | % 136.47/20.30 | | | (17) all_57_9 = e0 & op(e3, e0) = e0 % 136.47/20.30 | | | % 136.47/20.30 | | | REF_CLOSE: (3), (7), (17) are inconsistent by sub-proof #657. % 136.47/20.30 | | | % 136.47/20.30 | | End of split % 136.47/20.30 | | % 136.47/20.30 | End of split % 136.47/20.30 | % 136.47/20.30 End of proof % 136.47/20.30 % 136.47/20.30 Sub-proof #488 shows that the following formulas are inconsistent: % 136.47/20.30 ---------------------------------------------------------------- % 136.47/20.30 (1) all_57_6 = e0 % 136.47/20.30 (2) op(e3, e3) = e1 % 136.47/20.30 (3) all_57_11 = e1 % 136.47/20.30 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.30 (5) ~ (e3 = e0) % 136.47/20.30 (6) ~ (e3 = e2) % 136.47/20.30 (7) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.47/20.30 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.47/20.30 (8) all_57_11 = e3 & op(e1, e0) = e3 % 136.47/20.30 (9) all_57_2 = e2 % 136.47/20.30 (10) all_57_12 = e3 % 136.47/20.30 (11) ~ (e3 = e1) % 136.47/20.30 % 136.47/20.30 Begin of proof % 136.47/20.30 | % 136.47/20.30 | ALPHA: (8) implies: % 136.47/20.30 | (12) all_57_11 = e3 % 136.47/20.30 | % 136.47/20.30 | COMBINE_EQS: (3), (12) imply: % 136.47/20.30 | (13) e3 = e1 % 136.47/20.30 | % 136.47/20.30 | COMBINE_EQS: (10), (13) imply: % 136.47/20.30 | (14) all_57_12 = e1 % 136.47/20.30 | % 136.47/20.30 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (11), (14) are inconsistent by % 136.47/20.30 | sub-proof #587. % 136.47/20.30 | % 136.47/20.30 End of proof % 136.47/20.30 % 136.47/20.30 Sub-proof #489 shows that the following formulas are inconsistent: % 136.47/20.30 ---------------------------------------------------------------- % 136.47/20.30 (1) op(e3, e3) = e2 % 136.47/20.30 (2) ~ (e2 = e0) % 136.47/20.30 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | % 136.47/20.30 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1) % 136.47/20.30 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.30 (5) ~ (e2 = e1) % 136.47/20.30 (6) ~ (e3 = e0) % 136.47/20.30 (7) all_57_2 = e2 % 136.47/20.30 (8) all_57_12 = e3 % 136.47/20.30 (9) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.47/20.30 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.47/20.30 (10) ~ (e3 = e1) % 136.47/20.30 (11) ~ (e1 = e0) % 136.47/20.30 % 136.47/20.30 Begin of proof % 136.47/20.30 | % 136.47/20.30 | BETA: splitting (3) gives: % 136.47/20.30 | % 136.47/20.30 | Case 1: % 136.47/20.30 | | % 136.47/20.30 | | (12) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = % 136.47/20.30 | | e1) % 136.47/20.30 | | % 136.47/20.30 | | REF_CLOSE: (1), (4), (5), (7), (12) are inconsistent by sub-proof #496. % 136.47/20.30 | | % 136.47/20.30 | Case 2: % 136.47/20.30 | | % 136.47/20.30 | | (13) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = % 136.47/20.30 | | e1) % 136.47/20.30 | | % 136.47/20.30 | | BETA: splitting (13) gives: % 136.47/20.30 | | % 136.47/20.30 | | Case 1: % 136.47/20.30 | | | % 136.47/20.30 | | | (14) all_57_6 = e1 & op(e1, e3) = e1 % 136.47/20.30 | | | % 136.47/20.30 | | | ALPHA: (14) implies: % 136.47/20.30 | | | (15) all_57_6 = e1 % 136.47/20.30 | | | % 136.47/20.30 | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (11), (15) are inconsistent % 136.47/20.30 | | | by sub-proof #491. % 136.47/20.30 | | | % 136.47/20.30 | | Case 2: % 136.47/20.30 | | | % 136.47/20.30 | | | (16) all_57_12 = e1 & op(e0, e3) = e1 % 136.47/20.30 | | | % 136.47/20.30 | | | REF_CLOSE: (8), (10), (16) are inconsistent by sub-proof #490. % 136.47/20.30 | | | % 136.47/20.30 | | End of split % 136.47/20.30 | | % 136.47/20.30 | End of split % 136.47/20.30 | % 136.47/20.30 End of proof % 136.47/20.30 % 136.47/20.30 Sub-proof #490 shows that the following formulas are inconsistent: % 136.47/20.30 ---------------------------------------------------------------- % 136.47/20.30 (1) all_57_12 = e1 & op(e0, e3) = e1 % 136.47/20.30 (2) all_57_12 = e3 % 136.47/20.30 (3) ~ (e3 = e1) % 136.47/20.30 % 136.47/20.30 Begin of proof % 136.47/20.30 | % 136.47/20.30 | ALPHA: (1) implies: % 136.47/20.30 | (4) all_57_12 = e1 % 136.47/20.30 | % 136.47/20.30 | COMBINE_EQS: (2), (4) imply: % 136.47/20.30 | (5) e3 = e1 % 136.47/20.30 | % 136.47/20.30 | REDUCE: (3), (5) imply: % 136.47/20.30 | (6) $false % 136.47/20.30 | % 136.47/20.30 | CLOSE: (6) is inconsistent. % 136.47/20.30 | % 136.47/20.30 End of proof % 136.47/20.30 % 136.47/20.30 Sub-proof #491 shows that the following formulas are inconsistent: % 136.47/20.30 ---------------------------------------------------------------- % 136.47/20.30 (1) op(e3, e3) = e2 % 136.47/20.30 (2) all_57_6 = e1 % 136.47/20.30 (3) ~ (e2 = e0) % 136.47/20.30 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.30 (5) ~ (e3 = e0) % 136.47/20.30 (6) all_57_2 = e2 % 136.47/20.30 (7) all_57_12 = e3 % 136.47/20.30 (8) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.47/20.30 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.47/20.30 (9) ~ (e1 = e0) % 136.47/20.30 % 136.47/20.30 Begin of proof % 136.47/20.30 | % 136.47/20.30 | BETA: splitting (8) gives: % 136.47/20.30 | % 136.47/20.30 | Case 1: % 136.47/20.30 | | % 136.47/20.30 | | (10) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = % 136.47/20.30 | | e0) % 136.47/20.30 | | % 136.47/20.30 | | BETA: splitting (10) gives: % 136.47/20.30 | | % 136.47/20.30 | | Case 1: % 136.47/20.30 | | | % 136.47/20.30 | | | (11) all_57_0 = e0 & op(e3, e3) = e0 % 136.47/20.30 | | | % 136.47/20.30 | | | ALPHA: (11) implies: % 136.47/20.30 | | | (12) op(e3, e3) = e0 % 136.47/20.30 | | | % 136.47/20.30 | | | REF_CLOSE: (1), (3), (4), (12) are inconsistent by sub-proof #495. % 136.47/20.30 | | | % 136.47/20.30 | | Case 2: % 136.47/20.30 | | | % 136.47/20.30 | | | (13) all_57_2 = e0 & op(e2, e3) = e0 % 136.47/20.30 | | | % 136.47/20.30 | | | REF_CLOSE: (3), (6), (13) are inconsistent by sub-proof #494. % 136.47/20.30 | | | % 136.47/20.30 | | End of split % 136.47/20.30 | | % 136.47/20.30 | Case 2: % 136.47/20.30 | | % 136.47/20.30 | | (14) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = % 136.47/20.30 | | e0) % 136.47/20.30 | | % 136.47/20.30 | | BETA: splitting (14) gives: % 136.47/20.30 | | % 136.47/20.30 | | Case 1: % 136.47/20.30 | | | % 136.47/20.30 | | | (15) all_57_6 = e0 & op(e1, e3) = e0 % 136.47/20.30 | | | % 136.47/20.30 | | | ALPHA: (15) implies: % 136.47/20.30 | | | (16) all_57_6 = e0 % 136.47/20.30 | | | % 136.47/20.30 | | | REF_CLOSE: (2), (9), (16) are inconsistent by sub-proof #493. % 136.47/20.30 | | | % 136.47/20.30 | | Case 2: % 136.47/20.30 | | | % 136.47/20.30 | | | (17) all_57_12 = e0 & op(e0, e3) = e0 % 136.47/20.30 | | | % 136.47/20.30 | | | ALPHA: (17) implies: % 136.47/20.30 | | | (18) all_57_12 = e0 % 136.47/20.30 | | | % 136.47/20.30 | | | REF_CLOSE: (5), (7), (18) are inconsistent by sub-proof #492. % 136.47/20.30 | | | % 136.47/20.30 | | End of split % 136.47/20.30 | | % 136.47/20.30 | End of split % 136.47/20.30 | % 136.47/20.30 End of proof % 136.47/20.30 % 136.47/20.30 Sub-proof #492 shows that the following formulas are inconsistent: % 136.47/20.30 ---------------------------------------------------------------- % 136.47/20.30 (1) all_57_12 = e3 % 136.47/20.30 (2) all_57_12 = e0 % 136.47/20.30 (3) ~ (e3 = e0) % 136.47/20.30 % 136.47/20.30 Begin of proof % 136.47/20.30 | % 136.47/20.30 | COMBINE_EQS: (1), (2) imply: % 136.47/20.30 | (4) e3 = e0 % 136.47/20.30 | % 136.47/20.30 | SIMP: (4) implies: % 136.47/20.30 | (5) e3 = e0 % 136.47/20.30 | % 136.47/20.30 | REDUCE: (3), (5) imply: % 136.47/20.30 | (6) $false % 136.47/20.30 | % 136.47/20.30 | CLOSE: (6) is inconsistent. % 136.47/20.30 | % 136.47/20.30 End of proof % 136.47/20.30 % 136.47/20.30 Sub-proof #493 shows that the following formulas are inconsistent: % 136.47/20.30 ---------------------------------------------------------------- % 136.47/20.30 (1) all_57_6 = e1 % 136.47/20.30 (2) all_57_6 = e0 % 136.47/20.30 (3) ~ (e1 = e0) % 136.47/20.30 % 136.47/20.30 Begin of proof % 136.47/20.30 | % 136.47/20.30 | COMBINE_EQS: (1), (2) imply: % 136.47/20.30 | (4) e1 = e0 % 136.47/20.30 | % 136.47/20.30 | SIMP: (4) implies: % 136.47/20.30 | (5) e1 = e0 % 136.47/20.30 | % 136.47/20.30 | REDUCE: (3), (5) imply: % 136.47/20.30 | (6) $false % 136.47/20.30 | % 136.47/20.30 | CLOSE: (6) is inconsistent. % 136.47/20.30 | % 136.47/20.30 End of proof % 136.47/20.30 % 136.47/20.30 Sub-proof #494 shows that the following formulas are inconsistent: % 136.47/20.30 ---------------------------------------------------------------- % 136.47/20.30 (1) all_57_2 = e0 & op(e2, e3) = e0 % 136.47/20.30 (2) all_57_2 = e2 % 136.47/20.30 (3) ~ (e2 = e0) % 136.47/20.30 % 136.47/20.30 Begin of proof % 136.47/20.30 | % 136.47/20.30 | ALPHA: (1) implies: % 136.47/20.30 | (4) all_57_2 = e0 % 136.47/20.30 | % 136.47/20.30 | COMBINE_EQS: (2), (4) imply: % 136.47/20.30 | (5) e2 = e0 % 136.47/20.30 | % 136.47/20.30 | REDUCE: (3), (5) imply: % 136.47/20.30 | (6) $false % 136.47/20.30 | % 136.47/20.30 | CLOSE: (6) is inconsistent. % 136.47/20.30 | % 136.47/20.30 End of proof % 136.47/20.30 % 136.47/20.30 Sub-proof #495 shows that the following formulas are inconsistent: % 136.47/20.30 ---------------------------------------------------------------- % 136.47/20.30 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.30 (2) op(e3, e3) = e2 % 136.47/20.30 (3) op(e3, e3) = e0 % 136.47/20.30 (4) ~ (e2 = e0) % 136.47/20.30 % 136.47/20.30 Begin of proof % 136.47/20.30 | % 136.47/20.30 | GROUND_INST: instantiating (1) with e0, e2, e3, e3, simplifying with (2), (3) % 136.47/20.30 | gives: % 136.47/20.30 | (5) e2 = e0 % 136.47/20.30 | % 136.47/20.30 | REDUCE: (4), (5) imply: % 136.47/20.30 | (6) $false % 136.47/20.30 | % 136.47/20.30 | CLOSE: (6) is inconsistent. % 136.47/20.30 | % 136.47/20.30 End of proof % 136.47/20.30 % 136.47/20.30 Sub-proof #496 shows that the following formulas are inconsistent: % 136.47/20.30 ---------------------------------------------------------------- % 136.47/20.30 (1) op(e3, e3) = e2 % 136.47/20.30 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.30 (3) ~ (e2 = e1) % 136.47/20.30 (4) all_57_2 = e2 % 136.47/20.30 (5) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) % 136.47/20.30 % 136.47/20.30 Begin of proof % 136.47/20.30 | % 136.47/20.30 | BETA: splitting (5) gives: % 136.47/20.30 | % 136.47/20.30 | Case 1: % 136.47/20.30 | | % 136.47/20.30 | | (6) all_57_0 = e1 & op(e3, e3) = e1 % 136.47/20.30 | | % 136.47/20.30 | | ALPHA: (6) implies: % 136.47/20.30 | | (7) op(e3, e3) = e1 % 136.47/20.30 | | % 136.47/20.30 | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #743. % 136.47/20.30 | | % 136.47/20.30 | Case 2: % 136.47/20.30 | | % 136.47/20.30 | | (8) all_57_2 = e1 & op(e2, e3) = e1 % 136.47/20.30 | | % 136.47/20.30 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #497. % 136.47/20.30 | | % 136.47/20.30 | End of split % 136.47/20.30 | % 136.47/20.30 End of proof % 136.47/20.30 % 136.47/20.30 Sub-proof #497 shows that the following formulas are inconsistent: % 136.47/20.30 ---------------------------------------------------------------- % 136.47/20.30 (1) all_57_2 = e1 & op(e2, e3) = e1 % 136.47/20.30 (2) all_57_2 = e2 % 136.47/20.30 (3) ~ (e2 = e1) % 136.47/20.30 % 136.47/20.30 Begin of proof % 136.47/20.30 | % 136.47/20.30 | ALPHA: (1) implies: % 136.47/20.30 | (4) all_57_2 = e1 % 136.47/20.30 | % 136.47/20.30 | COMBINE_EQS: (2), (4) imply: % 136.47/20.30 | (5) e2 = e1 % 136.47/20.30 | % 136.47/20.30 | REDUCE: (3), (5) imply: % 136.47/20.30 | (6) $false % 136.47/20.30 | % 136.47/20.30 | CLOSE: (6) is inconsistent. % 136.47/20.30 | % 136.47/20.30 End of proof % 136.47/20.30 % 136.47/20.30 Sub-proof #498 shows that the following formulas are inconsistent: % 136.47/20.30 ---------------------------------------------------------------- % 136.47/20.30 (1) all_57_2 = e0 % 136.47/20.30 (2) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 136.47/20.30 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 136.47/20.30 (3) ~ (all_52_4 = e0) % 136.47/20.30 (4) op(e2, e2) = e0 % 136.47/20.30 (5) op(e2, e0) = all_52_13 % 136.47/20.30 (6) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.47/20.30 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 136.47/20.30 (7) ~ (e2 = e0) % 136.47/20.30 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.30 (9) ~ (e2 = e1) % 136.47/20.30 (10) ~ (e3 = e0) % 136.47/20.30 (11) ~ (e3 = e2) % 136.47/20.30 (12) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 136.47/20.30 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) % 136.47/20.30 (13) op(e0, e2) = all_52_7 % 136.47/20.30 (14) ~ (all_52_6 = e0) % 136.47/20.30 (15) ~ (all_52_13 = e2) % 136.47/20.30 (16) op(e1, e2) = all_52_6 % 136.47/20.30 (17) ~ (all_52_7 = e0) % 136.47/20.30 (18) op(e3, e2) = all_52_4 % 136.47/20.30 (19) ~ (e3 = e1) % 136.47/20.30 (20) ~ (e1 = e0) % 136.47/20.30 (21) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.47/20.30 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.47/20.30 % 136.47/20.30 Begin of proof % 136.47/20.30 | % 136.47/20.30 | BETA: splitting (2) gives: % 136.47/20.30 | % 136.47/20.30 | Case 1: % 136.47/20.30 | | % 136.47/20.30 | | (22) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = % 136.47/20.30 | | e2) % 136.47/20.30 | | % 136.47/20.30 | | BETA: splitting (22) gives: % 136.47/20.30 | | % 136.47/20.30 | | Case 1: % 136.47/20.30 | | | % 136.47/20.30 | | | (23) all_57_2 = e2 & op(e2, e3) = e2 % 136.47/20.30 | | | % 136.47/20.30 | | | REF_CLOSE: (1), (7), (23) are inconsistent by sub-proof #680. % 136.47/20.30 | | | % 136.47/20.30 | | Case 2: % 136.47/20.30 | | | % 136.47/20.30 | | | (24) all_57_3 = e2 & op(e2, e2) = e2 % 136.47/20.30 | | | % 136.47/20.30 | | | ALPHA: (24) implies: % 136.47/20.30 | | | (25) all_57_3 = e2 % 136.47/20.30 | | | % 136.47/20.30 | | | REF_CLOSE: (3), (6), (7), (8), (13), (14), (16), (17), (18), (25) are % 136.47/20.30 | | | inconsistent by sub-proof #503. % 136.47/20.30 | | | % 136.47/20.30 | | End of split % 136.47/20.30 | | % 136.47/20.30 | Case 2: % 136.47/20.30 | | % 136.47/20.30 | | (26) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = % 136.47/20.30 | | e2) % 136.47/20.30 | | % 136.47/20.30 | | BETA: splitting (26) gives: % 136.47/20.30 | | % 136.47/20.30 | | Case 1: % 136.47/20.30 | | | % 136.47/20.30 | | | (27) all_57_5 = e2 & op(e2, e1) = e2 % 136.47/20.30 | | | % 136.47/20.30 | | | ALPHA: (27) implies: % 136.47/20.30 | | | (28) all_57_5 = e2 % 136.47/20.30 | | | % 136.47/20.30 | | | BETA: splitting (12) gives: % 136.47/20.30 | | | % 136.47/20.30 | | | Case 1: % 136.47/20.30 | | | | % 136.47/20.30 | | | | (29) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) % 136.47/20.30 | | | | = e3) % 136.47/20.30 | | | | % 136.47/20.30 | | | | REF_CLOSE: (1), (4), (8), (10), (29) are inconsistent by sub-proof #502. % 136.47/20.30 | | | | % 136.47/20.30 | | | Case 2: % 136.47/20.30 | | | | % 136.47/20.30 | | | | (30) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) % 136.47/20.30 | | | | = e3) % 136.47/20.30 | | | | % 136.47/20.30 | | | | BETA: splitting (30) gives: % 136.47/20.30 | | | | % 136.47/20.30 | | | | Case 1: % 136.47/20.30 | | | | | % 136.47/20.30 | | | | | (31) all_57_5 = e3 & op(e2, e1) = e3 % 136.47/20.30 | | | | | % 136.47/20.30 | | | | | ALPHA: (31) implies: % 136.47/20.30 | | | | | (32) all_57_5 = e3 % 136.47/20.30 | | | | | % 136.47/20.30 | | | | | REF_CLOSE: (11), (28), (32) are inconsistent by sub-proof #501. % 136.47/20.30 | | | | | % 136.47/20.30 | | | | Case 2: % 136.47/20.30 | | | | | % 136.47/20.30 | | | | | (33) all_57_10 = e3 & op(e2, e0) = e3 % 136.47/20.30 | | | | | % 136.47/20.30 | | | | | ALPHA: (33) implies: % 136.47/20.30 | | | | | (34) all_57_10 = e3 % 136.47/20.30 | | | | | % 136.47/20.30 | | | | | REF_CLOSE: (1), (4), (8), (9), (19), (20), (21), (28), (34) are % 136.47/20.30 | | | | | inconsistent by sub-proof #499. % 136.47/20.30 | | | | | % 136.47/20.30 | | | | End of split % 136.47/20.30 | | | | % 136.47/20.30 | | | End of split % 136.47/20.30 | | | % 136.47/20.30 | | Case 2: % 136.47/20.30 | | | % 136.47/20.30 | | | (35) all_57_10 = e2 & op(e2, e0) = e2 % 136.47/20.30 | | | % 136.47/20.30 | | | ALPHA: (35) implies: % 136.47/20.30 | | | (36) op(e2, e0) = e2 % 136.47/20.30 | | | % 136.47/20.30 | | | REF_CLOSE: (5), (8), (15), (36) are inconsistent by sub-proof #768. % 136.47/20.30 | | | % 136.47/20.30 | | End of split % 136.47/20.30 | | % 136.47/20.30 | End of split % 136.47/20.30 | % 136.47/20.30 End of proof % 136.47/20.30 % 136.47/20.30 Sub-proof #499 shows that the following formulas are inconsistent: % 136.47/20.30 ---------------------------------------------------------------- % 136.47/20.30 (1) all_57_2 = e0 % 136.47/20.30 (2) op(e2, e2) = e0 % 136.47/20.30 (3) all_57_5 = e2 % 136.47/20.30 (4) all_57_10 = e3 % 136.47/20.30 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.30 (6) ~ (e2 = e1) % 136.47/20.30 (7) ~ (e3 = e1) % 136.47/20.30 (8) ~ (e1 = e0) % 136.47/20.30 (9) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.47/20.30 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.47/20.30 % 136.47/20.30 Begin of proof % 136.47/20.30 | % 136.47/20.30 | BETA: splitting (9) gives: % 136.47/20.30 | % 136.47/20.30 | Case 1: % 136.47/20.30 | | % 136.47/20.30 | | (10) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = % 136.47/20.30 | | e1) % 136.47/20.30 | | % 136.47/20.30 | | BETA: splitting (10) gives: % 136.47/20.30 | | % 136.47/20.30 | | Case 1: % 136.47/20.30 | | | % 136.47/20.30 | | | (11) all_57_2 = e1 & op(e2, e3) = e1 % 136.47/20.30 | | | % 136.47/20.30 | | | ALPHA: (11) implies: % 136.47/20.30 | | | (12) all_57_2 = e1 % 136.47/20.30 | | | % 136.47/20.30 | | | REF_CLOSE: (1), (8), (12) are inconsistent by sub-proof #646. % 136.47/20.30 | | | % 136.47/20.30 | | Case 2: % 136.47/20.30 | | | % 136.47/20.30 | | | (13) all_57_3 = e1 & op(e2, e2) = e1 % 136.47/20.30 | | | % 136.47/20.30 | | | ALPHA: (13) implies: % 136.47/20.30 | | | (14) op(e2, e2) = e1 % 136.47/20.30 | | | % 136.47/20.30 | | | REF_CLOSE: (2), (5), (8), (14) are inconsistent by sub-proof #675. % 136.47/20.30 | | | % 136.47/20.30 | | End of split % 136.47/20.30 | | % 136.47/20.30 | Case 2: % 136.47/20.30 | | % 136.47/20.30 | | (15) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = % 136.47/20.30 | | e1) % 136.47/20.30 | | % 136.47/20.30 | | BETA: splitting (15) gives: % 136.47/20.30 | | % 136.47/20.30 | | Case 1: % 136.47/20.30 | | | % 136.47/20.30 | | | (16) all_57_5 = e1 & op(e2, e1) = e1 % 136.47/20.30 | | | % 136.47/20.30 | | | REF_CLOSE: (3), (6), (16) are inconsistent by sub-proof #500. % 136.47/20.30 | | | % 136.47/20.30 | | Case 2: % 136.47/20.30 | | | % 136.47/20.30 | | | (17) all_57_10 = e1 & op(e2, e0) = e1 % 136.47/20.30 | | | % 136.47/20.30 | | | ALPHA: (17) implies: % 136.47/20.30 | | | (18) all_57_10 = e1 % 136.47/20.30 | | | % 136.47/20.30 | | | COMBINE_EQS: (4), (18) imply: % 136.47/20.30 | | | (19) e3 = e1 % 136.47/20.30 | | | % 136.47/20.30 | | | REDUCE: (7), (19) imply: % 136.47/20.30 | | | (20) $false % 136.47/20.30 | | | % 136.47/20.30 | | | CLOSE: (20) is inconsistent. % 136.47/20.30 | | | % 136.47/20.30 | | End of split % 136.47/20.30 | | % 136.47/20.30 | End of split % 136.47/20.30 | % 136.47/20.30 End of proof % 136.47/20.30 % 136.47/20.30 Sub-proof #500 shows that the following formulas are inconsistent: % 136.47/20.30 ---------------------------------------------------------------- % 136.47/20.30 (1) all_57_5 = e1 & op(e2, e1) = e1 % 136.47/20.30 (2) all_57_5 = e2 % 136.47/20.30 (3) ~ (e2 = e1) % 136.47/20.30 % 136.47/20.30 Begin of proof % 136.47/20.30 | % 136.47/20.30 | ALPHA: (1) implies: % 136.47/20.30 | (4) all_57_5 = e1 % 136.47/20.30 | % 136.47/20.30 | COMBINE_EQS: (2), (4) imply: % 136.47/20.30 | (5) e2 = e1 % 136.47/20.30 | % 136.47/20.30 | REDUCE: (3), (5) imply: % 136.47/20.30 | (6) $false % 136.47/20.30 | % 136.47/20.30 | CLOSE: (6) is inconsistent. % 136.47/20.30 | % 136.47/20.30 End of proof % 136.47/20.30 % 136.47/20.30 Sub-proof #501 shows that the following formulas are inconsistent: % 136.47/20.30 ---------------------------------------------------------------- % 136.47/20.30 (1) all_57_5 = e3 % 136.47/20.30 (2) all_57_5 = e2 % 136.47/20.30 (3) ~ (e3 = e2) % 136.47/20.30 % 136.47/20.30 Begin of proof % 136.47/20.30 | % 136.47/20.30 | COMBINE_EQS: (1), (2) imply: % 136.47/20.30 | (4) e3 = e2 % 136.47/20.30 | % 136.47/20.30 | SIMP: (4) implies: % 136.47/20.30 | (5) e3 = e2 % 136.47/20.30 | % 136.47/20.30 | REDUCE: (3), (5) imply: % 136.47/20.30 | (6) $false % 136.47/20.30 | % 136.47/20.30 | CLOSE: (6) is inconsistent. % 136.47/20.30 | % 136.47/20.30 End of proof % 136.47/20.30 % 136.47/20.30 Sub-proof #502 shows that the following formulas are inconsistent: % 136.47/20.30 ---------------------------------------------------------------- % 136.47/20.30 (1) all_57_2 = e0 % 136.47/20.30 (2) op(e2, e2) = e0 % 136.47/20.30 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.30 (4) ~ (e3 = e0) % 136.47/20.30 (5) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | BETA: splitting (5) gives: % 136.47/20.31 | % 136.47/20.31 | Case 1: % 136.47/20.31 | | % 136.47/20.31 | | (6) all_57_2 = e3 & op(e2, e3) = e3 % 136.47/20.31 | | % 136.47/20.31 | | ALPHA: (6) implies: % 136.47/20.31 | | (7) all_57_2 = e3 % 136.47/20.31 | | % 136.47/20.31 | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #593. % 136.47/20.31 | | % 136.47/20.31 | Case 2: % 136.47/20.31 | | % 136.47/20.31 | | (8) all_57_3 = e3 & op(e2, e2) = e3 % 136.47/20.31 | | % 136.47/20.31 | | ALPHA: (8) implies: % 136.47/20.31 | | (9) op(e2, e2) = e3 % 136.47/20.31 | | % 136.47/20.31 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #641. % 136.47/20.31 | | % 136.47/20.31 | End of split % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #503 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) ~ (all_52_4 = e0) % 136.47/20.31 (2) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | % 136.47/20.31 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 136.47/20.31 (3) ~ (e2 = e0) % 136.47/20.31 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.31 (5) op(e0, e2) = all_52_7 % 136.47/20.31 (6) ~ (all_52_6 = e0) % 136.47/20.31 (7) op(e1, e2) = all_52_6 % 136.47/20.31 (8) ~ (all_52_7 = e0) % 136.47/20.31 (9) op(e3, e2) = all_52_4 % 136.47/20.31 (10) all_57_3 = e2 % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | BETA: splitting (2) gives: % 136.47/20.31 | % 136.47/20.31 | Case 1: % 136.47/20.31 | | % 136.47/20.31 | | (11) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = % 136.47/20.31 | | e0) % 136.47/20.31 | | % 136.47/20.31 | | BETA: splitting (11) gives: % 136.47/20.31 | | % 136.47/20.31 | | Case 1: % 136.47/20.31 | | | % 136.47/20.31 | | | (12) all_57_1 = e0 & op(e3, e2) = e0 % 136.47/20.31 | | | % 136.47/20.31 | | | REF_CLOSE: (1), (4), (9), (12) are inconsistent by sub-proof #693. % 136.47/20.31 | | | % 136.47/20.31 | | Case 2: % 136.47/20.31 | | | % 136.47/20.31 | | | (13) all_57_3 = e0 & op(e2, e2) = e0 % 136.47/20.31 | | | % 136.47/20.31 | | | REF_CLOSE: (3), (10), (13) are inconsistent by sub-proof #627. % 136.47/20.31 | | | % 136.47/20.31 | | End of split % 136.47/20.31 | | % 136.47/20.31 | Case 2: % 136.47/20.31 | | % 136.47/20.31 | | (14) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = % 136.47/20.31 | | e0) % 136.47/20.31 | | % 136.47/20.31 | | REF_CLOSE: (4), (5), (6), (7), (8), (14) are inconsistent by sub-proof #504. % 136.47/20.31 | | % 136.47/20.31 | End of split % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #504 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.31 (2) op(e0, e2) = all_52_7 % 136.47/20.31 (3) ~ (all_52_6 = e0) % 136.47/20.31 (4) op(e1, e2) = all_52_6 % 136.47/20.31 (5) ~ (all_52_7 = e0) % 136.47/20.31 (6) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | BETA: splitting (6) gives: % 136.47/20.31 | % 136.47/20.31 | Case 1: % 136.47/20.31 | | % 136.47/20.31 | | (7) all_57_7 = e0 & op(e1, e2) = e0 % 136.47/20.31 | | % 136.47/20.31 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #505. % 136.47/20.31 | | % 136.47/20.31 | Case 2: % 136.47/20.31 | | % 136.47/20.31 | | (8) all_57_13 = e0 & op(e0, e2) = e0 % 136.47/20.31 | | % 136.47/20.31 | | ALPHA: (8) implies: % 136.47/20.31 | | (9) op(e0, e2) = e0 % 136.47/20.31 | | % 136.47/20.31 | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #545. % 136.47/20.31 | | % 136.47/20.31 | End of split % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #505 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) all_57_7 = e0 & op(e1, e2) = e0 % 136.47/20.31 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.31 (3) op(e1, e2) = all_52_6 % 136.47/20.31 (4) ~ (all_52_6 = e0) % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | ALPHA: (1) implies: % 136.47/20.31 | (5) op(e1, e2) = e0 % 136.47/20.31 | % 136.47/20.31 | GROUND_INST: instantiating (2) with all_52_6, e0, e2, e1, simplifying with % 136.47/20.31 | (3), (5) gives: % 136.47/20.31 | (6) all_52_6 = e0 % 136.47/20.31 | % 136.47/20.31 | REDUCE: (4), (6) imply: % 136.47/20.31 | (7) $false % 136.47/20.31 | % 136.47/20.31 | CLOSE: (7) is inconsistent. % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #506 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) all_54_10 = all_6_2 % 136.47/20.31 (2) all_54_10 = e0 % 136.47/20.31 (3) ~ (all_6_2 = e0) % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | COMBINE_EQS: (1), (2) imply: % 136.47/20.31 | (4) all_6_2 = e0 % 136.47/20.31 | % 136.47/20.31 | SIMP: (4) implies: % 136.47/20.31 | (5) all_6_2 = e0 % 136.47/20.31 | % 136.47/20.31 | REDUCE: (3), (5) imply: % 136.47/20.31 | (6) $false % 136.47/20.31 | % 136.47/20.31 | CLOSE: (6) is inconsistent. % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #507 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.47/20.31 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.47/20.31 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.47/20.31 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.47/20.31 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) % 136.47/20.31 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.31 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 136.47/20.31 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 136.47/20.31 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 136.47/20.31 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.31 (3) ~ (e3 = e2) % 136.47/20.31 (4) op(e0, e2) = all_52_7 % 136.47/20.31 (5) ~ (all_52_7 = e0) % 136.47/20.31 (6) op(e0, e0) = e2 % 136.47/20.31 (7) op(e0, e0) = all_56_31 % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | BETA: splitting (1) gives: % 136.47/20.31 | % 136.47/20.31 | Case 1: % 136.47/20.31 | | % 136.47/20.31 | | (8) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.47/20.31 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.31 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.47/20.31 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 136.47/20.31 | | $i(all_56_17) & $i(all_56_25) % 136.47/20.31 | | % 136.47/20.31 | | ALPHA: (8) implies: % 136.47/20.31 | | (9) all_56_31 = e3 % 136.47/20.31 | | % 136.47/20.31 | | REDUCE: (7), (9) imply: % 136.47/20.31 | | (10) op(e0, e0) = e3 % 136.47/20.31 | | % 136.47/20.31 | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #634. % 136.47/20.31 | | % 136.47/20.31 | Case 2: % 136.47/20.31 | | % 136.47/20.31 | | (11) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.47/20.31 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.47/20.31 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.47/20.31 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 136.47/20.31 | | $i(all_56_19) & $i(all_56_27) % 136.47/20.31 | | % 136.47/20.31 | | ALPHA: (11) implies: % 136.47/20.31 | | (12) op(e0, e2) = e0 % 136.47/20.31 | | % 136.47/20.31 | | REF_CLOSE: (2), (4), (5), (12) are inconsistent by sub-proof #545. % 136.47/20.31 | | % 136.47/20.31 | End of split % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #508 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.47/20.31 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.47/20.31 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.47/20.31 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.47/20.31 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ % 136.47/20.31 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 136.47/20.31 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = % 136.47/20.31 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.47/20.31 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.31 $i(all_56_29)) % 136.47/20.31 (2) op(e1, e1) = all_6_2 % 136.47/20.31 (3) op(e2, e2) = e0 % 136.47/20.31 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.31 (5) op(e1, e1) = e1 % 136.47/20.31 (6) ~ (e3 = e1) % 136.47/20.31 (7) ~ (e1 = e0) % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | BETA: splitting (1) gives: % 136.47/20.31 | % 136.47/20.31 | Case 1: % 136.47/20.31 | | % 136.47/20.31 | | (8) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.47/20.31 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.31 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.47/20.31 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) % 136.47/20.31 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.47/20.31 | | % 136.47/20.31 | | ALPHA: (8) implies: % 136.47/20.31 | | (9) op(e1, e1) = e3 % 136.47/20.31 | | % 136.47/20.31 | | REF_CLOSE: (2), (4), (5), (6), (9) are inconsistent by sub-proof #662. % 136.47/20.31 | | % 136.47/20.31 | Case 2: % 136.47/20.31 | | % 136.47/20.31 | | (10) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.47/20.31 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = % 136.47/20.31 | | e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.47/20.31 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.47/20.31 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.47/20.31 | | % 136.47/20.31 | | ALPHA: (10) implies: % 136.47/20.31 | | (11) op(e2, e2) = e1 % 136.47/20.31 | | % 136.47/20.31 | | REF_CLOSE: (3), (4), (7), (11) are inconsistent by sub-proof #675. % 136.47/20.31 | | % 136.47/20.31 | End of split % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #509 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 136.47/20.31 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 136.47/20.31 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.47/20.31 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.47/20.31 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.47/20.31 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.47/20.31 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 136.47/20.31 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.31 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.47/20.31 $i(all_56_21) & $i(all_56_29)) % 136.47/20.31 (2) op(e3, e3) = e1 % 136.47/20.31 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.31 (4) ~ (e2 = e1) % 136.47/20.31 (5) op(e1, e1) = e1 % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | BETA: splitting (1) gives: % 136.47/20.31 | % 136.47/20.31 | Case 1: % 136.47/20.31 | | % 136.47/20.31 | | (6) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.47/20.31 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.47/20.31 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.47/20.31 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.47/20.31 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.47/20.31 | | % 136.47/20.31 | | ALPHA: (6) implies: % 136.47/20.31 | | (7) op(e3, e3) = e2 % 136.47/20.31 | | % 136.47/20.31 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #743. % 136.47/20.31 | | % 136.47/20.31 | Case 2: % 136.47/20.31 | | % 136.47/20.31 | | (8) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.47/20.31 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 136.47/20.31 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.47/20.31 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.47/20.31 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.47/20.31 | | % 136.47/20.31 | | ALPHA: (8) implies: % 136.47/20.31 | | (9) ~ (all_56_21 = e1) % 136.47/20.31 | | (10) op(e1, e1) = all_56_21 % 136.47/20.31 | | % 136.47/20.31 | | REF_CLOSE: (3), (5), (9), (10) are inconsistent by sub-proof #510. % 136.47/20.31 | | % 136.47/20.31 | End of split % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #510 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.31 (2) op(e1, e1) = all_56_21 % 136.47/20.31 (3) op(e1, e1) = e1 % 136.47/20.31 (4) ~ (all_56_21 = e1) % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | GROUND_INST: instantiating (1) with e1, all_56_21, e1, e1, simplifying with % 136.47/20.31 | (2), (3) gives: % 136.47/20.31 | (5) all_56_21 = e1 % 136.47/20.31 | % 136.47/20.31 | REDUCE: (4), (5) imply: % 136.47/20.31 | (6) $false % 136.47/20.31 | % 136.47/20.31 | CLOSE: (6) is inconsistent. % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #511 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) op(e1, e1) = all_6_2 % 136.47/20.31 (2) ~ (all_52_11 = e2) % 136.47/20.31 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.31 (4) op(e0, e1) = all_52_11 % 136.47/20.31 (5) ~ (all_6_2 = e2) % 136.47/20.31 (6) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | BETA: splitting (6) gives: % 136.47/20.31 | % 136.47/20.31 | Case 1: % 136.47/20.31 | | % 136.47/20.31 | | (7) all_57_8 = e2 & op(e1, e1) = e2 % 136.47/20.31 | | % 136.47/20.31 | | ALPHA: (7) implies: % 136.47/20.31 | | (8) op(e1, e1) = e2 % 136.47/20.31 | | % 136.47/20.31 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #767. % 136.47/20.31 | | % 136.47/20.31 | Case 2: % 136.47/20.31 | | % 136.47/20.31 | | (9) all_57_14 = e2 & op(e0, e1) = e2 % 136.47/20.31 | | % 136.47/20.31 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #512. % 136.47/20.31 | | % 136.47/20.31 | End of split % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #512 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) all_57_14 = e2 & op(e0, e1) = e2 % 136.47/20.31 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.31 (3) op(e0, e1) = all_52_11 % 136.47/20.31 (4) ~ (all_52_11 = e2) % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | ALPHA: (1) implies: % 136.47/20.31 | (5) op(e0, e1) = e2 % 136.47/20.31 | % 136.47/20.31 | GROUND_INST: instantiating (2) with all_52_11, e2, e1, e0, simplifying with % 136.47/20.31 | (3), (5) gives: % 136.47/20.31 | (6) all_52_11 = e2 % 136.47/20.31 | % 136.47/20.31 | REDUCE: (4), (6) imply: % 136.47/20.31 | (7) $false % 136.47/20.31 | % 136.47/20.31 | CLOSE: (7) is inconsistent. % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #513 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) op(e1, e1) = all_6_2 % 136.47/20.31 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.31 (3) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2) % 136.47/20.31 (4) ~ (all_52_14 = e2) % 136.47/20.31 (5) ~ (all_6_2 = e2) % 136.47/20.31 (6) op(e1, e0) = all_52_14 % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | BETA: splitting (3) gives: % 136.47/20.31 | % 136.47/20.31 | Case 1: % 136.47/20.31 | | % 136.47/20.31 | | (7) all_57_8 = e2 & op(e1, e1) = e2 % 136.47/20.31 | | % 136.47/20.31 | | ALPHA: (7) implies: % 136.47/20.31 | | (8) op(e1, e1) = e2 % 136.47/20.31 | | % 136.47/20.31 | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #767. % 136.47/20.31 | | % 136.47/20.31 | Case 2: % 136.47/20.31 | | % 136.47/20.31 | | (9) all_57_11 = e2 & op(e1, e0) = e2 % 136.47/20.31 | | % 136.47/20.31 | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #514. % 136.47/20.31 | | % 136.47/20.31 | End of split % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #514 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) all_57_11 = e2 & op(e1, e0) = e2 % 136.47/20.31 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.31 (3) op(e1, e0) = all_52_14 % 136.47/20.31 (4) ~ (all_52_14 = e2) % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | ALPHA: (1) implies: % 136.47/20.31 | (5) op(e1, e0) = e2 % 136.47/20.31 | % 136.47/20.31 | GROUND_INST: instantiating (2) with all_52_14, e2, e0, e1, simplifying with % 136.47/20.31 | (3), (5) gives: % 136.47/20.31 | (6) all_52_14 = e2 % 136.47/20.31 | % 136.47/20.31 | REDUCE: (4), (6) imply: % 136.47/20.31 | (7) $false % 136.47/20.31 | % 136.47/20.31 | CLOSE: (7) is inconsistent. % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #515 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) all_57_7 = e2 & op(e1, e2) = e2 % 136.47/20.31 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.31 (3) op(e1, e2) = all_52_6 % 136.47/20.31 (4) ~ (all_52_6 = e2) % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | ALPHA: (1) implies: % 136.47/20.31 | (5) op(e1, e2) = e2 % 136.47/20.31 | % 136.47/20.31 | GROUND_INST: instantiating (2) with all_52_6, e2, e2, e1, simplifying with % 136.47/20.31 | (3), (5) gives: % 136.47/20.31 | (6) all_52_6 = e2 % 136.47/20.31 | % 136.47/20.31 | REDUCE: (4), (6) imply: % 136.47/20.31 | (7) $false % 136.47/20.31 | % 136.47/20.31 | CLOSE: (7) is inconsistent. % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #516 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) all_57_12 = e1 & op(e0, e3) = e1 % 136.47/20.31 (2) all_57_12 = e2 % 136.47/20.31 (3) ~ (e2 = e1) % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | ALPHA: (1) implies: % 136.47/20.31 | (4) all_57_12 = e1 % 136.47/20.31 | % 136.47/20.31 | COMBINE_EQS: (2), (4) imply: % 136.47/20.31 | (5) e2 = e1 % 136.47/20.31 | % 136.47/20.31 | REDUCE: (3), (5) imply: % 136.47/20.31 | (6) $false % 136.47/20.31 | % 136.47/20.31 | CLOSE: (6) is inconsistent. % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #517 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.31 (2) ~ (e2 = e1) % 136.47/20.31 (3) op(e1, e3) = e2 % 136.47/20.31 (4) op(e1, e3) = e1 % 136.47/20.31 (5) op(e1, e3) = all_52_2 % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | GROUND_INST: instantiating (1) with all_52_2, e1, e3, e1, simplifying with % 136.47/20.31 | (4), (5) gives: % 136.47/20.31 | (6) all_52_2 = e1 % 136.47/20.31 | % 136.47/20.31 | GROUND_INST: instantiating (1) with all_52_2, e2, e3, e1, simplifying with % 136.47/20.31 | (3), (5) gives: % 136.47/20.31 | (7) all_52_2 = e2 % 136.47/20.31 | % 136.47/20.31 | COMBINE_EQS: (6), (7) imply: % 136.47/20.31 | (8) e2 = e1 % 136.47/20.31 | % 136.47/20.31 | REDUCE: (2), (8) imply: % 136.47/20.31 | (9) $false % 136.47/20.31 | % 136.47/20.31 | CLOSE: (9) is inconsistent. % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #518 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) all_57_12 = e3 % 136.47/20.31 (2) all_57_12 = e2 % 136.47/20.31 (3) ~ (e3 = e2) % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | COMBINE_EQS: (1), (2) imply: % 136.47/20.31 | (4) e3 = e2 % 136.47/20.31 | % 136.47/20.31 | SIMP: (4) implies: % 136.47/20.31 | (5) e3 = e2 % 136.47/20.31 | % 136.47/20.31 | REDUCE: (3), (5) imply: % 136.47/20.31 | (6) $false % 136.47/20.31 | % 136.47/20.31 | CLOSE: (6) is inconsistent. % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #519 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) ~ (e2 = e0) % 136.47/20.31 (2) op(e3, e3) = e1 % 136.47/20.31 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.31 (4) ~ (e3 = e0) % 136.47/20.31 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.47/20.31 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.47/20.31 (6) all_57_2 = e3 % 136.47/20.31 (7) ~ (e1 = e0) % 136.47/20.31 (8) all_57_6 = e2 % 136.47/20.31 (9) all_57_12 = e2 % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | BETA: splitting (5) gives: % 136.47/20.31 | % 136.47/20.31 | Case 1: % 136.47/20.31 | | % 136.47/20.31 | | (10) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = % 136.47/20.31 | | e0) % 136.47/20.31 | | % 136.47/20.31 | | BETA: splitting (10) gives: % 136.47/20.31 | | % 136.47/20.31 | | Case 1: % 136.47/20.31 | | | % 136.47/20.31 | | | (11) all_57_0 = e0 & op(e3, e3) = e0 % 136.47/20.31 | | | % 136.47/20.31 | | | ALPHA: (11) implies: % 136.47/20.31 | | | (12) op(e3, e3) = e0 % 136.47/20.31 | | | % 136.47/20.31 | | | REF_CLOSE: (2), (3), (7), (12) are inconsistent by sub-proof #717. % 136.47/20.31 | | | % 136.47/20.31 | | Case 2: % 136.47/20.31 | | | % 136.47/20.31 | | | (13) all_57_2 = e0 & op(e2, e3) = e0 % 136.47/20.31 | | | % 136.47/20.31 | | | REF_CLOSE: (4), (6), (13) are inconsistent by sub-proof #521. % 136.47/20.31 | | | % 136.47/20.31 | | End of split % 136.47/20.31 | | % 136.47/20.31 | Case 2: % 136.47/20.31 | | % 136.47/20.31 | | (14) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = % 136.47/20.31 | | e0) % 136.47/20.31 | | % 136.47/20.31 | | BETA: splitting (14) gives: % 136.47/20.31 | | % 136.47/20.31 | | Case 1: % 136.47/20.31 | | | % 136.47/20.31 | | | (15) all_57_6 = e0 & op(e1, e3) = e0 % 136.47/20.31 | | | % 136.47/20.31 | | | REF_CLOSE: (1), (8), (15) are inconsistent by sub-proof #520. % 136.47/20.31 | | | % 136.47/20.31 | | Case 2: % 136.47/20.31 | | | % 136.47/20.31 | | | (16) all_57_12 = e0 & op(e0, e3) = e0 % 136.47/20.31 | | | % 136.47/20.31 | | | REF_CLOSE: (1), (9), (16) are inconsistent by sub-proof #578. % 136.47/20.31 | | | % 136.47/20.31 | | End of split % 136.47/20.31 | | % 136.47/20.31 | End of split % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #520 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) all_57_6 = e0 & op(e1, e3) = e0 % 136.47/20.31 (2) all_57_6 = e2 % 136.47/20.31 (3) ~ (e2 = e0) % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | ALPHA: (1) implies: % 136.47/20.31 | (4) all_57_6 = e0 % 136.47/20.31 | % 136.47/20.31 | COMBINE_EQS: (2), (4) imply: % 136.47/20.31 | (5) e2 = e0 % 136.47/20.31 | % 136.47/20.31 | REDUCE: (3), (5) imply: % 136.47/20.31 | (6) $false % 136.47/20.31 | % 136.47/20.31 | CLOSE: (6) is inconsistent. % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #521 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) all_57_2 = e0 & op(e2, e3) = e0 % 136.47/20.31 (2) all_57_2 = e3 % 136.47/20.31 (3) ~ (e3 = e0) % 136.47/20.31 % 136.47/20.31 Begin of proof % 136.47/20.31 | % 136.47/20.31 | ALPHA: (1) implies: % 136.47/20.31 | (4) all_57_2 = e0 % 136.47/20.31 | % 136.47/20.31 | COMBINE_EQS: (2), (4) imply: % 136.47/20.31 | (5) e3 = e0 % 136.47/20.31 | % 136.47/20.31 | REDUCE: (3), (5) imply: % 136.47/20.31 | (6) $false % 136.47/20.31 | % 136.47/20.31 | CLOSE: (6) is inconsistent. % 136.47/20.31 | % 136.47/20.31 End of proof % 136.47/20.31 % 136.47/20.31 Sub-proof #522 shows that the following formulas are inconsistent: % 136.47/20.31 ---------------------------------------------------------------- % 136.47/20.31 (1) op(e1, e1) = all_6_2 % 136.47/20.31 (2) op(e2, e0) = all_52_13 % 136.47/20.31 (3) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & % 136.47/20.31 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & % 136.47/20.31 $i(all_40_1)) % 136.47/20.31 (4) ~ (all_52_8 = all_52_9) % 136.47/20.31 (5) ~ (all_52_1 = all_52_2) % 136.47/20.31 (6) all_40_2 = all_6_2 % 136.47/20.31 (7) ~ (all_6_2 = e3) % 136.47/20.31 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.31 (9) ~ (e2 = e1) % 136.47/20.31 (10) op(e1, e3) = e2 % 136.47/20.31 (11) ~ (e3 = e2) % 136.47/20.31 (12) ~ (all_52_11 = all_6_2) % 136.47/20.31 (13) ~ (all_52_8 = all_52_11) % 136.47/20.31 (14) op(e0, e1) = all_52_11 % 136.47/20.31 (15) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 136.47/20.31 (16) ~ (all_10_2 = e0) % 136.47/20.31 (17) ~ (all_52_13 = e2) % 136.47/20.31 (18) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.47/20.31 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.47/20.31 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.47/20.31 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.47/20.31 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.47/20.31 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.47/20.31 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) % 136.47/20.31 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.31 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.47/20.31 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 136.47/20.31 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.47/20.31 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 136.47/20.31 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 136.47/20.31 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.47/20.31 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) % 136.47/20.31 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.47/20.31 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 136.47/20.31 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 136.47/20.31 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.47/20.31 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.47/20.31 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.31 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 136.47/20.31 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & % 136.47/20.31 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & % 136.47/20.31 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.47/20.31 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 136.47/20.31 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.31 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.47/20.31 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ % 136.47/20.31 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.47/20.31 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 136.47/20.31 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 136.47/20.31 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.47/20.31 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) % 136.47/20.31 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.31 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.47/20.31 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 % 136.47/20.31 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.47/20.31 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = % 136.47/20.31 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 136.47/20.31 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 136.47/20.31 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.47/20.31 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.47/20.31 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 136.47/20.31 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 136.47/20.31 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.47/20.31 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.47/20.31 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.47/20.31 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.47/20.31 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.47/20.31 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.47/20.31 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.47/20.31 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.47/20.31 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.47/20.31 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.47/20.31 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.47/20.31 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.31 $i(all_56_29)))) % 136.47/20.31 (19) ~ (all_52_8 = all_6_2) % 136.47/20.31 (20) op(e3, e3) = all_10_2 % 136.47/20.31 (21) op(e3, e1) = e2 % 136.47/20.32 (22) op(e2, e1) = all_52_9 % 136.47/20.32 (23) op(e1, e3) = all_52_2 % 136.47/20.32 (24) op(e0, e0) = e2 % 136.47/20.32 (25) op(e2, e3) = all_52_1 % 136.47/20.32 (26) op(e3, e1) = all_52_8 % 136.47/20.32 (27) all_54_14 = all_52_11 % 136.47/20.32 (28) ~ (all_52_8 = all_10_2) % 136.47/20.32 (29) op(e2, e2) = e2 % 136.47/20.32 % 136.47/20.32 Begin of proof % 136.47/20.32 | % 136.47/20.32 | GROUND_INST: instantiating (8) with all_52_2, e2, e3, e1, simplifying with % 136.47/20.32 | (10), (23) gives: % 136.47/20.32 | (30) all_52_2 = e2 % 136.47/20.32 | % 136.47/20.32 | GROUND_INST: instantiating (8) with all_52_8, e2, e1, e3, simplifying with % 136.47/20.32 | (21), (26) gives: % 136.47/20.32 | (31) all_52_8 = e2 % 136.47/20.32 | % 136.47/20.32 | REDUCE: (5), (30) imply: % 136.47/20.32 | (32) ~ (all_52_1 = e2) % 136.47/20.32 | % 136.47/20.32 | REDUCE: (4), (31) imply: % 136.47/20.32 | (33) ~ (all_52_9 = e2) % 136.47/20.32 | % 136.47/20.32 | SIMP: (33) implies: % 136.47/20.32 | (34) ~ (all_52_9 = e2) % 136.47/20.32 | % 136.47/20.32 | REDUCE: (13), (31) imply: % 136.47/20.32 | (35) ~ (all_52_11 = e2) % 136.47/20.32 | % 136.47/20.32 | SIMP: (35) implies: % 136.47/20.32 | (36) ~ (all_52_11 = e2) % 136.47/20.32 | % 136.47/20.32 | REDUCE: (28), (31) imply: % 136.47/20.32 | (37) ~ (all_10_2 = e2) % 136.47/20.32 | % 136.47/20.32 | SIMP: (37) implies: % 136.47/20.32 | (38) ~ (all_10_2 = e2) % 136.47/20.32 | % 136.47/20.32 | REDUCE: (19), (31) imply: % 136.47/20.32 | (39) ~ (all_6_2 = e2) % 136.47/20.32 | % 136.47/20.32 | SIMP: (39) implies: % 136.47/20.32 | (40) ~ (all_6_2 = e2) % 136.47/20.32 | % 136.47/20.32 | BETA: splitting (18) gives: % 136.47/20.32 | % 136.47/20.32 | Case 1: % 136.47/20.32 | | % 136.47/20.32 | | (41) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.47/20.32 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = % 136.47/20.32 | | e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.47/20.32 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.47/20.32 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.47/20.32 | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.47/20.32 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = % 136.47/20.32 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.47/20.32 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.47/20.32 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 136.47/20.32 | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 % 136.47/20.32 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = % 136.47/20.32 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 136.47/20.32 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 136.47/20.32 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 136.47/20.32 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.47/20.32 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.32 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.47/20.32 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 136.47/20.32 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 136.47/20.32 | | % 136.47/20.32 | | BETA: splitting (41) gives: % 136.47/20.32 | | % 136.47/20.32 | | Case 1: % 136.47/20.32 | | | % 136.47/20.32 | | | (42) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ % 136.47/20.32 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.32 | | | op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & % 136.47/20.32 | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 136.47/20.32 | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.47/20.32 | | | $i(all_56_27)) | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 % 136.47/20.32 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 136.47/20.32 | | | (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, % 136.47/20.32 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.32 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.47/20.32 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 136.47/20.32 | | | % 136.47/20.32 | | | BETA: splitting (42) gives: % 136.47/20.32 | | | % 136.47/20.32 | | | Case 1: % 136.47/20.32 | | | | % 136.47/20.32 | | | | (43) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ % 136.47/20.32 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.32 | | | | op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & % 136.47/20.32 | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 136.47/20.32 | | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.47/20.32 | | | | $i(all_56_27) % 136.47/20.32 | | | | % 136.47/20.32 | | | | ALPHA: (43) implies: % 136.47/20.32 | | | | (44) op(e3, e3) = e2 % 136.47/20.32 | | | | % 136.47/20.32 | | | | REF_CLOSE: (8), (20), (38), (44) are inconsistent by sub-proof #536. % 136.47/20.32 | | | | % 136.47/20.32 | | | Case 2: % 136.47/20.32 | | | | % 136.47/20.32 | | | | (45) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ % 136.47/20.32 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.47/20.32 | | | | op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & % 136.47/20.32 | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.47/20.32 | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.32 | | | | $i(all_56_29) % 136.47/20.32 | | | | % 136.47/20.32 | | | | ALPHA: (45) implies: % 136.47/20.32 | | | | (46) op(e3, e1) = e3 % 136.47/20.32 | | | | % 136.47/20.32 | | | | GROUND_INST: instantiating (8) with e2, e3, e1, e3, simplifying with % 136.47/20.32 | | | | (21), (46) gives: % 136.47/20.32 | | | | (47) e3 = e2 % 136.47/20.32 | | | | % 136.47/20.32 | | | | REDUCE: (11), (47) imply: % 136.47/20.32 | | | | (48) $false % 136.47/20.32 | | | | % 136.47/20.32 | | | | CLOSE: (48) is inconsistent. % 136.47/20.32 | | | | % 136.47/20.32 | | | End of split % 136.47/20.32 | | | % 136.47/20.32 | | Case 2: % 136.47/20.32 | | | % 136.47/20.32 | | | (49) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ % 136.47/20.32 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.47/20.32 | | | op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & % 136.47/20.32 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 136.47/20.32 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.47/20.32 | | | $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 % 136.47/20.32 | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 136.47/20.32 | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 % 136.47/20.32 | | | & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e2, e3) = % 136.47/20.32 | | | e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.47/20.32 | | | $i(all_56_17) & $i(all_56_25)) % 136.47/20.32 | | | % 136.47/20.32 | | | REF_CLOSE: (8), (16), (20), (25), (32), (49) are inconsistent by sub-proof % 136.47/20.32 | | | #533. % 136.47/20.32 | | | % 136.47/20.32 | | End of split % 136.47/20.32 | | % 136.47/20.32 | Case 2: % 136.47/20.32 | | % 136.47/20.32 | | (50) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.47/20.32 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.32 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.47/20.32 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & % 136.47/20.32 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.47/20.32 | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 136.47/20.32 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.47/20.32 | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, % 136.47/20.32 | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.47/20.32 | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.32 | | $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 136.47/20.32 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 % 136.47/20.32 | | = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 136.47/20.32 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.47/20.32 | | op(e0, e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 136.47/20.32 | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 % 136.47/20.32 | | & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 136.47/20.32 | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.47/20.32 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.47/20.32 | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 136.47/20.32 | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 & % 136.47/20.32 | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 136.47/20.32 | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 136.47/20.32 | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 136.47/20.32 | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.47/20.32 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) % 136.47/20.32 | | & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 136.47/20.32 | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 136.47/20.32 | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.47/20.32 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.47/20.32 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 136.47/20.32 | | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 136.47/20.32 | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 136.47/20.32 | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & % 136.47/20.32 | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 136.47/20.32 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 136.47/20.32 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.47/20.32 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.47/20.32 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.32 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.47/20.32 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.32 | | $i(all_56_29)))) % 136.47/20.32 | | % 136.47/20.32 | | BETA: splitting (50) gives: % 136.47/20.32 | | % 136.47/20.32 | | Case 1: % 136.47/20.32 | | | % 136.47/20.32 | | | (51) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ % 136.47/20.32 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.47/20.32 | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.47/20.32 | | | all_56_17 & op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 136.47/20.32 | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.47/20.32 | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 % 136.47/20.32 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 136.47/20.32 | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, % 136.47/20.32 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.32 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.47/20.32 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 136.47/20.32 | | | % 136.47/20.32 | | | REF_CLOSE: (1), (7), (8), (22), (34), (51) are inconsistent by sub-proof % 136.47/20.32 | | | #769. % 136.47/20.32 | | | % 136.47/20.32 | | Case 2: % 136.47/20.32 | | | % 136.47/20.32 | | | (52) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 136.47/20.32 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.47/20.32 | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & % 136.47/20.32 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 136.47/20.32 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.47/20.32 | | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 % 136.47/20.32 | | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 136.47/20.32 | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.47/20.32 | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.47/20.32 | | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) % 136.47/20.32 | | | & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 & % 136.47/20.32 | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 136.47/20.32 | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 136.47/20.32 | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 136.47/20.32 | | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.47/20.32 | | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 136.47/20.32 | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 136.47/20.32 | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ % 136.47/20.32 | | | (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.47/20.32 | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 136.47/20.32 | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 136.47/20.32 | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 136.47/20.32 | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.47/20.32 | | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, % 136.47/20.32 | | | e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 136.47/20.32 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.47/20.32 | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = % 136.47/20.32 | | | e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.47/20.32 | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, % 136.47/20.32 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.32 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.47/20.32 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.32 | | | $i(all_56_29)))) % 136.47/20.32 | | | % 136.47/20.32 | | | BETA: splitting (52) gives: % 136.47/20.32 | | | % 136.47/20.32 | | | Case 1: % 136.47/20.32 | | | | % 136.47/20.32 | | | | (53) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 136.47/20.32 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.47/20.32 | | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & % 136.47/20.32 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 136.47/20.32 | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.47/20.32 | | | | $i(all_56_31) % 136.47/20.32 | | | | % 136.47/20.32 | | | | ALPHA: (53) implies: % 136.47/20.32 | | | | (54) op(e2, e0) = e2 % 136.47/20.32 | | | | % 136.47/20.32 | | | | REF_CLOSE: (2), (8), (17), (54) are inconsistent by sub-proof #768. % 136.47/20.32 | | | | % 136.47/20.32 | | | Case 2: % 136.47/20.32 | | | | % 136.47/20.32 | | | | (55) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 136.47/20.32 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.32 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.47/20.32 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 136.47/20.32 | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.47/20.32 | | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 136.47/20.32 | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.47/20.32 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = % 136.47/20.32 | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 136.47/20.32 | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 136.47/20.32 | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.47/20.32 | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 136.47/20.32 | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 136.47/20.32 | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 136.47/20.32 | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.47/20.32 | | | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 136.47/20.32 | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.47/20.32 | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.47/20.32 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = % 136.47/20.32 | | | | e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 136.47/20.32 | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 % 136.47/20.32 | | | | & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 136.47/20.32 | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.47/20.32 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = % 136.47/20.32 | | | | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.47/20.32 | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, % 136.47/20.32 | | | | e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 136.47/20.32 | | | | & $i(all_56_29)))) % 136.47/20.32 | | | | % 136.47/20.32 | | | | BETA: splitting (55) gives: % 136.47/20.32 | | | | % 136.47/20.32 | | | | Case 1: % 136.47/20.32 | | | | | % 136.47/20.32 | | | | | (56) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 136.47/20.32 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.32 | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.47/20.32 | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 136.47/20.32 | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.47/20.32 | | | | | $i(all_56_27) % 136.47/20.32 | | | | | % 136.47/20.32 | | | | | ALPHA: (56) implies: % 136.47/20.32 | | | | | (57) op(e1, e1) = e2 % 136.47/20.32 | | | | | % 136.47/20.32 | | | | | REF_CLOSE: (1), (8), (40), (57) are inconsistent by sub-proof #767. % 136.47/20.32 | | | | | % 136.47/20.32 | | | | Case 2: % 136.47/20.32 | | | | | % 136.47/20.32 | | | | | (58) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 136.47/20.32 | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & % 136.47/20.32 | | | | | ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.32 | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 136.47/20.32 | | | | | & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) % 136.47/20.32 | | | | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.47/20.32 | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.47/20.32 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = % 136.47/20.32 | | | | | e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.47/20.32 | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 136.47/20.32 | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 136.47/20.32 | | | | | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 136.47/20.32 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 136.47/20.32 | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 136.47/20.32 | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.47/20.32 | | | | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & % 136.47/20.32 | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~ % 136.47/20.32 | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 136.47/20.32 | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 136.47/20.32 | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 136.47/20.32 | | | | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 136.47/20.32 | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))) % 136.47/20.32 | | | | | % 136.47/20.32 | | | | | ALPHA: (58) implies: % 136.47/20.32 | | | | | (59) op(e0, e0) = all_56_31 % 136.47/20.32 | | | | | (60) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.47/20.32 | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) % 136.47/20.32 | | | | | & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 136.47/20.32 | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.47/20.32 | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 136.47/20.32 | | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.47/20.32 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) % 136.47/20.32 | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.47/20.32 | | | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 % 136.47/20.32 | | | | | & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.47/20.32 | | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 136.47/20.32 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 136.47/20.32 | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & % 136.47/20.32 | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) % 136.47/20.32 | | | | | = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 136.47/20.32 | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.47/20.32 | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) % 136.47/20.32 | | | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, % 136.47/20.32 | | | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 % 136.47/20.32 | | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.32 | | | | | $i(all_56_29)) % 136.47/20.32 | | | | | % 136.47/20.32 | | | | | REF_CLOSE: (1), (3), (6), (8), (9), (11), (12), (14), (15), (24), % 136.47/20.32 | | | | | (27), (29), (36), (59), (60) are inconsistent by sub-proof % 136.47/20.32 | | | | | #523. % 136.47/20.32 | | | | | % 136.47/20.32 | | | | End of split % 136.47/20.32 | | | | % 136.47/20.32 | | | End of split % 136.47/20.32 | | | % 136.47/20.32 | | End of split % 136.47/20.32 | | % 136.47/20.32 | End of split % 136.47/20.32 | % 136.47/20.32 End of proof % 136.47/20.32 % 136.47/20.32 Sub-proof #523 shows that the following formulas are inconsistent: % 136.47/20.32 ---------------------------------------------------------------- % 136.47/20.32 (1) op(e1, e1) = all_6_2 % 136.47/20.32 (2) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & % 136.47/20.32 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & % 136.47/20.32 $i(all_40_1)) % 136.47/20.32 (3) ~ (all_52_11 = e2) % 136.47/20.32 (4) all_40_2 = all_6_2 % 136.47/20.32 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.32 (6) ~ (e2 = e1) % 136.47/20.32 (7) ~ (e3 = e2) % 136.47/20.32 (8) ~ (all_52_11 = all_6_2) % 136.47/20.32 (9) op(e0, e1) = all_52_11 % 136.47/20.32 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 136.47/20.32 (11) op(e0, e0) = e2 % 136.47/20.32 (12) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.47/20.32 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.32 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 136.47/20.32 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 136.47/20.32 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 136.47/20.32 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 136.47/20.32 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.47/20.32 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.47/20.32 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.47/20.32 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.47/20.32 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 136.47/20.32 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.47/20.32 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 136.47/20.32 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.47/20.32 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 136.47/20.32 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 136.47/20.32 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.47/20.32 $i(all_56_21) & $i(all_56_29)) % 136.47/20.32 (13) all_54_14 = all_52_11 % 136.47/20.32 (14) op(e2, e2) = e2 % 136.47/20.32 (15) op(e0, e0) = all_56_31 % 136.47/20.32 % 136.47/20.32 Begin of proof % 136.47/20.32 | % 136.47/20.32 | GROUND_INST: instantiating (5) with e2, all_56_31, e0, e0, simplifying with % 136.47/20.32 | (11), (15) gives: % 136.47/20.32 | (16) all_56_31 = e2 % 136.47/20.32 | % 136.47/20.32 | BETA: splitting (12) gives: % 136.47/20.32 | % 136.47/20.32 | Case 1: % 136.47/20.32 | | % 136.47/20.32 | | (17) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.47/20.32 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.32 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.47/20.32 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 136.47/20.32 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 136.47/20.32 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 136.47/20.32 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.47/20.32 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.47/20.32 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.47/20.32 | | $i(all_56_27)) % 136.47/20.32 | | % 136.47/20.32 | | REF_CLOSE: (5), (7), (14), (16), (17) are inconsistent by sub-proof #530. % 136.47/20.32 | | % 136.47/20.32 | Case 2: % 136.47/20.32 | | % 136.47/20.32 | | (18) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.47/20.32 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.47/20.32 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.47/20.32 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.47/20.32 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.47/20.32 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.47/20.32 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.47/20.32 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.47/20.32 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.32 | | $i(all_56_29)) % 136.47/20.32 | | % 136.47/20.32 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (16), % 136.47/20.32 | | (18) are inconsistent by sub-proof #524. % 136.47/20.32 | | % 136.47/20.32 | End of split % 136.47/20.32 | % 136.47/20.32 End of proof % 136.47/20.32 % 136.47/20.32 Sub-proof #524 shows that the following formulas are inconsistent: % 136.47/20.32 ---------------------------------------------------------------- % 136.47/20.32 (1) op(e1, e1) = all_6_2 % 136.47/20.32 (2) ~ (all_40_2 = e0) | ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & % 136.47/20.32 $i(all_40_0)) | ( ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & % 136.47/20.32 $i(all_40_1)) % 136.47/20.32 (3) ~ (all_52_11 = e2) % 136.47/20.32 (4) all_56_31 = e2 % 136.47/20.32 (5) all_40_2 = all_6_2 % 136.47/20.32 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.32 (7) ~ (e2 = e1) % 136.47/20.32 (8) ~ (all_52_11 = all_6_2) % 136.47/20.32 (9) op(e0, e1) = all_52_11 % 136.47/20.32 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 136.47/20.32 (11) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.47/20.32 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 136.47/20.32 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.47/20.32 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 136.47/20.32 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.47/20.32 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 136.47/20.32 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 136.47/20.32 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.47/20.32 $i(all_56_21) & $i(all_56_29)) % 136.47/20.32 (12) op(e0, e0) = e2 % 136.47/20.32 (13) all_54_14 = all_52_11 % 136.47/20.32 % 136.47/20.32 Begin of proof % 136.47/20.32 | % 136.47/20.32 | BETA: splitting (11) gives: % 136.47/20.32 | % 136.47/20.32 | Case 1: % 136.47/20.32 | | % 136.47/20.32 | | (14) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 % 136.47/20.32 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = % 136.47/20.32 | | e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = % 136.47/20.32 | | all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & % 136.47/20.32 | | $i(all_56_23) % 136.47/20.32 | | % 136.47/20.32 | | ALPHA: (14) implies: % 136.47/20.32 | | (15) ~ (all_56_23 = e1) % 136.47/20.32 | | (16) op(e0, e1) = all_56_23 % 136.47/20.32 | | (17) op(e1, e1) = e0 % 136.47/20.32 | | % 136.47/20.32 | | GROUND_INST: instantiating (6) with all_52_11, all_56_23, e1, e0, % 136.47/20.32 | | simplifying with (9), (16) gives: % 136.47/20.32 | | (18) all_56_23 = all_52_11 % 136.47/20.32 | | % 136.47/20.32 | | GROUND_INST: instantiating (6) with all_6_2, e0, e1, e1, simplifying with % 136.47/20.32 | | (1), (17) gives: % 136.47/20.32 | | (19) all_6_2 = e0 % 136.47/20.32 | | % 136.47/20.32 | | COMBINE_EQS: (5), (19) imply: % 136.47/20.32 | | (20) all_40_2 = e0 % 136.47/20.32 | | % 136.47/20.32 | | REDUCE: (15), (18) imply: % 136.47/20.32 | | (21) ~ (all_52_11 = e1) % 136.47/20.32 | | % 136.47/20.32 | | REDUCE: (8), (19) imply: % 136.47/20.32 | | (22) ~ (all_52_11 = e0) % 136.47/20.32 | | % 136.47/20.32 | | BETA: splitting (2) gives: % 136.47/20.32 | | % 136.47/20.32 | | Case 1: % 136.47/20.32 | | | % 136.47/20.32 | | | (23) ~ (all_40_2 = e0) % 136.47/20.32 | | | % 136.47/20.32 | | | REDUCE: (20), (23) imply: % 136.47/20.32 | | | (24) $false % 136.47/20.32 | | | % 136.47/20.32 | | | CLOSE: (24) is inconsistent. % 136.47/20.32 | | | % 136.47/20.32 | | Case 2: % 136.47/20.32 | | | % 136.47/20.32 | | | (25) ( ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & $i(all_40_0)) | ( ~ % 136.47/20.32 | | | (all_40_1 = e2) & op(e0, e0) = all_40_1 & $i(all_40_1)) % 136.47/20.32 | | | % 136.47/20.32 | | | BETA: splitting (10) gives: % 136.47/20.32 | | | % 136.47/20.32 | | | Case 1: % 136.47/20.32 | | | | % 136.47/20.32 | | | | (26) all_54_14 = e3 % 136.47/20.32 | | | | % 136.47/20.32 | | | | COMBINE_EQS: (13), (26) imply: % 136.47/20.32 | | | | (27) all_52_11 = e3 % 136.47/20.32 | | | | % 136.47/20.32 | | | | SIMP: (27) implies: % 136.47/20.32 | | | | (28) all_52_11 = e3 % 136.47/20.32 | | | | % 136.47/20.32 | | | | REDUCE: (9), (28) imply: % 136.47/20.32 | | | | (29) op(e0, e1) = e3 % 136.47/20.32 | | | | % 136.47/20.32 | | | | BETA: splitting (25) gives: % 136.47/20.32 | | | | % 136.47/20.32 | | | | Case 1: % 136.47/20.32 | | | | | % 136.47/20.32 | | | | | (30) ~ (all_40_0 = e3) & op(e0, e1) = all_40_0 & $i(all_40_0) % 136.47/20.32 | | | | | % 136.47/20.32 | | | | | ALPHA: (30) implies: % 136.47/20.32 | | | | | (31) ~ (all_40_0 = e3) % 136.47/20.32 | | | | | (32) op(e0, e1) = all_40_0 % 136.47/20.32 | | | | | % 136.47/20.32 | | | | | REF_CLOSE: (6), (29), (31), (32) are inconsistent by sub-proof #529. % 136.47/20.32 | | | | | % 136.47/20.32 | | | | Case 2: % 136.47/20.32 | | | | | % 136.47/20.32 | | | | | (33) ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & $i(all_40_1) % 136.47/20.32 | | | | | % 136.47/20.32 | | | | | REF_CLOSE: (6), (12), (33) are inconsistent by sub-proof #528. % 136.47/20.32 | | | | | % 136.47/20.32 | | | | End of split % 136.47/20.32 | | | | % 136.47/20.32 | | | Case 2: % 136.47/20.32 | | | | % 136.47/20.32 | | | | (34) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 136.47/20.32 | | | | % 136.47/20.32 | | | | REF_CLOSE: (3), (13), (21), (22), (34) are inconsistent by sub-proof % 136.47/20.32 | | | | #526. % 136.47/20.32 | | | | % 136.47/20.32 | | | End of split % 136.47/20.32 | | | % 136.47/20.32 | | End of split % 136.47/20.32 | | % 136.47/20.32 | Case 2: % 136.47/20.32 | | % 136.47/20.32 | | (35) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.47/20.32 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 136.47/20.32 | | all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 136.47/20.32 | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.47/20.32 | | $i(all_56_21) & $i(all_56_29) % 136.47/20.32 | | % 136.47/20.32 | | REF_CLOSE: (4), (7), (35) are inconsistent by sub-proof #525. % 136.47/20.32 | | % 136.47/20.32 | End of split % 136.47/20.32 | % 136.47/20.32 End of proof % 136.47/20.32 % 136.47/20.32 Sub-proof #525 shows that the following formulas are inconsistent: % 136.47/20.32 ---------------------------------------------------------------- % 136.47/20.32 (1) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.47/20.32 e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 % 136.47/20.32 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.47/20.32 all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.47/20.32 $i(all_56_21) & $i(all_56_29) % 136.47/20.32 (2) all_56_31 = e2 % 136.47/20.32 (3) ~ (e2 = e1) % 136.47/20.32 % 136.47/20.32 Begin of proof % 136.47/20.32 | % 136.47/20.32 | ALPHA: (1) implies: % 136.47/20.32 | (4) all_56_31 = e1 % 136.47/20.32 | % 136.47/20.32 | COMBINE_EQS: (2), (4) imply: % 136.47/20.32 | (5) e2 = e1 % 136.47/20.32 | % 136.47/20.32 | REDUCE: (3), (5) imply: % 136.47/20.32 | (6) $false % 136.47/20.32 | % 136.47/20.32 | CLOSE: (6) is inconsistent. % 136.47/20.32 | % 136.47/20.32 End of proof % 136.47/20.32 % 136.47/20.32 Sub-proof #526 shows that the following formulas are inconsistent: % 136.47/20.32 ---------------------------------------------------------------- % 136.47/20.32 (1) ~ (all_52_11 = e1) % 136.47/20.32 (2) ~ (all_52_11 = e2) % 136.47/20.32 (3) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0 % 136.47/20.32 (4) ~ (all_52_11 = e0) % 136.47/20.32 (5) all_54_14 = all_52_11 % 136.47/20.32 % 136.47/20.32 Begin of proof % 136.47/20.32 | % 136.47/20.32 | BETA: splitting (3) gives: % 136.47/20.32 | % 136.47/20.32 | Case 1: % 136.47/20.32 | | % 136.47/20.32 | | (6) all_54_14 = e2 % 136.47/20.32 | | % 136.47/20.32 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #527. % 136.47/20.32 | | % 136.47/20.32 | Case 2: % 136.47/20.32 | | % 136.47/20.32 | | (7) all_54_14 = e1 | all_54_14 = e0 % 136.47/20.32 | | % 136.47/20.32 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #755. % 136.47/20.32 | | % 136.47/20.32 | End of split % 136.47/20.32 | % 136.47/20.32 End of proof % 136.47/20.32 % 136.47/20.32 Sub-proof #527 shows that the following formulas are inconsistent: % 136.47/20.32 ---------------------------------------------------------------- % 136.47/20.32 (1) all_54_14 = all_52_11 % 136.47/20.33 (2) all_54_14 = e2 % 136.47/20.33 (3) ~ (all_52_11 = e2) % 136.47/20.33 % 136.47/20.33 Begin of proof % 136.47/20.33 | % 136.47/20.33 | COMBINE_EQS: (1), (2) imply: % 136.47/20.33 | (4) all_52_11 = e2 % 136.47/20.33 | % 136.47/20.33 | SIMP: (4) implies: % 136.47/20.33 | (5) all_52_11 = e2 % 136.47/20.33 | % 136.47/20.33 | REDUCE: (3), (5) imply: % 136.47/20.33 | (6) $false % 136.47/20.33 | % 136.47/20.33 | CLOSE: (6) is inconsistent. % 136.47/20.33 | % 136.47/20.33 End of proof % 136.47/20.33 % 136.47/20.33 Sub-proof #528 shows that the following formulas are inconsistent: % 136.47/20.33 ---------------------------------------------------------------- % 136.47/20.33 (1) ~ (all_40_1 = e2) & op(e0, e0) = all_40_1 & $i(all_40_1) % 136.47/20.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.33 (3) op(e0, e0) = e2 % 136.47/20.33 % 136.47/20.33 Begin of proof % 136.47/20.33 | % 136.47/20.33 | ALPHA: (1) implies: % 136.47/20.33 | (4) ~ (all_40_1 = e2) % 136.47/20.33 | (5) op(e0, e0) = all_40_1 % 136.47/20.33 | % 136.47/20.33 | GROUND_INST: instantiating (2) with e2, all_40_1, e0, e0, simplifying with % 136.47/20.33 | (3), (5) gives: % 136.47/20.33 | (6) all_40_1 = e2 % 136.47/20.33 | % 136.47/20.33 | REDUCE: (4), (6) imply: % 136.47/20.33 | (7) $false % 136.47/20.33 | % 136.47/20.33 | CLOSE: (7) is inconsistent. % 136.47/20.33 | % 136.47/20.33 End of proof % 136.47/20.33 % 136.47/20.33 Sub-proof #529 shows that the following formulas are inconsistent: % 136.47/20.33 ---------------------------------------------------------------- % 136.47/20.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.33 (2) op(e0, e1) = all_40_0 % 136.47/20.33 (3) op(e0, e1) = e3 % 136.47/20.33 (4) ~ (all_40_0 = e3) % 136.47/20.33 % 136.47/20.33 Begin of proof % 136.47/20.33 | % 136.47/20.33 | GROUND_INST: instantiating (1) with e3, all_40_0, e1, e0, simplifying with % 136.47/20.33 | (2), (3) gives: % 136.47/20.33 | (5) all_40_0 = e3 % 136.47/20.33 | % 136.47/20.33 | REDUCE: (4), (5) imply: % 136.47/20.33 | (6) $false % 136.47/20.33 | % 136.47/20.33 | CLOSE: (6) is inconsistent. % 136.47/20.33 | % 136.47/20.33 End of proof % 136.47/20.33 % 136.47/20.33 Sub-proof #530 shows that the following formulas are inconsistent: % 136.47/20.33 ---------------------------------------------------------------- % 136.47/20.33 (1) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.47/20.33 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.47/20.33 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.47/20.33 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.47/20.33 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) % 136.47/20.33 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.33 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 136.47/20.33 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 136.47/20.33 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 136.47/20.33 (2) all_56_31 = e2 % 136.47/20.33 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.33 (4) ~ (e3 = e2) % 136.47/20.33 (5) op(e2, e2) = e2 % 136.47/20.33 % 136.47/20.33 Begin of proof % 136.47/20.33 | % 136.47/20.33 | BETA: splitting (1) gives: % 136.47/20.33 | % 136.47/20.33 | Case 1: % 136.47/20.33 | | % 136.47/20.33 | | (6) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.47/20.33 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.33 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.47/20.33 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 136.47/20.33 | | $i(all_56_17) & $i(all_56_25) % 136.47/20.33 | | % 136.47/20.33 | | ALPHA: (6) implies: % 136.47/20.33 | | (7) all_56_31 = e3 % 136.47/20.33 | | % 136.47/20.33 | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #532. % 136.47/20.33 | | % 136.47/20.33 | Case 2: % 136.47/20.33 | | % 136.47/20.33 | | (8) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.47/20.33 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.47/20.33 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.47/20.33 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 136.47/20.33 | | $i(all_56_19) & $i(all_56_27) % 136.47/20.33 | | % 136.47/20.33 | | ALPHA: (8) implies: % 136.47/20.33 | | (9) ~ (all_56_11 = e2) % 136.47/20.33 | | (10) op(e2, e2) = all_56_11 % 136.47/20.33 | | % 136.47/20.33 | | REF_CLOSE: (3), (5), (9), (10) are inconsistent by sub-proof #531. % 136.47/20.33 | | % 136.47/20.33 | End of split % 136.47/20.33 | % 136.47/20.33 End of proof % 136.47/20.33 % 136.47/20.33 Sub-proof #531 shows that the following formulas are inconsistent: % 136.47/20.33 ---------------------------------------------------------------- % 136.47/20.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.33 (2) op(e2, e2) = all_56_11 % 136.47/20.33 (3) op(e2, e2) = e2 % 136.47/20.33 (4) ~ (all_56_11 = e2) % 136.47/20.33 % 136.47/20.33 Begin of proof % 136.47/20.33 | % 136.47/20.33 | GROUND_INST: instantiating (1) with e2, all_56_11, e2, e2, simplifying with % 136.47/20.33 | (2), (3) gives: % 136.47/20.33 | (5) all_56_11 = e2 % 136.47/20.33 | % 136.47/20.33 | REDUCE: (4), (5) imply: % 136.47/20.33 | (6) $false % 136.47/20.33 | % 136.47/20.33 | CLOSE: (6) is inconsistent. % 136.47/20.33 | % 136.47/20.33 End of proof % 136.47/20.33 % 136.47/20.33 Sub-proof #532 shows that the following formulas are inconsistent: % 136.47/20.33 ---------------------------------------------------------------- % 136.47/20.33 (1) all_56_31 = e3 % 136.47/20.33 (2) all_56_31 = e2 % 136.47/20.33 (3) ~ (e3 = e2) % 136.47/20.33 % 136.47/20.33 Begin of proof % 136.47/20.33 | % 136.47/20.33 | COMBINE_EQS: (1), (2) imply: % 136.47/20.33 | (4) e3 = e2 % 136.47/20.33 | % 136.47/20.33 | SIMP: (4) implies: % 136.47/20.33 | (5) e3 = e2 % 136.47/20.33 | % 136.47/20.33 | REDUCE: (3), (5) imply: % 136.47/20.33 | (6) $false % 136.47/20.33 | % 136.47/20.33 | CLOSE: (6) is inconsistent. % 136.47/20.33 | % 136.47/20.33 End of proof % 136.47/20.33 % 136.47/20.33 Sub-proof #533 shows that the following formulas are inconsistent: % 136.47/20.33 ---------------------------------------------------------------- % 136.47/20.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.33 (2) ~ (all_10_2 = e0) % 136.47/20.33 (3) op(e3, e3) = all_10_2 % 136.47/20.33 (4) ~ (all_52_1 = e2) % 136.47/20.33 (5) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.47/20.33 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.47/20.33 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.47/20.33 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.47/20.33 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 136.47/20.33 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 136.47/20.33 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 136.47/20.33 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.47/20.33 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.47/20.33 $i(all_56_17) & $i(all_56_25)) % 136.47/20.33 (6) op(e2, e3) = all_52_1 % 136.47/20.33 % 136.47/20.33 Begin of proof % 136.47/20.33 | % 136.47/20.33 | BETA: splitting (5) gives: % 136.47/20.33 | % 136.47/20.33 | Case 1: % 136.47/20.33 | | % 136.47/20.33 | | (7) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.47/20.33 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.47/20.33 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.47/20.33 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.47/20.33 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.47/20.33 | | % 136.47/20.33 | | ALPHA: (7) implies: % 136.47/20.33 | | (8) op(e3, e3) = e0 % 136.47/20.33 | | % 136.47/20.33 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #534. % 136.47/20.33 | | % 136.47/20.33 | Case 2: % 136.47/20.33 | | % 136.47/20.33 | | (9) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.47/20.33 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.33 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.47/20.33 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) % 136.47/20.33 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.47/20.33 | | % 136.47/20.33 | | ALPHA: (9) implies: % 136.47/20.33 | | (10) op(e2, e3) = e2 % 136.47/20.33 | | % 136.47/20.33 | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #779. % 136.47/20.33 | | % 136.47/20.33 | End of split % 136.47/20.33 | % 136.47/20.33 End of proof % 136.47/20.33 % 136.47/20.33 Sub-proof #534 shows that the following formulas are inconsistent: % 136.47/20.33 ---------------------------------------------------------------- % 136.47/20.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.33 (2) op(e3, e3) = all_10_2 % 136.47/20.33 (3) op(e3, e3) = e0 % 136.47/20.33 (4) ~ (all_10_2 = e0) % 136.47/20.33 % 136.47/20.33 Begin of proof % 136.47/20.33 | % 136.47/20.33 | GROUND_INST: instantiating (1) with all_10_2, e0, e3, e3, simplifying with % 136.47/20.33 | (2), (3) gives: % 136.47/20.33 | (5) all_10_2 = e0 % 136.47/20.33 | % 136.47/20.33 | REDUCE: (4), (5) imply: % 136.47/20.33 | (6) $false % 136.47/20.33 | % 136.47/20.33 | CLOSE: (6) is inconsistent. % 136.47/20.33 | % 136.47/20.33 End of proof % 136.47/20.33 % 136.47/20.33 Sub-proof #535 shows that the following formulas are inconsistent: % 136.47/20.33 ---------------------------------------------------------------- % 136.47/20.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.33 (2) op(e3, e3) = all_10_2 % 136.47/20.33 (3) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) % 136.47/20.33 (4) ~ (all_52_1 = e2) % 136.47/20.33 (5) ~ (all_10_2 = e2) % 136.47/20.33 (6) op(e2, e3) = all_52_1 % 136.47/20.33 % 136.47/20.33 Begin of proof % 136.47/20.33 | % 136.47/20.33 | BETA: splitting (3) gives: % 136.47/20.33 | % 136.47/20.33 | Case 1: % 136.47/20.33 | | % 136.47/20.33 | | (7) all_57_0 = e2 & op(e3, e3) = e2 % 136.47/20.33 | | % 136.47/20.33 | | ALPHA: (7) implies: % 136.47/20.33 | | (8) op(e3, e3) = e2 % 136.47/20.33 | | % 136.47/20.33 | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #536. % 136.47/20.33 | | % 136.47/20.33 | Case 2: % 136.47/20.33 | | % 136.47/20.33 | | (9) all_57_2 = e2 & op(e2, e3) = e2 % 136.47/20.33 | | % 136.47/20.33 | | ALPHA: (9) implies: % 136.47/20.33 | | (10) op(e2, e3) = e2 % 136.47/20.33 | | % 136.47/20.33 | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #779. % 136.47/20.33 | | % 136.47/20.33 | End of split % 136.47/20.33 | % 136.47/20.33 End of proof % 136.47/20.33 % 136.47/20.33 Sub-proof #536 shows that the following formulas are inconsistent: % 136.47/20.33 ---------------------------------------------------------------- % 136.47/20.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.33 (2) op(e3, e3) = all_10_2 % 136.47/20.33 (3) op(e3, e3) = e2 % 136.47/20.33 (4) ~ (all_10_2 = e2) % 136.47/20.33 % 136.47/20.33 Begin of proof % 136.47/20.33 | % 136.47/20.33 | GROUND_INST: instantiating (1) with all_10_2, e2, e3, e3, simplifying with % 136.47/20.33 | (2), (3) gives: % 136.47/20.33 | (5) all_10_2 = e2 % 136.47/20.33 | % 136.47/20.33 | REDUCE: (4), (5) imply: % 136.47/20.33 | (6) $false % 136.47/20.33 | % 136.47/20.33 | CLOSE: (6) is inconsistent. % 136.47/20.33 | % 136.47/20.33 End of proof % 136.47/20.33 % 136.47/20.33 Sub-proof #537 shows that the following formulas are inconsistent: % 136.47/20.33 ---------------------------------------------------------------- % 136.47/20.33 (1) op(e1, e1) = all_6_2 % 136.47/20.33 (2) op(e0, e0) = e3 % 136.47/20.33 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.33 (4) ~ (e3 = e0) % 136.47/20.33 (5) op(e3, e0) = e0 % 136.47/20.33 (6) op(e1, e1) = e3 % 136.47/20.33 (7) op(e0, e2) = all_52_7 % 136.47/20.33 (8) ~ (all_6_2 = e2) % 136.47/20.33 (9) ~ (all_52_7 = e0) % 136.47/20.33 (10) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.47/20.33 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.47/20.33 all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.47/20.33 e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & % 136.47/20.33 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = % 136.47/20.33 all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ % 136.47/20.33 (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 136.47/20.33 (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 136.47/20.33 op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 % 136.47/20.33 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.47/20.33 (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.47/20.33 (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.33 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.47/20.33 all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.47/20.33 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.47/20.33 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.47/20.33 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.47/20.33 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.47/20.33 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.47/20.33 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.47/20.33 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.47/20.33 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.47/20.33 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.47/20.33 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.33 $i(all_56_29)))) % 136.47/20.33 (11) ~ (e3 = e1) % 136.47/20.33 % 136.47/20.33 Begin of proof % 136.47/20.33 | % 136.47/20.33 | BETA: splitting (10) gives: % 136.47/20.33 | % 136.47/20.33 | Case 1: % 136.47/20.33 | | % 136.47/20.33 | | (12) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.47/20.33 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.47/20.33 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.47/20.33 | | e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) % 136.47/20.33 | | & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.47/20.33 | | % 136.47/20.33 | | ALPHA: (12) implies: % 136.47/20.33 | | (13) op(e1, e1) = e2 % 136.47/20.33 | | % 136.47/20.33 | | REF_CLOSE: (1), (3), (8), (13) are inconsistent by sub-proof #767. % 136.47/20.33 | | % 136.47/20.33 | Case 2: % 136.47/20.33 | | % 136.47/20.33 | | (14) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 % 136.47/20.33 | | = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = % 136.47/20.33 | | e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) % 136.47/20.33 | | = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.47/20.33 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.47/20.33 | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 % 136.47/20.33 | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 136.47/20.33 | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.47/20.33 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.47/20.33 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.47/20.33 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 % 136.47/20.33 | | = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.47/20.33 | | (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, % 136.47/20.33 | | e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 136.47/20.33 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 136.47/20.33 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.47/20.33 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.47/20.33 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.33 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.47/20.33 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29))) % 136.47/20.33 | | % 136.47/20.33 | | ALPHA: (14) implies: % 136.47/20.33 | | (15) op(e0, e0) = all_56_31 % 136.47/20.33 | | (16) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.47/20.33 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.33 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.47/20.33 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 136.47/20.33 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 136.47/20.33 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 136.47/20.33 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.47/20.33 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.47/20.33 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.47/20.33 | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = % 136.47/20.33 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 % 136.47/20.33 | | = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 136.47/20.33 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.47/20.33 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & % 136.47/20.33 | | all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.47/20.33 | | (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 136.47/20.33 | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.47/20.33 | | all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.47/20.33 | | $i(all_56_21) & $i(all_56_29)) % 136.47/20.33 | | % 136.47/20.33 | | BETA: splitting (16) gives: % 136.47/20.33 | | % 136.47/20.33 | | Case 1: % 136.47/20.33 | | | % 136.47/20.33 | | | (17) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.47/20.33 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.47/20.33 | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.47/20.33 | | | all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.47/20.33 | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.47/20.33 | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.47/20.33 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.33 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.47/20.33 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.47/20.33 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 136.47/20.33 | | | % 136.47/20.33 | | | REF_CLOSE: (3), (5), (7), (9), (17) are inconsistent by sub-proof #538. % 136.47/20.33 | | | % 136.47/20.33 | | Case 2: % 136.47/20.33 | | | % 136.47/20.33 | | | (18) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.47/20.33 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.47/20.33 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 136.47/20.33 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.47/20.33 | | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = % 136.47/20.33 | | | e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 136.47/20.33 | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) % 136.47/20.33 | | | = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.47/20.33 | | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.33 | | | $i(all_56_29)) % 136.47/20.33 | | | % 136.47/20.33 | | | BETA: splitting (18) gives: % 136.47/20.33 | | | % 136.47/20.33 | | | Case 1: % 136.47/20.33 | | | | % 136.47/20.33 | | | | (19) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.47/20.33 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.47/20.33 | | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 136.47/20.33 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.47/20.33 | | | | $i(all_56_15) & $i(all_56_23) % 136.47/20.33 | | | | % 136.47/20.33 | | | | ALPHA: (19) implies: % 136.47/20.33 | | | | (20) op(e1, e1) = e0 % 136.47/20.33 | | | | % 136.47/20.33 | | | | REF_CLOSE: (3), (4), (6), (20) are inconsistent by sub-proof #753. % 136.47/20.33 | | | | % 136.47/20.33 | | | Case 2: % 136.47/20.33 | | | | % 136.47/20.33 | | | | (21) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.47/20.33 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.47/20.33 | | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.33 | | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.47/20.33 | | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.47/20.33 | | | | % 136.47/20.33 | | | | ALPHA: (21) implies: % 136.47/20.33 | | | | (22) all_56_31 = e1 % 136.47/20.33 | | | | % 136.47/20.33 | | | | REDUCE: (15), (22) imply: % 136.47/20.33 | | | | (23) op(e0, e0) = e1 % 136.47/20.33 | | | | % 136.47/20.33 | | | | REF_CLOSE: (2), (3), (11), (23) are inconsistent by sub-proof #606. % 136.47/20.33 | | | | % 136.47/20.33 | | | End of split % 136.47/20.33 | | | % 136.47/20.33 | | End of split % 136.47/20.33 | | % 136.47/20.33 | End of split % 136.47/20.33 | % 136.47/20.33 End of proof % 136.47/20.33 % 136.47/20.33 Sub-proof #538 shows that the following formulas are inconsistent: % 136.47/20.33 ---------------------------------------------------------------- % 136.47/20.33 (1) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.47/20.33 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.47/20.33 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.47/20.33 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.47/20.33 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) % 136.47/20.33 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.33 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 136.47/20.33 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 136.47/20.33 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 136.47/20.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.33 (3) op(e3, e0) = e0 % 136.47/20.33 (4) op(e0, e2) = all_52_7 % 136.47/20.33 (5) ~ (all_52_7 = e0) % 136.47/20.33 % 136.47/20.33 Begin of proof % 136.47/20.33 | % 136.47/20.33 | BETA: splitting (1) gives: % 136.47/20.33 | % 136.47/20.33 | Case 1: % 136.47/20.33 | | % 136.47/20.33 | | (6) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.47/20.33 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.33 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.47/20.33 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 136.47/20.33 | | $i(all_56_17) & $i(all_56_25) % 136.47/20.33 | | % 136.47/20.33 | | ALPHA: (6) implies: % 136.47/20.33 | | (7) ~ (all_56_25 = e0) % 136.47/20.33 | | (8) op(e3, e0) = all_56_25 % 136.47/20.33 | | % 136.47/20.33 | | REF_CLOSE: (2), (3), (7), (8) are inconsistent by sub-proof #642. % 136.47/20.33 | | % 136.47/20.33 | Case 2: % 136.47/20.33 | | % 136.47/20.33 | | (9) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.47/20.33 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.47/20.33 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.47/20.33 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 136.47/20.33 | | $i(all_56_19) & $i(all_56_27) % 136.47/20.33 | | % 136.47/20.33 | | ALPHA: (9) implies: % 136.47/20.33 | | (10) op(e0, e2) = e0 % 136.47/20.33 | | % 136.47/20.33 | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #545. % 136.47/20.33 | | % 136.47/20.33 | End of split % 136.47/20.33 | % 136.47/20.33 End of proof % 136.47/20.33 % 136.47/20.33 Sub-proof #539 shows that the following formulas are inconsistent: % 136.47/20.33 ---------------------------------------------------------------- % 136.47/20.33 (1) ~ (all_42_0 = e1) % 136.47/20.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.33 (3) op(e0, e2) = all_42_0 % 136.47/20.33 (4) ~ (all_56_15 = e2) % 136.47/20.33 (5) op(e0, e2) = all_56_15 % 136.47/20.33 (6) ~ (all_42_0 = e0) % 136.47/20.33 (7) all_54_13 = all_42_0 % 136.47/20.33 (8) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0 % 136.47/20.33 % 136.47/20.33 Begin of proof % 136.47/20.33 | % 136.47/20.33 | BETA: splitting (8) gives: % 136.47/20.33 | % 136.47/20.33 | Case 1: % 136.47/20.33 | | % 136.47/20.33 | | (9) all_54_13 = e2 % 136.47/20.33 | | % 136.47/20.33 | | COMBINE_EQS: (7), (9) imply: % 136.47/20.33 | | (10) all_42_0 = e2 % 136.47/20.33 | | % 136.47/20.33 | | SIMP: (10) implies: % 136.47/20.33 | | (11) all_42_0 = e2 % 136.47/20.33 | | % 136.47/20.33 | | REDUCE: (3), (11) imply: % 136.47/20.33 | | (12) op(e0, e2) = e2 % 136.47/20.33 | | % 136.47/20.33 | | REF_CLOSE: (2), (4), (5), (12) are inconsistent by sub-proof #609. % 136.47/20.33 | | % 136.47/20.33 | Case 2: % 136.47/20.33 | | % 136.47/20.33 | | (13) all_54_13 = e1 | all_54_13 = e0 % 136.47/20.33 | | % 136.47/20.33 | | REF_CLOSE: (1), (6), (7), (13) are inconsistent by sub-proof #604. % 136.47/20.33 | | % 136.47/20.33 | End of split % 136.47/20.33 | % 136.47/20.33 End of proof % 136.47/20.33 % 136.47/20.33 Sub-proof #540 shows that the following formulas are inconsistent: % 136.47/20.33 ---------------------------------------------------------------- % 136.47/20.33 (1) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.47/20.33 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.47/20.33 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.47/20.33 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.47/20.33 $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ % 136.47/20.33 (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 136.47/20.33 (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = % 136.47/20.33 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) % 136.47/20.33 = all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.33 $i(all_56_29)) % 136.47/20.33 (2) op(e2, e2) = e0 % 136.47/20.33 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.33 (4) op(e3, e0) = e0 % 136.47/20.33 (5) ~ (e1 = e0) % 136.47/20.33 % 136.47/20.33 Begin of proof % 136.47/20.33 | % 136.47/20.33 | BETA: splitting (1) gives: % 136.47/20.33 | % 136.47/20.33 | Case 1: % 136.47/20.33 | | % 136.47/20.33 | | (6) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.47/20.33 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.33 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.47/20.33 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) % 136.47/20.33 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.47/20.33 | | % 136.47/20.33 | | ALPHA: (6) implies: % 136.47/20.33 | | (7) ~ (all_56_25 = e0) % 136.47/20.33 | | (8) op(e3, e0) = all_56_25 % 136.47/20.33 | | % 136.47/20.33 | | REF_CLOSE: (3), (4), (7), (8) are inconsistent by sub-proof #642. % 136.47/20.33 | | % 136.47/20.33 | Case 2: % 136.47/20.33 | | % 136.47/20.33 | | (9) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.47/20.33 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 % 136.47/20.33 | | & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.47/20.33 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.47/20.33 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.47/20.33 | | % 136.47/20.33 | | ALPHA: (9) implies: % 136.47/20.33 | | (10) op(e2, e2) = e1 % 136.47/20.33 | | % 136.47/20.33 | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #675. % 136.47/20.33 | | % 136.47/20.33 | End of split % 136.47/20.33 | % 136.47/20.33 End of proof % 136.47/20.33 % 136.47/20.33 Sub-proof #541 shows that the following formulas are inconsistent: % 136.47/20.33 ---------------------------------------------------------------- % 136.47/20.33 (1) all_54_0 = all_10_2 % 136.47/20.33 (2) op(e0, e0) = all_4_2 % 136.47/20.33 (3) op(e1, e1) = all_6_2 % 136.47/20.33 (4) op(e2, e2) = e0 % 136.47/20.33 (5) op(e2, e0) = all_52_13 % 136.47/20.33 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.33 (7) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | % 136.47/20.33 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) % 136.47/20.33 (8) op(e1, e1) = e3 % 136.47/20.33 (9) op(e0, e2) = all_52_7 % 136.47/20.33 (10) ~ (all_52_12 = all_10_2) % 136.47/20.33 (11) ~ (all_10_2 = e0) % 136.47/20.33 (12) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 136.47/20.33 (13) ~ (all_4_2 = e1) % 136.47/20.33 (14) ~ (all_6_2 = e2) % 136.47/20.34 (15) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.47/20.34 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.47/20.34 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.47/20.34 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.47/20.34 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.47/20.34 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.47/20.34 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) % 136.47/20.34 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.34 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.47/20.34 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 136.47/20.34 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.47/20.34 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 136.47/20.34 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 136.47/20.34 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.47/20.34 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) % 136.47/20.34 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.47/20.34 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 136.47/20.34 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 136.47/20.34 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.47/20.34 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.47/20.34 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.34 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 136.47/20.34 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & % 136.47/20.34 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & % 136.47/20.34 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.47/20.34 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 136.47/20.34 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.34 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.47/20.34 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ % 136.47/20.34 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.47/20.34 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 136.47/20.34 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 136.47/20.34 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.47/20.34 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) % 136.47/20.34 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.34 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.47/20.34 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 % 136.47/20.34 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.47/20.34 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = % 136.47/20.34 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 136.47/20.34 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 136.47/20.34 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.47/20.34 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.47/20.34 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 136.47/20.34 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 136.47/20.34 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.47/20.34 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.47/20.34 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.47/20.34 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.47/20.34 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.47/20.34 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.47/20.34 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.47/20.34 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.47/20.34 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.47/20.34 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.47/20.34 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.47/20.34 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.34 $i(all_56_29)))) % 136.47/20.34 (16) op(e3, e3) = all_10_2 % 136.47/20.34 (17) ~ (all_52_7 = e0) % 136.47/20.34 (18) ~ (all_52_9 = e3) % 136.47/20.34 (19) op(e2, e1) = all_52_9 % 136.47/20.34 (20) ~ (all_52_1 = all_10_2) % 136.47/20.34 (21) op(e3, e0) = all_52_12 % 136.47/20.34 (22) ~ (all_10_2 = e2) % 136.47/20.34 (23) op(e2, e3) = all_52_1 % 136.47/20.34 (24) ~ (e1 = e0) % 136.47/20.34 (25) ~ (all_10_2 = e1) % 136.47/20.34 % 136.47/20.34 Begin of proof % 136.47/20.34 | % 136.47/20.34 | BETA: splitting (12) gives: % 136.47/20.34 | % 136.47/20.34 | Case 1: % 136.47/20.34 | | % 136.47/20.34 | | (26) all_54_0 = e3 % 136.47/20.34 | | % 136.47/20.34 | | COMBINE_EQS: (1), (26) imply: % 136.47/20.34 | | (27) all_10_2 = e3 % 136.47/20.34 | | % 136.47/20.34 | | SIMP: (27) implies: % 136.47/20.34 | | (28) all_10_2 = e3 % 136.47/20.34 | | % 136.47/20.34 | | REDUCE: (20), (28) imply: % 136.47/20.34 | | (29) ~ (all_52_1 = e3) % 136.47/20.34 | | % 136.47/20.34 | | REDUCE: (10), (28) imply: % 136.47/20.34 | | (30) ~ (all_52_12 = e3) % 136.47/20.34 | | % 136.47/20.34 | | REDUCE: (22), (28) imply: % 136.47/20.34 | | (31) ~ (e3 = e2) % 136.47/20.34 | | % 136.47/20.34 | | REDUCE: (25), (28) imply: % 136.47/20.34 | | (32) ~ (e3 = e1) % 136.47/20.34 | | % 136.47/20.34 | | REDUCE: (11), (28) imply: % 136.47/20.34 | | (33) ~ (e3 = e0) % 136.47/20.34 | | % 136.47/20.34 | | REDUCE: (16), (28) imply: % 136.47/20.34 | | (34) op(e3, e3) = e3 % 136.47/20.34 | | % 136.47/20.34 | | BETA: splitting (7) gives: % 136.47/20.34 | | % 136.47/20.34 | | Case 1: % 136.47/20.34 | | | % 136.47/20.34 | | | (35) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = % 136.47/20.34 | | | e3) % 136.47/20.34 | | | % 136.47/20.34 | | | BETA: splitting (35) gives: % 136.47/20.34 | | | % 136.47/20.34 | | | Case 1: % 136.47/20.34 | | | | % 136.47/20.34 | | | | (36) all_57_2 = e3 & op(e2, e3) = e3 % 136.47/20.34 | | | | % 136.47/20.34 | | | | ALPHA: (36) implies: % 136.47/20.34 | | | | (37) op(e2, e3) = e3 % 136.47/20.34 | | | | % 136.47/20.34 | | | | REF_CLOSE: (6), (23), (29), (37) are inconsistent by sub-proof #763. % 136.47/20.34 | | | | % 136.47/20.34 | | | Case 2: % 136.47/20.34 | | | | % 136.47/20.34 | | | | (38) all_57_3 = e3 & op(e2, e2) = e3 % 136.47/20.34 | | | | % 136.47/20.34 | | | | ALPHA: (38) implies: % 136.47/20.34 | | | | (39) op(e2, e2) = e3 % 136.47/20.34 | | | | % 136.47/20.34 | | | | REF_CLOSE: (4), (6), (33), (39) are inconsistent by sub-proof #641. % 136.47/20.34 | | | | % 136.47/20.34 | | | End of split % 136.47/20.34 | | | % 136.47/20.34 | | Case 2: % 136.47/20.34 | | | % 136.47/20.34 | | | (40) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = % 136.47/20.34 | | | e3) % 136.47/20.34 | | | % 136.47/20.34 | | | BETA: splitting (40) gives: % 136.47/20.34 | | | % 136.47/20.34 | | | Case 1: % 136.47/20.34 | | | | % 136.47/20.34 | | | | (41) all_57_5 = e3 & op(e2, e1) = e3 % 136.47/20.34 | | | | % 136.47/20.34 | | | | REF_CLOSE: (6), (18), (19), (41) are inconsistent by sub-proof #547. % 136.47/20.34 | | | | % 136.47/20.34 | | | Case 2: % 136.47/20.34 | | | | % 136.47/20.34 | | | | (42) all_57_10 = e3 & op(e2, e0) = e3 % 136.47/20.34 | | | | % 136.47/20.34 | | | | ALPHA: (42) implies: % 136.47/20.34 | | | | (43) op(e2, e0) = e3 % 136.47/20.34 | | | | % 136.47/20.34 | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (13), (14), (15), (17), % 136.47/20.34 | | | | (21), (24), (30), (31), (32), (33), (34), (43) are % 136.47/20.34 | | | | inconsistent by sub-proof #542. % 136.47/20.34 | | | | % 136.47/20.34 | | | End of split % 136.47/20.34 | | | % 136.47/20.34 | | End of split % 136.47/20.34 | | % 136.47/20.34 | Case 2: % 136.47/20.34 | | % 136.47/20.34 | | (44) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0 % 136.47/20.34 | | % 136.47/20.34 | | REF_CLOSE: (1), (11), (22), (25), (44) are inconsistent by sub-proof #777. % 136.47/20.34 | | % 136.47/20.34 | End of split % 136.47/20.34 | % 136.47/20.34 End of proof % 136.47/20.34 % 136.47/20.34 Sub-proof #542 shows that the following formulas are inconsistent: % 136.47/20.34 ---------------------------------------------------------------- % 136.47/20.34 (1) op(e0, e0) = all_4_2 % 136.47/20.34 (2) op(e1, e1) = all_6_2 % 136.47/20.34 (3) op(e2, e2) = e0 % 136.47/20.34 (4) op(e2, e0) = all_52_13 % 136.47/20.34 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.34 (6) ~ (e3 = e0) % 136.47/20.34 (7) op(e2, e0) = e3 % 136.47/20.34 (8) ~ (e3 = e2) % 136.47/20.34 (9) op(e1, e1) = e3 % 136.47/20.34 (10) op(e0, e2) = all_52_7 % 136.47/20.34 (11) ~ (all_4_2 = e1) % 136.47/20.34 (12) ~ (all_6_2 = e2) % 136.47/20.34 (13) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.47/20.34 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.47/20.34 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.47/20.34 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.47/20.34 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.47/20.34 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.47/20.34 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) % 136.47/20.34 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.34 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.47/20.34 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 136.47/20.34 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.47/20.34 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 136.47/20.34 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 136.47/20.34 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.47/20.34 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) % 136.47/20.34 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.47/20.34 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 136.47/20.34 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 136.47/20.34 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.47/20.34 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.47/20.34 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.34 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 136.47/20.34 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & % 136.47/20.34 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & % 136.47/20.34 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.47/20.34 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 136.47/20.34 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.34 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.47/20.34 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ % 136.47/20.34 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.47/20.34 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 136.47/20.34 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 136.47/20.34 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.47/20.34 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) % 136.47/20.34 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.34 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.47/20.34 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 % 136.47/20.34 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.47/20.34 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = % 136.47/20.34 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 136.47/20.34 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 136.47/20.34 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.47/20.34 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.47/20.34 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 136.47/20.34 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 136.47/20.34 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.47/20.34 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.47/20.34 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.47/20.34 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.47/20.34 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.47/20.34 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.47/20.34 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.47/20.34 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.47/20.34 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.47/20.34 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.47/20.34 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.47/20.34 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.34 $i(all_56_29)))) % 136.47/20.34 (14) ~ (all_52_7 = e0) % 136.47/20.34 (15) op(e3, e3) = e3 % 136.47/20.34 (16) op(e3, e0) = all_52_12 % 136.47/20.34 (17) ~ (e3 = e1) % 136.47/20.34 (18) ~ (e1 = e0) % 136.47/20.34 (19) ~ (all_52_12 = e3) % 136.47/20.34 % 136.47/20.34 Begin of proof % 136.47/20.34 | % 136.47/20.34 | BETA: splitting (13) gives: % 136.47/20.34 | % 136.47/20.34 | Case 1: % 136.47/20.34 | | % 136.47/20.34 | | (20) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.47/20.34 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = % 136.47/20.34 | | e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.47/20.34 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.47/20.34 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.47/20.34 | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.47/20.34 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = % 136.47/20.34 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.47/20.34 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.47/20.34 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 136.47/20.34 | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 % 136.47/20.34 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = % 136.47/20.34 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 136.47/20.34 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 136.47/20.34 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 136.47/20.34 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.47/20.34 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.34 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.47/20.34 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 136.47/20.34 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 136.47/20.34 | | % 136.47/20.34 | | BETA: splitting (20) gives: % 136.47/20.34 | | % 136.47/20.34 | | Case 1: % 136.47/20.34 | | | % 136.47/20.34 | | | (21) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ % 136.47/20.34 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.34 | | | op(e3, e3) = e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & % 136.47/20.34 | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = % 136.47/20.34 | | | all_56_27 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.47/20.34 | | | $i(all_56_27)) | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 % 136.47/20.34 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 136.47/20.34 | | | (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = e3 & op(e1, % 136.47/20.34 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.34 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.47/20.34 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 136.47/20.34 | | | % 136.47/20.34 | | | REF_CLOSE: (5), (8), (15), (17), (21) are inconsistent by sub-proof #623. % 136.47/20.34 | | | % 136.47/20.34 | | Case 2: % 136.47/20.34 | | | % 136.47/20.34 | | | (22) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ % 136.47/20.34 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.47/20.34 | | | op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & % 136.47/20.34 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 136.47/20.34 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.47/20.34 | | | $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 % 136.47/20.34 | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 136.47/20.34 | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 % 136.47/20.34 | | | & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e2, e3) = % 136.47/20.34 | | | e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.47/20.34 | | | $i(all_56_17) & $i(all_56_25)) % 136.47/20.34 | | | % 136.47/20.34 | | | REF_CLOSE: (3), (5), (6), (16), (19), (22) are inconsistent by sub-proof % 136.47/20.34 | | | #622. % 136.47/20.34 | | | % 136.47/20.34 | | End of split % 136.47/20.34 | | % 136.47/20.34 | Case 2: % 136.47/20.34 | | % 136.47/20.34 | | (23) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.47/20.34 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.34 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.47/20.34 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & % 136.47/20.34 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.47/20.34 | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 136.47/20.34 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.47/20.34 | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, % 136.47/20.34 | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.47/20.34 | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.34 | | $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = % 136.47/20.34 | | e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 % 136.47/20.34 | | = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 136.47/20.34 | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.47/20.34 | | op(e0, e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & % 136.47/20.34 | | $i(all_56_23) & $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 % 136.47/20.34 | | & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 136.47/20.34 | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.47/20.34 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.47/20.34 | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) & % 136.47/20.34 | | $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 & % 136.47/20.34 | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = % 136.47/20.34 | | e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 136.47/20.34 | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 136.47/20.34 | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.47/20.34 | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) % 136.47/20.34 | | & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 136.47/20.34 | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & % 136.47/20.34 | | ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.47/20.34 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.47/20.34 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 136.47/20.34 | | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 136.47/20.34 | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & % 136.47/20.34 | | ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & % 136.47/20.34 | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 136.47/20.34 | | all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 136.47/20.34 | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.47/20.34 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.47/20.34 | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.34 | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.47/20.34 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.34 | | $i(all_56_29)))) % 136.47/20.34 | | % 136.47/20.34 | | BETA: splitting (23) gives: % 136.47/20.34 | | % 136.47/20.34 | | Case 1: % 136.47/20.34 | | | % 136.47/20.34 | | | (24) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ % 136.47/20.34 | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.47/20.34 | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.47/20.34 | | | all_56_17 & op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 136.47/20.34 | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.47/20.34 | | | $i(all_56_25)) | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 % 136.47/20.34 | | | = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ % 136.47/20.34 | | | (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, % 136.47/20.34 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.34 | | | all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.47/20.34 | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) % 136.47/20.34 | | | % 136.47/20.34 | | | BETA: splitting (24) gives: % 136.47/20.34 | | | % 136.47/20.34 | | | Case 1: % 136.47/20.34 | | | | % 136.47/20.34 | | | | (25) all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ % 136.47/20.34 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.47/20.34 | | | | op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = % 136.47/20.34 | | | | all_56_17 & op(e3, e0) = all_56_25 & op(e1, e3) = e1 & op(e1, % 136.47/20.34 | | | | e1) = e3 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.47/20.34 | | | | $i(all_56_25) % 136.47/20.34 | | | | % 136.47/20.34 | | | | ALPHA: (25) implies: % 136.47/20.34 | | | | (26) ~ (all_56_1 = e3) % 136.47/20.34 | | | | (27) op(e3, e3) = all_56_1 % 136.47/20.34 | | | | % 136.47/20.34 | | | | REF_CLOSE: (5), (15), (26), (27) are inconsistent by sub-proof #766. % 136.47/20.34 | | | | % 136.47/20.34 | | | Case 2: % 136.47/20.34 | | | | % 136.47/20.34 | | | | (28) all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 136.47/20.34 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.47/20.34 | | | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & % 136.47/20.34 | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.47/20.34 | | | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.34 | | | | $i(all_56_29) % 136.47/20.34 | | | | % 136.47/20.34 | | | | ALPHA: (28) implies: % 136.47/20.34 | | | | (29) op(e2, e2) = e1 % 136.47/20.34 | | | | % 136.47/20.34 | | | | REF_CLOSE: (3), (5), (18), (29) are inconsistent by sub-proof #675. % 136.47/20.34 | | | | % 136.47/20.34 | | | End of split % 136.47/20.34 | | | % 136.47/20.34 | | Case 2: % 136.47/20.34 | | | % 136.47/20.34 | | | (30) (all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 136.47/20.34 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.47/20.34 | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & % 136.47/20.34 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 136.47/20.34 | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.47/20.34 | | | $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 % 136.47/20.34 | | | = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 136.47/20.34 | | | (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.47/20.34 | | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.47/20.34 | | | op(e1, e2) = e1 & op(e1, e1) = e2 & $i(all_56_3) & $i(all_56_11) % 136.47/20.34 | | | & $i(all_56_19) & $i(all_56_27)) | (op(e0, e0) = all_56_31 & % 136.47/20.34 | | | $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 % 136.47/20.34 | | | = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ % 136.47/20.34 | | | (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 136.47/20.34 | | | all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.47/20.34 | | | op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 136.47/20.34 | | | $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 % 136.47/20.34 | | | = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ % 136.47/20.34 | | | (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.47/20.34 | | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & % 136.47/20.34 | | | op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 136.47/20.34 | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21 % 136.47/20.34 | | | = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.47/20.34 | | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, % 136.47/20.34 | | | e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & % 136.47/20.34 | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & % 136.47/20.34 | | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 = % 136.47/20.34 | | | e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.47/20.34 | | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, % 136.47/20.34 | | | e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.34 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.47/20.34 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.34 | | | $i(all_56_29)))) % 136.47/20.34 | | | % 136.47/20.34 | | | BETA: splitting (30) gives: % 136.47/20.34 | | | % 136.47/20.34 | | | Case 1: % 136.47/20.34 | | | | % 136.47/20.34 | | | | (31) all_56_11 = e0 & all_56_27 = e2 & ~ (all_56_7 = e3) & ~ % 136.47/20.34 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.47/20.34 | | | | op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = all_56_7 & % 136.47/20.34 | | | | op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = % 136.47/20.34 | | | | all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.47/20.34 | | | | $i(all_56_31) % 136.47/20.34 | | | | % 136.47/20.34 | | | | ALPHA: (31) implies: % 136.47/20.34 | | | | (32) op(e2, e0) = e2 % 136.47/20.34 | | | | % 136.47/20.34 | | | | REF_CLOSE: (4), (5), (7), (8), (32) are inconsistent by sub-proof #546. % 136.47/20.34 | | | | % 136.47/20.34 | | | Case 2: % 136.47/20.34 | | | | % 136.47/20.34 | | | | (33) (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 136.47/20.34 | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.34 | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.47/20.34 | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 136.47/20.34 | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.47/20.34 | | | | $i(all_56_27)) | (op(e0, e0) = all_56_31 & $i(all_56_31) & % 136.47/20.34 | | | | ((all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.47/20.34 | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = % 136.47/20.34 | | | | e0) & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & % 136.47/20.34 | | | | op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & op(e0, % 136.47/20.34 | | | | e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.47/20.34 | | | | $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 136.47/20.34 | | | | (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 136.47/20.34 | | | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & % 136.47/20.34 | | | | op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.47/20.34 | | | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 136.47/20.34 | | | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.47/20.34 | | | | (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.47/20.34 | | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = % 136.47/20.34 | | | | e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = % 136.47/20.34 | | | | all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 % 136.47/20.34 | | | | & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | % 136.47/20.34 | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.47/20.34 | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = % 136.47/20.34 | | | | e0) & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.47/20.34 | | | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, % 136.47/20.34 | | | | e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) % 136.47/20.34 | | | | & $i(all_56_29)))) % 136.47/20.34 | | | | % 136.47/20.34 | | | | BETA: splitting (33) gives: % 136.47/20.34 | | | | % 136.47/20.34 | | | | Case 1: % 136.47/20.34 | | | | | % 136.47/20.34 | | | | | (34) all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) & ~ % 136.47/20.34 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.34 | | | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.47/20.34 | | | | | all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, % 136.47/20.34 | | | | | e1) = e2 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.47/20.34 | | | | | $i(all_56_27) % 136.47/20.34 | | | | | % 136.47/20.34 | | | | | ALPHA: (34) implies: % 136.47/20.34 | | | | | (35) op(e1, e1) = e2 % 136.47/20.34 | | | | | % 136.47/20.34 | | | | | REF_CLOSE: (2), (5), (12), (35) are inconsistent by sub-proof #767. % 136.47/20.34 | | | | | % 136.47/20.34 | | | | Case 2: % 136.47/20.34 | | | | | % 136.47/20.34 | | | | | (36) op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & % 136.47/20.34 | | | | | all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & % 136.47/20.34 | | | | | ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.34 | | | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 136.47/20.34 | | | | | & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) % 136.47/20.34 | | | | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.47/20.34 | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.47/20.34 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = % 136.47/20.34 | | | | | e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.47/20.34 | | | | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, % 136.47/20.34 | | | | | e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) % 136.47/20.34 | | | | | & $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 136.47/20.34 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = % 136.47/20.34 | | | | | e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) % 136.47/20.34 | | | | | = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.47/20.34 | | | | | op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & % 136.47/20.34 | | | | | $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 & ~ % 136.47/20.34 | | | | | (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = % 136.47/20.34 | | | | | e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & % 136.47/20.34 | | | | | op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 136.47/20.34 | | | | | e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & % 136.47/20.34 | | | | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29))) % 136.47/20.34 | | | | | % 136.47/20.34 | | | | | ALPHA: (36) implies: % 136.47/20.34 | | | | | (37) op(e0, e0) = all_56_31 % 136.47/20.34 | | | | | (38) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ % 136.47/20.34 | | | | | (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) % 136.47/20.34 | | | | | & op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) % 136.47/20.34 | | | | | = all_56_17 & op(e3, e0) = all_56_25 & op(e0, e3) = e0 & % 136.47/20.34 | | | | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 136.47/20.34 | | | | | | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.47/20.34 | | | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) % 136.47/20.34 | | | | | & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.47/20.34 | | | | | e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 % 136.47/20.34 | | | | | & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.47/20.34 | | | | | $i(all_56_27)) | (all_56_21 = e0 & all_56_29 = e1 & ~ % 136.47/20.34 | | | | | (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) % 136.47/20.34 | | | | | & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = e1 & % 136.47/20.34 | | | | | op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) % 136.47/20.34 | | | | | = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 136.47/20.34 | | | | | | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.47/20.34 | | | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) % 136.47/20.34 | | | | | & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, % 136.47/20.34 | | | | | e1) = all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 % 136.47/20.34 | | | | | & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.34 | | | | | $i(all_56_29)) % 136.47/20.34 | | | | | % 136.47/20.34 | | | | | REF_CLOSE: (1), (5), (6), (9), (10), (11), (14), (15), (37), (38) are % 136.47/20.34 | | | | | inconsistent by sub-proof #543. % 136.47/20.34 | | | | | % 136.47/20.34 | | | | End of split % 136.47/20.34 | | | | % 136.47/20.34 | | | End of split % 136.47/20.34 | | | % 136.47/20.34 | | End of split % 136.47/20.34 | | % 136.47/20.34 | End of split % 136.47/20.34 | % 136.47/20.34 End of proof % 136.47/20.34 % 136.47/20.34 Sub-proof #543 shows that the following formulas are inconsistent: % 136.47/20.34 ---------------------------------------------------------------- % 136.47/20.34 (1) op(e0, e0) = all_4_2 % 136.47/20.34 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.34 (3) ~ (e3 = e0) % 136.47/20.34 (4) op(e1, e1) = e3 % 136.47/20.34 (5) op(e0, e2) = all_52_7 % 136.47/20.34 (6) ~ (all_4_2 = e1) % 136.47/20.34 (7) ~ (all_52_7 = e0) % 136.47/20.34 (8) op(e3, e3) = e3 % 136.47/20.35 (9) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.47/20.35 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.47/20.35 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.47/20.35 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.47/20.35 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) % 136.47/20.35 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.35 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 136.47/20.35 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 136.47/20.35 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_21 = e0 & % 136.47/20.35 all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ % 136.47/20.35 (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & op(e1, e0) = % 136.47/20.35 e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = % 136.47/20.35 all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) | (all_56_23 % 136.47/20.35 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.47/20.35 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, % 136.47/20.35 e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.47/20.35 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.35 $i(all_56_29)) % 136.47/20.35 (10) op(e0, e0) = all_56_31 % 136.47/20.35 % 136.47/20.35 Begin of proof % 136.47/20.35 | % 136.47/20.35 | BETA: splitting (9) gives: % 136.47/20.35 | % 136.47/20.35 | Case 1: % 136.47/20.35 | | % 136.47/20.35 | | (11) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.47/20.35 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.35 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.47/20.35 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 136.47/20.35 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 136.47/20.35 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 136.47/20.35 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.47/20.35 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.47/20.35 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.47/20.35 | | $i(all_56_27)) % 136.47/20.35 | | % 136.47/20.35 | | REF_CLOSE: (2), (5), (7), (8), (11) are inconsistent by sub-proof #544. % 136.47/20.35 | | % 136.47/20.35 | Case 2: % 136.47/20.35 | | % 136.47/20.35 | | (12) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.47/20.35 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.47/20.35 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.47/20.35 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.47/20.35 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.47/20.35 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.47/20.35 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.47/20.35 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.47/20.35 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.35 | | $i(all_56_29)) % 136.47/20.35 | | % 136.47/20.35 | | BETA: splitting (12) gives: % 136.47/20.35 | | % 136.47/20.35 | | Case 1: % 136.47/20.35 | | | % 136.47/20.35 | | | (13) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.47/20.35 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.47/20.35 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.47/20.35 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.47/20.35 | | | $i(all_56_15) & $i(all_56_23) % 136.47/20.35 | | | % 136.47/20.35 | | | ALPHA: (13) implies: % 136.47/20.35 | | | (14) op(e1, e1) = e0 % 136.47/20.35 | | | % 136.47/20.35 | | | REF_CLOSE: (2), (3), (4), (14) are inconsistent by sub-proof #753. % 136.47/20.35 | | | % 136.47/20.35 | | Case 2: % 136.47/20.35 | | | % 136.47/20.35 | | | (15) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.47/20.35 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.47/20.35 | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.35 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.47/20.35 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.47/20.35 | | | % 136.47/20.35 | | | ALPHA: (15) implies: % 136.47/20.35 | | | (16) all_56_31 = e1 % 136.47/20.35 | | | % 136.47/20.35 | | | REDUCE: (10), (16) imply: % 136.47/20.35 | | | (17) op(e0, e0) = e1 % 136.47/20.35 | | | % 136.47/20.35 | | | GROUND_INST: instantiating (2) with all_4_2, e1, e0, e0, simplifying with % 136.47/20.35 | | | (1), (17) gives: % 136.47/20.35 | | | (18) all_4_2 = e1 % 136.47/20.35 | | | % 136.47/20.35 | | | REDUCE: (6), (18) imply: % 136.47/20.35 | | | (19) $false % 136.47/20.35 | | | % 136.47/20.35 | | | CLOSE: (19) is inconsistent. % 136.47/20.35 | | | % 136.47/20.35 | | End of split % 136.47/20.35 | | % 136.47/20.35 | End of split % 136.47/20.35 | % 136.47/20.35 End of proof % 136.47/20.35 % 136.47/20.35 Sub-proof #544 shows that the following formulas are inconsistent: % 136.47/20.35 ---------------------------------------------------------------- % 136.47/20.35 (1) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) % 136.47/20.35 & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & % 136.47/20.35 op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 % 136.47/20.35 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.47/20.35 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) % 136.47/20.35 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.35 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 % 136.47/20.35 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & % 136.47/20.35 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) % 136.47/20.35 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.35 (3) op(e0, e2) = all_52_7 % 136.47/20.35 (4) ~ (all_52_7 = e0) % 136.47/20.35 (5) op(e3, e3) = e3 % 136.47/20.35 % 136.47/20.35 Begin of proof % 136.47/20.35 | % 136.47/20.35 | BETA: splitting (1) gives: % 136.47/20.35 | % 136.47/20.35 | Case 1: % 136.47/20.35 | | % 136.47/20.35 | | (6) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.47/20.35 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.35 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.47/20.35 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 136.47/20.35 | | $i(all_56_17) & $i(all_56_25) % 136.47/20.35 | | % 136.47/20.35 | | ALPHA: (6) implies: % 136.47/20.35 | | (7) ~ (all_56_1 = e3) % 136.47/20.35 | | (8) op(e3, e3) = all_56_1 % 136.47/20.35 | | % 136.47/20.35 | | REF_CLOSE: (2), (5), (7), (8) are inconsistent by sub-proof #766. % 136.47/20.35 | | % 136.47/20.35 | Case 2: % 136.47/20.35 | | % 136.47/20.35 | | (9) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.47/20.35 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e2, e3) = % 136.47/20.35 | | all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = all_56_19 & op(e2, % 136.47/20.35 | | e0) = all_56_27 & op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & % 136.47/20.35 | | $i(all_56_19) & $i(all_56_27) % 136.47/20.35 | | % 136.47/20.35 | | ALPHA: (9) implies: % 136.47/20.35 | | (10) op(e0, e2) = e0 % 136.47/20.35 | | % 136.47/20.35 | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #545. % 136.47/20.35 | | % 136.47/20.35 | End of split % 136.47/20.35 | % 136.47/20.35 End of proof % 136.47/20.35 % 136.47/20.35 Sub-proof #545 shows that the following formulas are inconsistent: % 136.47/20.35 ---------------------------------------------------------------- % 136.47/20.35 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.35 (2) op(e0, e2) = all_52_7 % 136.47/20.35 (3) op(e0, e2) = e0 % 136.47/20.35 (4) ~ (all_52_7 = e0) % 136.47/20.35 % 136.47/20.35 Begin of proof % 136.47/20.35 | % 136.47/20.35 | GROUND_INST: instantiating (1) with all_52_7, e0, e2, e0, simplifying with % 136.47/20.35 | (2), (3) gives: % 136.47/20.35 | (5) all_52_7 = e0 % 136.47/20.35 | % 136.47/20.35 | REDUCE: (4), (5) imply: % 136.47/20.35 | (6) $false % 136.47/20.35 | % 136.47/20.35 | CLOSE: (6) is inconsistent. % 136.47/20.35 | % 136.47/20.35 End of proof % 136.47/20.35 % 136.47/20.35 Sub-proof #546 shows that the following formulas are inconsistent: % 136.47/20.35 ---------------------------------------------------------------- % 136.47/20.35 (1) op(e2, e0) = all_52_13 % 136.47/20.35 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.35 (3) op(e2, e0) = e3 % 136.47/20.35 (4) ~ (e3 = e2) % 136.47/20.35 (5) op(e2, e0) = e2 % 136.47/20.35 % 136.47/20.35 Begin of proof % 136.47/20.35 | % 136.47/20.35 | GROUND_INST: instantiating (2) with all_52_13, e2, e0, e2, simplifying with % 136.47/20.35 | (1), (5) gives: % 136.47/20.35 | (6) all_52_13 = e2 % 136.47/20.35 | % 136.47/20.35 | GROUND_INST: instantiating (2) with all_52_13, e3, e0, e2, simplifying with % 136.47/20.35 | (1), (3) gives: % 136.47/20.35 | (7) all_52_13 = e3 % 136.47/20.35 | % 136.47/20.35 | COMBINE_EQS: (6), (7) imply: % 136.47/20.35 | (8) e3 = e2 % 136.47/20.35 | % 136.47/20.35 | REDUCE: (4), (8) imply: % 136.47/20.35 | (9) $false % 136.47/20.35 | % 136.47/20.35 | CLOSE: (9) is inconsistent. % 136.47/20.35 | % 136.47/20.35 End of proof % 136.47/20.35 % 136.47/20.35 Sub-proof #547 shows that the following formulas are inconsistent: % 136.47/20.35 ---------------------------------------------------------------- % 136.47/20.35 (1) all_57_5 = e3 & op(e2, e1) = e3 % 136.47/20.35 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.35 (3) op(e2, e1) = all_52_9 % 136.47/20.35 (4) ~ (all_52_9 = e3) % 136.47/20.35 % 136.47/20.35 Begin of proof % 136.47/20.35 | % 136.47/20.35 | ALPHA: (1) implies: % 136.47/20.35 | (5) op(e2, e1) = e3 % 136.47/20.35 | % 136.47/20.35 | GROUND_INST: instantiating (2) with all_52_9, e3, e1, e2, simplifying with % 136.47/20.35 | (3), (5) gives: % 136.47/20.35 | (6) all_52_9 = e3 % 136.47/20.35 | % 136.47/20.35 | REDUCE: (4), (6) imply: % 136.47/20.35 | (7) $false % 136.47/20.35 | % 136.47/20.35 | CLOSE: (7) is inconsistent. % 136.47/20.35 | % 136.47/20.35 End of proof % 136.47/20.35 % 136.47/20.35 Sub-proof #548 shows that the following formulas are inconsistent: % 136.47/20.35 ---------------------------------------------------------------- % 136.47/20.35 (1) op(e0, e0) = all_4_2 % 136.47/20.35 (2) ~ (e2 = e0) % 136.47/20.35 (3) op(e3, e3) = e1 % 136.47/20.35 (4) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.47/20.35 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.47/20.35 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.35 (6) ~ (e2 = e1) % 136.47/20.35 (7) ~ (all_4_2 = e2) % 136.47/20.35 (8) ~ (e3 = e0) % 136.47/20.35 (9) op(e1, e1) = e3 % 136.47/20.35 (10) ~ (all_4_2 = e1) % 136.47/20.35 (11) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 136.47/20.35 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 136.47/20.35 (12) ~ (all_52_4 = e2) % 136.47/20.35 (13) ~ (all_52_3 = e1) % 136.47/20.35 (14) op(e3, e2) = all_52_4 % 136.47/20.35 (15) op(e0, e3) = all_52_3 % 136.47/20.35 (16) op(e3, e0) = all_52_12 % 136.47/20.35 (17) op(e3, e1) = all_52_8 % 136.47/20.35 (18) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.47/20.35 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.35 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 136.47/20.35 = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & % 136.47/20.35 $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ % 136.47/20.35 (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ % 136.47/20.35 (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.47/20.35 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.47/20.35 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.47/20.35 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.47/20.35 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e1, e1) = e0 & % 136.47/20.35 op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.47/20.35 op(e0, e1) = all_56_23 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23)) % 136.47/20.35 | (all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.47/20.35 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e1, e3) = % 136.47/20.35 all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, % 136.47/20.35 e0) = all_56_29 & op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & % 136.47/20.35 $i(all_56_21) & $i(all_56_29)) % 136.47/20.35 (19) ~ (all_52_3 = all_4_2) % 136.47/20.35 (20) ~ (all_34_2 = e3) | ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & % 136.47/20.35 $i(all_34_0)) | ( ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 & % 136.47/20.35 $i(all_34_1)) % 136.47/20.35 (21) ~ (all_52_12 = all_4_2) % 136.47/20.35 (22) all_34_2 = all_4_2 % 136.47/20.35 (23) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.47/20.35 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.47/20.35 (24) op(e0, e0) = all_56_31 % 136.47/20.35 (25) ~ (all_52_8 = e3) % 136.47/20.35 % 136.47/20.35 Begin of proof % 136.47/20.35 | % 136.47/20.35 | GROUND_INST: instantiating (5) with all_4_2, all_56_31, e0, e0, simplifying % 136.47/20.35 | with (1), (24) gives: % 136.47/20.35 | (26) all_56_31 = all_4_2 % 136.47/20.35 | % 136.47/20.35 | BETA: splitting (18) gives: % 136.47/20.35 | % 136.47/20.35 | Case 1: % 136.47/20.35 | | % 136.47/20.35 | | (27) (all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.47/20.35 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.35 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.47/20.35 | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 136.47/20.35 | | & $i(all_56_17) & $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = % 136.47/20.35 | | e2 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = % 136.47/20.35 | | e1) & ~ (all_56_27 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.47/20.35 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.47/20.35 | | op(e0, e2) = e0 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & % 136.47/20.35 | | $i(all_56_27)) % 136.47/20.35 | | % 136.47/20.35 | | BETA: splitting (27) gives: % 136.47/20.35 | | % 136.47/20.35 | | Case 1: % 136.47/20.35 | | | % 136.47/20.35 | | | (28) all_56_7 = e0 & all_56_31 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.47/20.35 | | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.35 | | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.47/20.35 | | | e0) = all_56_25 & op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) % 136.47/20.35 | | | & $i(all_56_17) & $i(all_56_25) % 136.47/20.35 | | | % 136.47/20.35 | | | ALPHA: (28) implies: % 136.47/20.35 | | | (29) all_56_31 = e3 % 136.47/20.35 | | | (30) ~ (all_56_25 = e0) % 136.47/20.35 | | | (31) op(e0, e3) = e0 % 136.47/20.35 | | | (32) op(e3, e0) = all_56_25 % 136.47/20.35 | | | (33) op(e3, e2) = all_56_9 % 136.47/20.35 | | | (34) op(e3, e3) = all_56_1 % 136.47/20.35 | | | % 136.47/20.35 | | | COMBINE_EQS: (26), (29) imply: % 136.47/20.35 | | | (35) all_4_2 = e3 % 136.47/20.35 | | | % 136.47/20.35 | | | COMBINE_EQS: (22), (35) imply: % 136.47/20.35 | | | (36) all_34_2 = e3 % 136.47/20.35 | | | % 136.47/20.35 | | | REDUCE: (19), (35) imply: % 136.47/20.35 | | | (37) ~ (all_52_3 = e3) % 136.47/20.35 | | | % 136.47/20.35 | | | REDUCE: (21), (35) imply: % 136.47/20.35 | | | (38) ~ (all_52_12 = e3) % 136.47/20.35 | | | % 136.47/20.35 | | | REDUCE: (1), (35) imply: % 136.47/20.35 | | | (39) op(e0, e0) = e3 % 136.47/20.35 | | | % 136.47/20.35 | | | BETA: splitting (20) gives: % 136.47/20.35 | | | % 136.47/20.35 | | | Case 1: % 136.47/20.35 | | | | % 136.47/20.35 | | | | (40) ~ (all_34_2 = e3) % 136.47/20.35 | | | | % 136.47/20.35 | | | | REDUCE: (36), (40) imply: % 136.47/20.35 | | | | (41) $false % 136.47/20.35 | | | | % 136.47/20.35 | | | | CLOSE: (41) is inconsistent. % 136.47/20.35 | | | | % 136.47/20.35 | | | Case 2: % 136.47/20.35 | | | | % 136.47/20.35 | | | | (42) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & $i(all_34_0)) | ( % 136.47/20.35 | | | | ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 & $i(all_34_1)) % 136.47/20.35 | | | | % 136.47/20.35 | | | | BETA: splitting (23) gives: % 136.47/20.35 | | | | % 136.47/20.35 | | | | Case 1: % 136.47/20.35 | | | | | % 136.47/20.35 | | | | | (43) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, % 136.47/20.35 | | | | | e2) = e3) % 136.47/20.35 | | | | | % 136.47/20.35 | | | | | BETA: splitting (43) gives: % 136.47/20.35 | | | | | % 136.47/20.35 | | | | | Case 1: % 136.47/20.35 | | | | | | % 136.47/20.35 | | | | | | (44) all_57_0 = e3 & op(e3, e3) = e3 % 136.47/20.35 | | | | | | % 136.47/20.35 | | | | | | ALPHA: (44) implies: % 136.47/20.35 | | | | | | (45) op(e3, e3) = e3 % 136.47/20.35 | | | | | | % 136.47/20.35 | | | | | | REF_CLOSE: (1), (5), (7), (8), (9), (10), (18), (24), (39), (45) are % 136.47/20.35 | | | | | | inconsistent by sub-proof #751. % 136.47/20.35 | | | | | | % 136.47/20.35 | | | | | Case 2: % 136.47/20.35 | | | | | | % 136.47/20.35 | | | | | | (46) all_57_1 = e3 & op(e3, e2) = e3 % 136.47/20.35 | | | | | | % 136.47/20.35 | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (11), (12), (13), (14), (15), % 136.47/20.35 | | | | | | (16), (30), (31), (32), (33), (34), (37), (42), (46) are % 136.47/20.35 | | | | | | inconsistent by sub-proof #549. % 136.47/20.35 | | | | | | % 136.47/20.35 | | | | | End of split % 136.47/20.35 | | | | | % 136.47/20.35 | | | | Case 2: % 136.47/20.35 | | | | | % 136.47/20.35 | | | | | (47) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, % 136.47/20.35 | | | | | e0) = e3) % 136.47/20.35 | | | | | % 136.47/20.35 | | | | | REF_CLOSE: (5), (16), (17), (25), (38), (47) are inconsistent by % 136.47/20.35 | | | | | sub-proof #650. % 136.47/20.35 | | | | | % 136.47/20.35 | | | | End of split % 136.47/20.35 | | | | % 136.47/20.35 | | | End of split % 136.47/20.35 | | | % 136.47/20.35 | | Case 2: % 136.47/20.35 | | | % 136.47/20.35 | | | (48) all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = e3) & ~ % 136.47/20.35 | | | (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.47/20.35 | | | op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.47/20.35 | | | all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.47/20.35 | | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.47/20.35 | | | % 136.47/20.35 | | | REF_CLOSE: (7), (26), (48) are inconsistent by sub-proof #765. % 136.47/20.35 | | | % 136.47/20.35 | | End of split % 136.47/20.35 | | % 136.47/20.35 | Case 2: % 136.47/20.35 | | % 136.47/20.35 | | (49) (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.47/20.35 | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.47/20.35 | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.47/20.35 | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.47/20.35 | | $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.47/20.35 | | & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.47/20.35 | | ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.47/20.35 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.47/20.35 | | op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.47/20.35 | | $i(all_56_29)) % 136.47/20.35 | | % 136.47/20.35 | | BETA: splitting (49) gives: % 136.47/20.35 | | % 136.47/20.35 | | Case 1: % 136.47/20.35 | | | % 136.47/20.35 | | | (50) all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.47/20.35 | | | (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.47/20.35 | | | op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.47/20.35 | | | e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.47/20.35 | | | $i(all_56_15) & $i(all_56_23) % 136.47/20.35 | | | % 136.47/20.35 | | | ALPHA: (50) implies: % 136.47/20.35 | | | (51) op(e1, e1) = e0 % 136.47/20.35 | | | % 136.47/20.35 | | | REF_CLOSE: (5), (8), (9), (51) are inconsistent by sub-proof #753. % 136.47/20.35 | | | % 136.47/20.35 | | Case 2: % 136.47/20.35 | | | % 136.47/20.35 | | | (52) all_56_23 = e0 & all_56_31 = e1 & ~ (all_56_5 = e3) & ~ % 136.47/20.35 | | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.47/20.35 | | | op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.35 | | | all_56_21 & op(e1, e0) = all_56_29 & op(e0, e1) = e0 & % 136.47/20.35 | | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.47/20.35 | | | % 136.47/20.35 | | | REF_CLOSE: (10), (26), (52) are inconsistent by sub-proof #745. % 136.47/20.35 | | | % 136.47/20.35 | | End of split % 136.47/20.35 | | % 136.47/20.35 | End of split % 136.47/20.35 | % 136.47/20.35 End of proof % 136.47/20.35 % 136.47/20.35 Sub-proof #549 shows that the following formulas are inconsistent: % 136.47/20.35 ---------------------------------------------------------------- % 136.47/20.35 (1) all_57_1 = e3 & op(e3, e2) = e3 % 136.47/20.35 (2) ~ (e2 = e0) % 136.47/20.35 (3) op(e3, e3) = e1 % 136.47/20.35 (4) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.47/20.35 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.47/20.35 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.35 (6) ~ (e2 = e1) % 136.47/20.35 (7) ~ (all_56_25 = e0) % 136.47/20.35 (8) ~ (all_52_3 = e3) % 136.47/20.35 (9) op(e3, e3) = all_56_1 % 136.47/20.35 (10) op(e3, e0) = all_56_25 % 136.47/20.35 (11) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 136.47/20.35 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 136.47/20.35 (12) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & $i(all_34_0)) | ( ~ % 136.47/20.35 (all_34_1 = e1) & op(e3, e3) = all_34_1 & $i(all_34_1)) % 136.47/20.35 (13) ~ (all_52_4 = e2) % 136.47/20.35 (14) ~ (all_52_3 = e1) % 136.47/20.35 (15) op(e3, e2) = all_52_4 % 136.47/20.35 (16) op(e0, e3) = all_52_3 % 136.47/20.35 (17) op(e3, e0) = all_52_12 % 136.47/20.35 (18) op(e3, e2) = all_56_9 % 136.47/20.35 (19) op(e0, e3) = e0 % 136.47/20.35 % 136.47/20.35 Begin of proof % 136.47/20.35 | % 136.47/20.35 | ALPHA: (1) implies: % 136.47/20.35 | (20) all_57_1 = e3 % 136.47/20.35 | (21) op(e3, e2) = e3 % 136.47/20.35 | % 136.47/20.35 | GROUND_INST: instantiating (5) with all_52_3, e0, e3, e0, simplifying with % 136.47/20.35 | (16), (19) gives: % 136.47/20.35 | (22) all_52_3 = e0 % 136.47/20.35 | % 136.47/20.35 | GROUND_INST: instantiating (5) with all_52_12, all_56_25, e0, e3, simplifying % 136.47/20.35 | with (10), (17) gives: % 136.47/20.35 | (23) all_56_25 = all_52_12 % 136.47/20.35 | % 136.47/20.35 | GROUND_INST: instantiating (5) with all_52_4, all_56_9, e2, e3, simplifying % 136.47/20.35 | with (15), (18) gives: % 136.47/20.35 | (24) all_56_9 = all_52_4 % 136.47/20.35 | % 136.47/20.35 | GROUND_INST: instantiating (5) with e3, all_56_9, e2, e3, simplifying with % 136.47/20.35 | (18), (21) gives: % 136.47/20.35 | (25) all_56_9 = e3 % 136.47/20.35 | % 136.47/20.35 | GROUND_INST: instantiating (5) with e1, all_56_1, e3, e3, simplifying with % 136.47/20.35 | (3), (9) gives: % 136.47/20.35 | (26) all_56_1 = e1 % 136.47/20.35 | % 136.47/20.35 | COMBINE_EQS: (24), (25) imply: % 136.47/20.35 | (27) all_52_4 = e3 % 136.47/20.35 | % 136.47/20.35 | SIMP: (27) implies: % 136.47/20.35 | (28) all_52_4 = e3 % 136.47/20.35 | % 136.47/20.35 | REDUCE: (7), (23) imply: % 136.47/20.35 | (29) ~ (all_52_12 = e0) % 136.47/20.35 | % 136.47/20.35 | REDUCE: (8), (22) imply: % 136.47/20.35 | (30) ~ (e3 = e0) % 136.47/20.35 | % 136.47/20.35 | SIMP: (30) implies: % 136.47/20.35 | (31) ~ (e3 = e0) % 136.47/20.35 | % 136.47/20.35 | REDUCE: (14), (22) imply: % 136.47/20.35 | (32) ~ (e1 = e0) % 136.47/20.35 | % 136.47/20.35 | SIMP: (32) implies: % 136.47/20.35 | (33) ~ (e1 = e0) % 136.47/20.35 | % 136.47/20.35 | REDUCE: (13), (28) imply: % 136.47/20.35 | (34) ~ (e3 = e2) % 136.47/20.35 | % 136.47/20.35 | BETA: splitting (4) gives: % 136.47/20.35 | % 136.47/20.35 | Case 1: % 136.47/20.35 | | % 136.47/20.35 | | (35) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = % 136.47/20.35 | | e0) % 136.47/20.35 | | % 136.47/20.35 | | REF_CLOSE: (3), (5), (20), (31), (33), (35) are inconsistent by sub-proof % 136.47/20.35 | | #648. % 136.47/20.35 | | % 136.47/20.35 | Case 2: % 136.47/20.35 | | % 136.47/20.35 | | (36) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = % 136.47/20.35 | | e0) % 136.47/20.35 | | % 136.47/20.35 | | BETA: splitting (36) gives: % 136.47/20.35 | | % 136.47/20.35 | | Case 1: % 136.47/20.35 | | | % 136.47/20.35 | | | (37) all_57_4 = e0 & op(e3, e1) = e0 % 136.47/20.35 | | | % 136.47/20.35 | | | ALPHA: (37) implies: % 136.47/20.35 | | | (38) all_57_4 = e0 % 136.47/20.35 | | | % 136.47/20.35 | | | REF_CLOSE: (2), (3), (5), (6), (11), (12), (20), (34), (38) are % 136.47/20.35 | | | inconsistent by sub-proof #550. % 136.47/20.35 | | | % 136.47/20.35 | | Case 2: % 136.47/20.35 | | | % 136.47/20.35 | | | (39) all_57_9 = e0 & op(e3, e0) = e0 % 136.47/20.35 | | | % 136.47/20.35 | | | REF_CLOSE: (5), (17), (29), (39) are inconsistent by sub-proof #618. % 136.47/20.35 | | | % 136.47/20.35 | | End of split % 136.47/20.35 | | % 136.47/20.35 | End of split % 136.47/20.35 | % 136.47/20.35 End of proof % 136.47/20.35 % 136.47/20.35 Sub-proof #550 shows that the following formulas are inconsistent: % 136.47/20.35 ---------------------------------------------------------------- % 136.47/20.35 (1) all_57_1 = e3 % 136.47/20.35 (2) ~ (e2 = e0) % 136.47/20.35 (3) op(e3, e3) = e1 % 136.47/20.35 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.35 (5) ~ (e2 = e1) % 136.47/20.35 (6) ~ (e3 = e2) % 136.47/20.35 (7) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 136.47/20.35 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 136.47/20.35 (8) ( ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & $i(all_34_0)) | ( ~ % 136.47/20.35 (all_34_1 = e1) & op(e3, e3) = all_34_1 & $i(all_34_1)) % 136.47/20.35 (9) all_57_4 = e0 % 136.47/20.35 % 136.47/20.35 Begin of proof % 136.47/20.35 | % 136.47/20.35 | BETA: splitting (8) gives: % 136.47/20.35 | % 136.47/20.35 | Case 1: % 136.47/20.35 | | % 136.47/20.35 | | (10) ~ (all_34_0 = e2) & op(e3, e0) = all_34_0 & $i(all_34_0) % 136.47/20.35 | | % 136.47/20.35 | | ALPHA: (10) implies: % 136.47/20.35 | | (11) ~ (all_34_0 = e2) % 136.47/20.35 | | (12) op(e3, e0) = all_34_0 % 136.47/20.35 | | % 136.47/20.35 | | BETA: splitting (7) gives: % 136.47/20.35 | | % 136.47/20.35 | | Case 1: % 136.47/20.35 | | | % 136.47/20.35 | | | (13) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = % 136.47/20.35 | | | e2) % 136.47/20.35 | | | % 136.47/20.35 | | | REF_CLOSE: (1), (3), (4), (5), (6), (13) are inconsistent by sub-proof % 136.47/20.35 | | | #562. % 136.47/20.35 | | | % 136.47/20.35 | | Case 2: % 136.47/20.35 | | | % 136.47/20.35 | | | (14) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = % 136.47/20.35 | | | e2) % 136.47/20.35 | | | % 136.47/20.35 | | | BETA: splitting (14) gives: % 136.47/20.35 | | | % 136.47/20.35 | | | Case 1: % 136.47/20.35 | | | | % 136.47/20.35 | | | | (15) all_57_4 = e2 & op(e3, e1) = e2 % 136.47/20.35 | | | | % 136.47/20.35 | | | | REF_CLOSE: (2), (9), (15) are inconsistent by sub-proof #689. % 136.47/20.35 | | | | % 136.47/20.35 | | | Case 2: % 136.47/20.35 | | | | % 136.47/20.35 | | | | (16) all_57_9 = e2 & op(e3, e0) = e2 % 136.47/20.35 | | | | % 136.47/20.35 | | | | ALPHA: (16) implies: % 136.47/20.35 | | | | (17) op(e3, e0) = e2 % 136.47/20.35 | | | | % 136.47/20.35 | | | | REF_CLOSE: (4), (11), (12), (17) are inconsistent by sub-proof #551. % 136.47/20.35 | | | | % 136.47/20.35 | | | End of split % 136.47/20.35 | | | % 136.47/20.35 | | End of split % 136.47/20.35 | | % 136.47/20.35 | Case 2: % 136.47/20.35 | | % 136.47/20.35 | | (18) ~ (all_34_1 = e1) & op(e3, e3) = all_34_1 & $i(all_34_1) % 136.47/20.35 | | % 136.47/20.35 | | ALPHA: (18) implies: % 136.47/20.35 | | (19) ~ (all_34_1 = e1) % 136.47/20.35 | | (20) op(e3, e3) = all_34_1 % 136.47/20.35 | | % 136.47/20.35 | | REF_CLOSE: (3), (4), (19), (20) are inconsistent by sub-proof #626. % 136.47/20.35 | | % 136.47/20.35 | End of split % 136.47/20.35 | % 136.47/20.35 End of proof % 136.47/20.35 % 136.47/20.35 Sub-proof #551 shows that the following formulas are inconsistent: % 136.47/20.35 ---------------------------------------------------------------- % 136.47/20.35 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.35 (2) op(e3, e0) = all_34_0 % 136.47/20.35 (3) op(e3, e0) = e2 % 136.47/20.35 (4) ~ (all_34_0 = e2) % 136.47/20.35 % 136.47/20.35 Begin of proof % 136.47/20.35 | % 136.47/20.35 | GROUND_INST: instantiating (1) with e2, all_34_0, e0, e3, simplifying with % 136.47/20.35 | (2), (3) gives: % 136.47/20.35 | (5) all_34_0 = e2 % 136.47/20.35 | % 136.47/20.35 | REDUCE: (4), (5) imply: % 136.47/20.35 | (6) $false % 136.47/20.35 | % 136.47/20.35 | CLOSE: (6) is inconsistent. % 136.47/20.35 | % 136.47/20.35 End of proof % 136.47/20.35 % 136.47/20.35 Sub-proof #552 shows that the following formulas are inconsistent: % 136.47/20.35 ---------------------------------------------------------------- % 136.47/20.36 (1) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = e2) % 136.47/20.36 & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & op(e3, % 136.47/20.36 e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.47/20.36 e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.47/20.36 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.47/20.36 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.47/20.36 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) = % 136.47/20.36 e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.47/20.36 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.47/20.36 $i(all_56_21) & $i(all_56_29)) % 136.47/20.36 (2) op(e3, e3) = e1 % 136.47/20.36 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.36 (4) ~ (e2 = e1) % 136.47/20.36 (5) op(e3, e1) = all_52_8 % 136.47/20.36 (6) ~ (all_52_8 = e3) % 136.47/20.36 % 136.47/20.36 Begin of proof % 136.47/20.36 | % 136.47/20.36 | BETA: splitting (1) gives: % 136.47/20.36 | % 136.47/20.36 | Case 1: % 136.47/20.36 | | % 136.47/20.36 | | (7) all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.47/20.36 | | e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.47/20.36 | | op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.47/20.36 | | op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.47/20.36 | | $i(all_56_11) & $i(all_56_19) & $i(all_56_27) % 136.47/20.36 | | % 136.47/20.36 | | ALPHA: (7) implies: % 136.47/20.36 | | (8) op(e3, e3) = e2 % 136.47/20.36 | | % 136.47/20.36 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #743. % 136.47/20.36 | | % 136.47/20.36 | Case 2: % 136.47/20.36 | | % 136.47/20.36 | | (9) all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = % 136.47/20.36 | | e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & % 136.47/20.36 | | op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & % 136.47/20.36 | | op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & % 136.47/20.36 | | $i(all_56_13) & $i(all_56_21) & $i(all_56_29) % 136.47/20.36 | | % 136.47/20.36 | | ALPHA: (9) implies: % 136.47/20.36 | | (10) op(e3, e1) = e3 % 136.47/20.36 | | % 136.47/20.36 | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #705. % 136.47/20.36 | | % 136.47/20.36 | End of split % 136.47/20.36 | % 136.47/20.36 End of proof % 136.47/20.36 % 136.47/20.36 Sub-proof #553 shows that the following formulas are inconsistent: % 136.47/20.36 ---------------------------------------------------------------- % 136.47/20.36 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.36 (2) (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.47/20.36 e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.47/20.36 op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.47/20.36 op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.47/20.36 $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | (all_56_3 = e2 & % 136.47/20.36 all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ % 136.47/20.36 (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, % 136.47/20.36 e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.47/20.36 op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) & $i(all_56_9) & % 136.47/20.36 $i(all_56_17) & $i(all_56_25)) % 136.47/20.36 (3) op(e3, e3) = e3 % 136.47/20.36 (4) op(e3, e0) = all_52_12 % 136.47/20.36 (5) ~ (all_52_12 = e3) % 136.47/20.36 % 136.47/20.36 Begin of proof % 136.47/20.36 | % 136.47/20.36 | BETA: splitting (2) gives: % 136.47/20.36 | % 136.47/20.36 | Case 1: % 136.47/20.36 | | % 136.47/20.36 | | (6) all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 = % 136.47/20.36 | | e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = e0 & % 136.47/20.36 | | op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = all_56_15 & % 136.47/20.36 | | op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & $i(all_56_7) & % 136.47/20.36 | | $i(all_56_15) & $i(all_56_23) & $i(all_56_31) % 136.47/20.36 | | % 136.47/20.36 | | ALPHA: (6) implies: % 136.47/20.36 | | (7) op(e3, e0) = e3 % 136.47/20.36 | | % 136.47/20.36 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #733. % 136.47/20.36 | | % 136.47/20.36 | Case 2: % 136.47/20.36 | | % 136.47/20.36 | | (8) all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.47/20.36 | | e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.47/20.36 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.47/20.36 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & $i(all_56_1) % 136.47/20.36 | | & $i(all_56_9) & $i(all_56_17) & $i(all_56_25) % 136.47/20.36 | | % 136.47/20.36 | | ALPHA: (8) implies: % 136.47/20.36 | | (9) ~ (all_56_1 = e3) % 136.47/20.36 | | (10) op(e3, e3) = all_56_1 % 136.47/20.36 | | % 136.47/20.36 | | REF_CLOSE: (1), (3), (9), (10) are inconsistent by sub-proof #766. % 136.47/20.36 | | % 136.47/20.36 | End of split % 136.47/20.36 | % 136.47/20.36 End of proof % 136.47/20.36 % 136.47/20.36 Sub-proof #554 shows that the following formulas are inconsistent: % 136.47/20.36 ---------------------------------------------------------------- % 136.47/20.36 (1) all_54_5 = all_8_2 % 136.47/20.36 (2) all_54_5 = e3 % 136.47/20.36 (3) ~ (all_8_2 = e3) % 136.47/20.36 % 136.47/20.36 Begin of proof % 136.47/20.36 | % 136.47/20.36 | COMBINE_EQS: (1), (2) imply: % 136.47/20.36 | (4) all_8_2 = e3 % 136.47/20.36 | % 136.47/20.36 | SIMP: (4) implies: % 136.47/20.36 | (5) all_8_2 = e3 % 136.47/20.36 | % 136.47/20.36 | REDUCE: (3), (5) imply: % 136.47/20.36 | (6) $false % 136.47/20.36 | % 136.47/20.36 | CLOSE: (6) is inconsistent. % 136.47/20.36 | % 136.47/20.36 End of proof % 136.47/20.36 % 136.47/20.36 Sub-proof #555 shows that the following formulas are inconsistent: % 136.47/20.36 ---------------------------------------------------------------- % 136.47/20.36 (1) ~ (all_52_6 = e3) % 136.47/20.36 (2) ~ (all_52_7 = e3) % 136.47/20.36 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.36 (4) op(e0, e2) = all_52_7 % 136.47/20.36 (5) op(e1, e2) = all_52_6 % 136.47/20.36 (6) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) % 136.47/20.36 % 136.47/20.36 Begin of proof % 136.47/20.36 | % 136.47/20.36 | BETA: splitting (6) gives: % 136.47/20.36 | % 136.47/20.36 | Case 1: % 136.47/20.36 | | % 136.47/20.36 | | (7) all_57_7 = e3 & op(e1, e2) = e3 % 136.47/20.36 | | % 136.47/20.36 | | ALPHA: (7) implies: % 136.47/20.36 | | (8) op(e1, e2) = e3 % 136.47/20.36 | | % 136.47/20.36 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #654. % 136.47/20.36 | | % 136.47/20.36 | Case 2: % 136.47/20.36 | | % 136.47/20.36 | | (9) all_57_13 = e3 & op(e0, e2) = e3 % 136.47/20.36 | | % 136.47/20.36 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #556. % 136.47/20.36 | | % 136.47/20.36 | End of split % 136.47/20.36 | % 136.47/20.36 End of proof % 136.47/20.36 % 136.47/20.36 Sub-proof #556 shows that the following formulas are inconsistent: % 136.47/20.36 ---------------------------------------------------------------- % 136.47/20.36 (1) all_57_13 = e3 & op(e0, e2) = e3 % 136.47/20.36 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.36 (3) op(e0, e2) = all_52_7 % 136.47/20.36 (4) ~ (all_52_7 = e3) % 136.47/20.36 % 136.47/20.36 Begin of proof % 136.47/20.36 | % 136.47/20.36 | ALPHA: (1) implies: % 136.47/20.36 | (5) op(e0, e2) = e3 % 136.47/20.36 | % 136.47/20.36 | GROUND_INST: instantiating (2) with all_52_7, e3, e2, e0, simplifying with % 136.47/20.36 | (3), (5) gives: % 136.47/20.36 | (6) all_52_7 = e3 % 136.47/20.36 | % 136.47/20.36 | REDUCE: (4), (6) imply: % 136.47/20.36 | (7) $false % 136.47/20.36 | % 136.47/20.36 | CLOSE: (7) is inconsistent. % 136.47/20.36 | % 136.47/20.36 End of proof % 136.47/20.36 % 136.47/20.36 Sub-proof #557 shows that the following formulas are inconsistent: % 136.47/20.36 ---------------------------------------------------------------- % 136.47/20.36 (1) op(e1, e0) = e2 % 136.47/20.36 (2) op(e0, e0) = e3 % 136.47/20.36 (3) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1) % 136.47/20.36 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.36 (5) ~ (e2 = e1) % 136.47/20.36 (6) ~ (e3 = e1) % 136.47/20.36 % 136.47/20.36 Begin of proof % 136.47/20.36 | % 136.47/20.36 | BETA: splitting (3) gives: % 136.47/20.36 | % 136.47/20.36 | Case 1: % 136.47/20.36 | | % 136.47/20.36 | | (7) all_57_11 = e1 & op(e1, e0) = e1 % 136.47/20.36 | | % 136.47/20.36 | | ALPHA: (7) implies: % 136.47/20.36 | | (8) op(e1, e0) = e1 % 136.47/20.36 | | % 136.47/20.36 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #720. % 136.47/20.36 | | % 136.47/20.36 | Case 2: % 136.47/20.36 | | % 136.47/20.36 | | (9) all_57_15 = e1 & op(e0, e0) = e1 % 136.47/20.36 | | % 136.47/20.36 | | ALPHA: (9) implies: % 136.47/20.36 | | (10) op(e0, e0) = e1 % 136.47/20.36 | | % 136.47/20.36 | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #606. % 136.47/20.36 | | % 136.47/20.36 | End of split % 136.47/20.36 | % 136.47/20.36 End of proof % 136.47/20.36 % 136.47/20.36 Sub-proof #558 shows that the following formulas are inconsistent: % 136.47/20.36 ---------------------------------------------------------------- % 136.47/20.36 (1) op(e1, e1) = all_6_2 % 136.47/20.36 (2) ~ (e2 = e0) % 136.47/20.36 (3) ~ (all_6_2 = e3) % 136.47/20.36 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.36 (5) ~ (e2 = e1) % 136.47/20.36 (6) ~ (e3 = e0) % 136.47/20.36 (7) ~ (e3 = e2) % 136.47/20.36 (8) ~ (all_6_2 = e2) % 136.47/20.36 (9) all_57_4 = e0 % 136.47/20.36 (10) ~ (e3 = e1) % 136.47/20.36 (11) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) | % 136.47/20.36 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) % 136.47/20.36 (12) all_57_14 = e1 % 136.47/20.36 (13) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | % 136.47/20.36 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 136.47/20.36 % 136.47/20.36 Begin of proof % 136.47/20.36 | % 136.47/20.36 | BETA: splitting (13) gives: % 136.47/20.36 | % 136.47/20.36 | Case 1: % 136.47/20.36 | | % 136.47/20.36 | | (14) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = % 136.47/20.36 | | e2) % 136.47/20.36 | | % 136.47/20.36 | | BETA: splitting (14) gives: % 136.47/20.36 | | % 136.47/20.36 | | Case 1: % 136.47/20.36 | | | % 136.47/20.36 | | | (15) all_57_4 = e2 & op(e3, e1) = e2 % 136.47/20.36 | | | % 136.47/20.36 | | | REF_CLOSE: (2), (9), (15) are inconsistent by sub-proof #689. % 136.47/20.36 | | | % 136.47/20.36 | | Case 2: % 136.47/20.36 | | | % 136.47/20.36 | | | (16) all_57_5 = e2 & op(e2, e1) = e2 % 136.47/20.36 | | | % 136.47/20.36 | | | ALPHA: (16) implies: % 136.47/20.36 | | | (17) all_57_5 = e2 % 136.47/20.36 | | | % 136.47/20.36 | | | BETA: splitting (11) gives: % 136.47/20.36 | | | % 136.47/20.36 | | | Case 1: % 136.47/20.36 | | | | % 136.47/20.36 | | | | (18) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) % 136.47/20.36 | | | | = e3) % 136.47/20.36 | | | | % 136.47/20.36 | | | | BETA: splitting (18) gives: % 136.47/20.36 | | | | % 136.47/20.36 | | | | Case 1: % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | (19) all_57_4 = e3 & op(e3, e1) = e3 % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | REF_CLOSE: (6), (9), (19) are inconsistent by sub-proof #691. % 136.47/20.36 | | | | | % 136.47/20.36 | | | | Case 2: % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | (20) all_57_5 = e3 & op(e2, e1) = e3 % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | REF_CLOSE: (7), (17), (20) are inconsistent by sub-proof #663. % 136.47/20.36 | | | | | % 136.47/20.36 | | | | End of split % 136.47/20.36 | | | | % 136.47/20.36 | | | Case 2: % 136.47/20.36 | | | | % 136.47/20.36 | | | | (21) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) % 136.47/20.36 | | | | = e3) % 136.47/20.36 | | | | % 136.47/20.36 | | | | BETA: splitting (21) gives: % 136.47/20.36 | | | | % 136.47/20.36 | | | | Case 1: % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | (22) all_57_8 = e3 & op(e1, e1) = e3 % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | ALPHA: (22) implies: % 136.47/20.36 | | | | | (23) op(e1, e1) = e3 % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | REF_CLOSE: (1), (3), (4), (23) are inconsistent by sub-proof #771. % 136.47/20.36 | | | | | % 136.47/20.36 | | | | Case 2: % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | (24) all_57_14 = e3 & op(e0, e1) = e3 % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | ALPHA: (24) implies: % 136.47/20.36 | | | | | (25) all_57_14 = e3 % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | REF_CLOSE: (10), (12), (25) are inconsistent by sub-proof #561. % 136.47/20.36 | | | | | % 136.47/20.36 | | | | End of split % 136.47/20.36 | | | | % 136.47/20.36 | | | End of split % 136.47/20.36 | | | % 136.47/20.36 | | End of split % 136.47/20.36 | | % 136.47/20.36 | Case 2: % 136.47/20.36 | | % 136.47/20.36 | | (26) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = % 136.47/20.36 | | e2) % 136.47/20.36 | | % 136.47/20.36 | | REF_CLOSE: (1), (4), (5), (8), (12), (26) are inconsistent by sub-proof % 136.47/20.36 | | #559. % 136.47/20.36 | | % 136.47/20.36 | End of split % 136.47/20.36 | % 136.47/20.36 End of proof % 136.47/20.36 % 136.47/20.36 Sub-proof #559 shows that the following formulas are inconsistent: % 136.47/20.36 ---------------------------------------------------------------- % 136.47/20.36 (1) op(e1, e1) = all_6_2 % 136.47/20.36 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.36 (3) ~ (e2 = e1) % 136.47/20.36 (4) ~ (all_6_2 = e2) % 136.47/20.36 (5) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 136.47/20.36 (6) all_57_14 = e1 % 136.47/20.36 % 136.47/20.36 Begin of proof % 136.47/20.36 | % 136.47/20.36 | BETA: splitting (5) gives: % 136.47/20.36 | % 136.47/20.36 | Case 1: % 136.47/20.36 | | % 136.47/20.36 | | (7) all_57_8 = e2 & op(e1, e1) = e2 % 136.47/20.36 | | % 136.47/20.36 | | ALPHA: (7) implies: % 136.47/20.36 | | (8) op(e1, e1) = e2 % 136.47/20.36 | | % 136.47/20.36 | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #767. % 136.47/20.36 | | % 136.47/20.36 | Case 2: % 136.47/20.36 | | % 136.47/20.36 | | (9) all_57_14 = e2 & op(e0, e1) = e2 % 136.47/20.36 | | % 136.47/20.36 | | ALPHA: (9) implies: % 136.47/20.36 | | (10) all_57_14 = e2 % 136.47/20.36 | | % 136.47/20.36 | | REF_CLOSE: (3), (6), (10) are inconsistent by sub-proof #560. % 136.47/20.36 | | % 136.47/20.36 | End of split % 136.47/20.36 | % 136.47/20.36 End of proof % 136.47/20.36 % 136.47/20.36 Sub-proof #560 shows that the following formulas are inconsistent: % 136.47/20.36 ---------------------------------------------------------------- % 136.47/20.36 (1) all_57_14 = e2 % 136.47/20.36 (2) all_57_14 = e1 % 136.47/20.36 (3) ~ (e2 = e1) % 136.47/20.36 % 136.47/20.36 Begin of proof % 136.47/20.36 | % 136.47/20.36 | COMBINE_EQS: (1), (2) imply: % 136.47/20.36 | (4) e2 = e1 % 136.47/20.36 | % 136.47/20.36 | SIMP: (4) implies: % 136.47/20.36 | (5) e2 = e1 % 136.47/20.36 | % 136.47/20.36 | REDUCE: (3), (5) imply: % 136.47/20.36 | (6) $false % 136.47/20.36 | % 136.47/20.36 | CLOSE: (6) is inconsistent. % 136.47/20.36 | % 136.47/20.36 End of proof % 136.47/20.36 % 136.47/20.36 Sub-proof #561 shows that the following formulas are inconsistent: % 136.47/20.36 ---------------------------------------------------------------- % 136.47/20.36 (1) all_57_14 = e3 % 136.47/20.36 (2) all_57_14 = e1 % 136.47/20.36 (3) ~ (e3 = e1) % 136.47/20.36 % 136.47/20.36 Begin of proof % 136.47/20.36 | % 136.47/20.36 | COMBINE_EQS: (1), (2) imply: % 136.47/20.36 | (4) e3 = e1 % 136.47/20.36 | % 136.47/20.36 | SIMP: (4) implies: % 136.47/20.36 | (5) e3 = e1 % 136.47/20.36 | % 136.47/20.36 | REDUCE: (3), (5) imply: % 136.47/20.36 | (6) $false % 136.47/20.36 | % 136.47/20.36 | CLOSE: (6) is inconsistent. % 136.47/20.36 | % 136.47/20.36 End of proof % 136.47/20.36 % 136.47/20.36 Sub-proof #562 shows that the following formulas are inconsistent: % 136.47/20.36 ---------------------------------------------------------------- % 136.47/20.36 (1) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) % 136.47/20.36 (2) all_57_1 = e3 % 136.47/20.36 (3) op(e3, e3) = e1 % 136.47/20.36 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.36 (5) ~ (e2 = e1) % 136.47/20.36 (6) ~ (e3 = e2) % 136.47/20.36 % 136.47/20.36 Begin of proof % 136.47/20.36 | % 136.47/20.36 | BETA: splitting (1) gives: % 136.47/20.36 | % 136.47/20.36 | Case 1: % 136.47/20.36 | | % 136.47/20.36 | | (7) all_57_0 = e2 & op(e3, e3) = e2 % 136.47/20.36 | | % 136.47/20.36 | | ALPHA: (7) implies: % 136.47/20.36 | | (8) op(e3, e3) = e2 % 136.47/20.36 | | % 136.47/20.36 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #743. % 136.47/20.36 | | % 136.47/20.36 | Case 2: % 136.47/20.36 | | % 136.47/20.36 | | (9) all_57_1 = e2 & op(e3, e2) = e2 % 136.47/20.36 | | % 136.47/20.36 | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #563. % 136.47/20.36 | | % 136.47/20.36 | End of split % 136.47/20.36 | % 136.47/20.36 End of proof % 136.47/20.36 % 136.47/20.36 Sub-proof #563 shows that the following formulas are inconsistent: % 136.47/20.36 ---------------------------------------------------------------- % 136.47/20.36 (1) all_57_1 = e2 & op(e3, e2) = e2 % 136.47/20.36 (2) all_57_1 = e3 % 136.47/20.36 (3) ~ (e3 = e2) % 136.47/20.36 % 136.47/20.36 Begin of proof % 136.47/20.36 | % 136.47/20.36 | ALPHA: (1) implies: % 136.47/20.36 | (4) all_57_1 = e2 % 136.47/20.36 | % 136.47/20.36 | COMBINE_EQS: (2), (4) imply: % 136.47/20.36 | (5) e3 = e2 % 136.47/20.36 | % 136.47/20.36 | REDUCE: (3), (5) imply: % 136.47/20.36 | (6) $false % 136.47/20.36 | % 136.47/20.36 | CLOSE: (6) is inconsistent. % 136.47/20.36 | % 136.47/20.36 End of proof % 136.47/20.36 % 136.47/20.36 Sub-proof #564 shows that the following formulas are inconsistent: % 136.47/20.36 ---------------------------------------------------------------- % 136.47/20.36 (1) op(e2, e2) = e0 % 136.47/20.36 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.36 (3) op(e3, e2) = all_52_4 % 136.47/20.36 (4) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) % 136.47/20.36 (5) ~ (e1 = e0) % 136.47/20.36 (6) ~ (all_52_4 = e1) % 136.47/20.36 % 136.47/20.36 Begin of proof % 136.47/20.36 | % 136.47/20.36 | BETA: splitting (4) gives: % 136.47/20.36 | % 136.47/20.36 | Case 1: % 136.47/20.36 | | % 136.47/20.36 | | (7) all_57_1 = e1 & op(e3, e2) = e1 % 136.47/20.36 | | % 136.47/20.36 | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #684. % 136.47/20.36 | | % 136.47/20.36 | Case 2: % 136.47/20.36 | | % 136.47/20.36 | | (8) all_57_3 = e1 & op(e2, e2) = e1 % 136.47/20.36 | | % 136.47/20.36 | | ALPHA: (8) implies: % 136.47/20.36 | | (9) op(e2, e2) = e1 % 136.47/20.36 | | % 136.47/20.36 | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #675. % 136.47/20.36 | | % 136.47/20.36 | End of split % 136.47/20.36 | % 136.47/20.36 End of proof % 136.47/20.36 % 136.47/20.36 Sub-proof #565 shows that the following formulas are inconsistent: % 136.47/20.36 ---------------------------------------------------------------- % 136.47/20.36 (1) op(e1, e1) = all_6_2 % 136.47/20.36 (2) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) | % 136.47/20.36 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) % 136.47/20.36 (3) op(e0, e0) = e3 % 136.47/20.36 (4) ~ (all_52_4 = e0) % 136.47/20.36 (5) op(e2, e2) = e0 % 136.47/20.36 (6) ~ (all_52_6 = e3) % 136.47/20.36 (7) ~ (all_52_14 = e3) % 136.47/20.36 (8) ~ (e2 = e0) % 136.47/20.36 (9) all_57_3 = e0 % 136.47/20.36 (10) op(e3, e3) = e1 % 136.47/20.36 (11) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.47/20.36 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.47/20.36 (12) ~ (all_6_2 = e3) % 136.47/20.36 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.36 (14) ~ (e2 = e1) % 136.47/20.36 (15) ~ (all_52_6 = e2) % 136.47/20.36 (16) ~ (e3 = e0) % 136.47/20.36 (17) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) % 136.47/20.36 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = % 136.47/20.36 e2) % 136.47/20.36 (18) ~ (e3 = e2) % 136.47/20.36 (19) all_57_13 = e1 % 136.47/20.36 (20) ~ (all_46_2 = e0) | ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 & % 136.47/20.36 $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0) = all_46_1 & % 136.47/20.36 $i(all_46_1)) % 136.47/20.36 (21) ~ (all_52_6 = all_6_2) % 136.47/20.36 (22) ~ (all_52_1 = e1) % 136.47/20.36 (23) op(e0, e1) = all_52_11 % 136.47/20.36 (24) ~ (all_52_6 = e0) % 136.47/20.36 (25) all_54_9 = all_52_6 % 136.47/20.36 (26) all_54_10 = all_6_2 % 136.47/20.36 (27) ~ (all_52_11 = e3) % 136.47/20.36 (28) ~ (all_6_2 = e2) % 136.47/20.36 (29) op(e1, e2) = all_52_6 % 136.47/20.36 (30) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | % 136.47/20.36 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2) % 136.47/20.36 (31) ~ (all_52_8 = all_6_2) % 136.47/20.36 (32) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 136.47/20.36 (33) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) | % 136.47/20.36 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2) % 136.47/20.36 (34) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.47/20.36 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.47/20.36 (35) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 136.47/20.36 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 136.47/20.36 (36) op(e3, e2) = all_52_4 % 136.47/20.36 (37) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 136.47/20.36 (38) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 136.47/20.36 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 136.47/20.36 (39) all_46_2 = all_6_2 % 136.47/20.36 (40) op(e2, e3) = all_52_1 % 136.47/20.36 (41) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0) % 136.47/20.36 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) % 136.47/20.36 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & % 136.47/20.36 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))) % 136.47/20.36 (42) op(e3, e1) = all_52_8 % 136.47/20.36 (43) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) | % 136.47/20.36 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) % 136.47/20.36 (44) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | % 136.47/20.36 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 136.47/20.36 (45) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | % 136.47/20.36 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) % 136.47/20.36 (46) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) | % 136.47/20.36 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3) % 136.47/20.36 (47) op(e1, e0) = all_52_14 % 136.47/20.36 (48) ~ (all_52_8 = e3) % 136.47/20.36 (49) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | % 136.47/20.36 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2) % 136.47/20.36 % 136.47/20.36 Begin of proof % 136.47/20.36 | % 136.47/20.36 | BETA: splitting (17) gives: % 136.47/20.36 | % 136.47/20.36 | Case 1: % 136.47/20.36 | | % 136.47/20.36 | | (50) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = % 136.47/20.36 | | e2) % 136.47/20.36 | | % 136.47/20.36 | | BETA: splitting (50) gives: % 136.47/20.36 | | % 136.47/20.36 | | Case 1: % 136.47/20.36 | | | % 136.47/20.36 | | | (51) all_57_12 = e2 & op(e0, e3) = e2 % 136.47/20.36 | | | % 136.47/20.36 | | | ALPHA: (51) implies: % 136.47/20.36 | | | (52) all_57_12 = e2 % 136.47/20.36 | | | % 136.47/20.36 | | | BETA: splitting (37) gives: % 136.47/20.36 | | | % 136.47/20.36 | | | Case 1: % 136.47/20.36 | | | | % 136.47/20.36 | | | | (53) all_54_9 = e2 % 136.47/20.36 | | | | % 136.47/20.36 | | | | REF_CLOSE: (15), (25), (53) are inconsistent by sub-proof #582. % 136.47/20.36 | | | | % 136.47/20.36 | | | Case 2: % 136.47/20.36 | | | | % 136.47/20.36 | | | | (54) ~ (all_54_9 = e2) % 136.47/20.36 | | | | (55) all_54_9 = e1 | all_54_9 = e0 % 136.47/20.36 | | | | % 136.47/20.36 | | | | BETA: splitting (55) gives: % 136.47/20.36 | | | | % 136.47/20.36 | | | | Case 1: % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | (56) all_54_9 = e1 % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | COMBINE_EQS: (25), (56) imply: % 136.47/20.36 | | | | | (57) all_52_6 = e1 % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | SIMP: (57) implies: % 136.47/20.36 | | | | | (58) all_52_6 = e1 % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | REDUCE: (21), (58) imply: % 136.47/20.36 | | | | | (59) ~ (all_6_2 = e1) % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | SIMP: (59) implies: % 136.47/20.36 | | | | | (60) ~ (all_6_2 = e1) % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | REDUCE: (6), (58) imply: % 136.47/20.36 | | | | | (61) ~ (e3 = e1) % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | SIMP: (61) implies: % 136.47/20.36 | | | | | (62) ~ (e3 = e1) % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | REDUCE: (15), (58) imply: % 136.47/20.36 | | | | | (63) ~ (e2 = e1) % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | REDUCE: (24), (58) imply: % 136.47/20.36 | | | | | (64) ~ (e1 = e0) % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | BETA: splitting (32) gives: % 136.47/20.36 | | | | | % 136.47/20.36 | | | | | Case 1: % 136.47/20.36 | | | | | | % 136.47/20.36 | | | | | | (65) all_54_10 = e3 % 136.47/20.36 | | | | | | % 136.47/20.36 | | | | | | REF_CLOSE: (12), (26), (65) are inconsistent by sub-proof #742. % 136.47/20.36 | | | | | | % 136.47/20.36 | | | | | Case 2: % 136.47/20.36 | | | | | | % 136.47/20.36 | | | | | | (66) ~ (all_54_10 = e3) % 136.47/20.36 | | | | | | (67) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 136.47/20.36 | | | | | | % 136.47/20.36 | | | | | | BETA: splitting (67) gives: % 136.47/20.36 | | | | | | % 136.47/20.36 | | | | | | Case 1: % 136.47/20.36 | | | | | | | % 136.47/20.36 | | | | | | | (68) all_54_10 = e2 % 136.47/20.36 | | | | | | | % 136.47/20.36 | | | | | | | REF_CLOSE: (26), (28), (68) are inconsistent by sub-proof #741. % 136.47/20.36 | | | | | | | % 136.47/20.36 | | | | | | Case 2: % 136.47/20.36 | | | | | | | % 136.47/20.36 | | | | | | | (69) ~ (all_54_10 = e2) % 136.47/20.36 | | | | | | | (70) all_54_10 = e1 | all_54_10 = e0 % 136.47/20.36 | | | | | | | % 136.47/20.36 | | | | | | | BETA: splitting (43) gives: % 136.47/20.36 | | | | | | | % 136.47/20.36 | | | | | | | Case 1: % 136.47/20.36 | | | | | | | | % 136.47/20.36 | | | | | | | | (71) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & % 136.47/20.36 | | | | | | | | op(e2, e1) = e3) % 136.47/20.36 | | | | | | | | % 136.47/20.36 | | | | | | | | BETA: splitting (71) gives: % 136.47/20.36 | | | | | | | | % 136.47/20.36 | | | | | | | | Case 1: % 136.47/20.36 | | | | | | | | | % 136.47/20.36 | | | | | | | | | (72) all_57_4 = e3 & op(e3, e1) = e3 % 136.47/20.36 | | | | | | | | | % 136.47/20.36 | | | | | | | | | ALPHA: (72) implies: % 136.47/20.36 | | | | | | | | | (73) op(e3, e1) = e3 % 136.47/20.36 | | | | | | | | | % 136.47/20.36 | | | | | | | | | REF_CLOSE: (13), (42), (48), (73) are inconsistent by % 136.47/20.36 | | | | | | | | | sub-proof #705. % 136.47/20.36 | | | | | | | | | % 136.47/20.36 | | | | | | | | Case 2: % 136.47/20.36 | | | | | | | | | % 136.47/20.36 | | | | | | | | | (74) all_57_5 = e3 & op(e2, e1) = e3 % 136.47/20.36 | | | | | | | | | % 136.47/20.36 | | | | | | | | | ALPHA: (74) implies: % 136.47/20.36 | | | | | | | | | (75) all_57_5 = e3 % 136.47/20.36 | | | | | | | | | % 136.47/20.36 | | | | | | | | | BETA: splitting (35) gives: % 136.47/20.36 | | | | | | | | | % 136.47/20.36 | | | | | | | | | Case 1: % 136.47/20.36 | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | (76) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & % 136.47/20.36 | | | | | | | | | | op(e1, e2) = e3) % 136.47/20.36 | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | BETA: splitting (76) gives: % 136.47/20.36 | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | Case 1: % 136.47/20.36 | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | (77) all_57_6 = e3 & op(e1, e3) = e3 % 136.47/20.36 | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | ALPHA: (77) implies: % 136.47/20.36 | | | | | | | | | | | (78) all_57_6 = e3 % 136.47/20.36 | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | BETA: splitting (33) gives: % 136.47/20.36 | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | Case 1: % 136.47/20.36 | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | (79) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = % 136.47/20.36 | | | | | | | | | | | | e2 & op(e2, e0) = e2) % 136.47/20.36 | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | BETA: splitting (79) gives: % 136.47/20.36 | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | Case 1: % 136.47/20.36 | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | (80) all_57_9 = e2 & op(e3, e0) = e2 % 136.47/20.36 | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | ALPHA: (80) implies: % 136.47/20.36 | | | | | | | | | | | | | (81) all_57_9 = e2 % 136.47/20.36 | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | BETA: splitting (11) gives: % 136.47/20.36 | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | Case 1: % 136.47/20.36 | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | (82) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 % 136.47/20.36 | | | | | | | | | | | | | | & op(e3, e2) = e0) % 136.47/20.36 | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | REF_CLOSE: (4), (10), (13), (36), (64), (82) are inconsistent % 136.47/20.36 | | | | | | | | | | | | | | by sub-proof #692. % 136.47/20.36 | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | Case 2: % 136.47/20.36 | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | (83) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 % 136.47/20.36 | | | | | | | | | | | | | | & op(e3, e0) = e0) % 136.47/20.36 | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | BETA: splitting (83) gives: % 136.47/20.36 | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | Case 1: % 136.47/20.36 | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | | (84) all_57_4 = e0 & op(e3, e1) = e0 % 136.47/20.36 | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | | ALPHA: (84) implies: % 136.47/20.36 | | | | | | | | | | | | | | | (85) op(e3, e1) = e0 % 136.47/20.36 | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | | BETA: splitting (70) gives: % 136.47/20.36 | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | | Case 1: % 136.47/20.36 | | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | | | (86) all_54_10 = e1 % 136.47/20.36 | | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | | | REF_CLOSE: (26), (60), (86) are inconsistent by sub-proof % 136.47/20.36 | | | | | | | | | | | | | | | | #736. % 136.47/20.36 | | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | | Case 2: % 136.47/20.36 | | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | | | (87) all_54_10 = e0 % 136.47/20.36 | | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (87) imply: % 136.47/20.36 | | | | | | | | | | | | | | | | (88) all_6_2 = e0 % 136.47/20.36 | | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | | | SIMP: (88) implies: % 136.47/20.36 | | | | | | | | | | | | | | | | (89) all_6_2 = e0 % 136.47/20.36 | | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | | | REDUCE: (1), (89) imply: % 136.47/20.36 | | | | | | | | | | | | | | | | (90) op(e1, e1) = e0 % 136.47/20.36 | | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (13), (31), (42), (85), (90) are inconsistent % 136.47/20.36 | | | | | | | | | | | | | | | | by sub-proof #619. % 136.47/20.36 | | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | | End of split % 136.47/20.36 | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | Case 2: % 136.47/20.36 | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | | (91) all_57_9 = e0 & op(e3, e0) = e0 % 136.47/20.36 | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | | ALPHA: (91) implies: % 136.47/20.36 | | | | | | | | | | | | | | | (92) all_57_9 = e0 % 136.47/20.36 | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | | REF_CLOSE: (8), (81), (92) are inconsistent by sub-proof % 136.47/20.36 | | | | | | | | | | | | | | | #696. % 136.47/20.36 | | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | | End of split % 136.47/20.36 | | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | End of split % 136.47/20.36 | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | Case 2: % 136.47/20.36 | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | (93) all_57_10 = e2 & op(e2, e0) = e2 % 136.47/20.36 | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | ALPHA: (93) implies: % 136.47/20.36 | | | | | | | | | | | | | (94) all_57_10 = e2 % 136.47/20.36 | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | BETA: splitting (49) gives: % 136.47/20.36 | | | | | | | | | | | | | % 136.47/20.36 | | | | | | | | | | | | | Case 1: % 136.47/20.36 | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | (95) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 136.47/20.37 | | | | | | | | | | | | | | & op(e2, e1) = e2) % 136.47/20.37 | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | BETA: splitting (95) gives: % 136.47/20.37 | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | Case 1: % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | (96) all_57_4 = e2 & op(e3, e1) = e2 % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | ALPHA: (96) implies: % 136.47/20.37 | | | | | | | | | | | | | | | (97) all_57_4 = e2 % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (10), (11), (13), (14), (16), (18), % 136.47/20.37 | | | | | | | | | | | | | | | (22), (30), (36), (40), (45), (46), (62), (64), % 136.47/20.37 | | | | | | | | | | | | | | | (75), (94), (97) are inconsistent by sub-proof % 136.47/20.37 | | | | | | | | | | | | | | | #666. % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | (98) all_57_5 = e2 & op(e2, e1) = e2 % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | REF_CLOSE: (18), (75), (98) are inconsistent by sub-proof % 136.47/20.37 | | | | | | | | | | | | | | | #677. % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | (99) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 136.47/20.37 | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 136.47/20.37 | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | BETA: splitting (99) gives: % 136.47/20.37 | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | Case 1: % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | (100) all_57_8 = e2 & op(e1, e1) = e2 % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | ALPHA: (100) implies: % 136.47/20.37 | | | | | | | | | | | | | | | (101) op(e1, e1) = e2 % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | REF_CLOSE: (1), (13), (28), (101) are inconsistent by % 136.47/20.37 | | | | | | | | | | | | | | | sub-proof #767. % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | (102) all_57_14 = e2 & op(e0, e1) = e2 % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | ALPHA: (102) implies: % 136.47/20.37 | | | | | | | | | | | | | | | (103) all_57_14 = e2 % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | BETA: splitting (45) gives: % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | Case 1: % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | (104) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 % 136.47/20.37 | | | | | | | | | | | | | | | | & op(e2, e2) = e1) % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13), (22), (40), (64), (104) are % 136.47/20.37 | | | | | | | | | | | | | | | | inconsistent by sub-proof #674. % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | (105) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = % 136.47/20.37 | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1) % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | BETA: splitting (105) gives: % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | Case 1: % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | (106) all_57_5 = e1 & op(e2, e1) = e1 % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (75), (106) are inconsistent by sub-proof % 136.47/20.37 | | | | | | | | | | | | | | | | | #673. % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | (107) all_57_10 = e1 & op(e2, e0) = e1 % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | ALPHA: (107) implies: % 136.47/20.37 | | | | | | | | | | | | | | | | | (108) all_57_10 = e1 % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (108) imply: % 136.47/20.37 | | | | | | | | | | | | | | | | | (109) e2 = e1 % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | SIMP: (109) implies: % 136.47/20.37 | | | | | | | | | | | | | | | | | (110) e2 = e1 % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (110) imply: % 136.47/20.37 | | | | | | | | | | | | | | | | | (111) all_57_12 = e1 % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | BETA: splitting (41) gives: % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | Case 1: % 136.47/20.37 | | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | | (112) all_57_15 = e0 & op(e0, e0) = e0 % 136.47/20.37 | | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | | ALPHA: (112) implies: % 136.47/20.37 | | | | | | | | | | | | | | | | | | (113) op(e0, e0) = e0 % 136.47/20.37 | | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (13), (16), (113) are inconsistent by % 136.47/20.37 | | | | | | | | | | | | | | | | | | sub-proof #715. % 136.47/20.37 | | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | | (114) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = % 136.47/20.37 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & % 136.47/20.37 | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, % 136.47/20.37 | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) = % 136.47/20.37 | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) % 136.47/20.37 | | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | | ALPHA: (114) implies: % 136.47/20.37 | | | | | | | | | | | | | | | | | | (115) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = % 136.47/20.37 | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, % 136.47/20.37 | | | | | | | | | | | | | | | | | | e1) = e0) % 136.47/20.37 | | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives: % 136.47/20.37 | | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | | Case 1: % 136.47/20.37 | | | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | | | (116) all_57_12 = e0 & op(e0, e3) = e0 % 136.47/20.37 | | | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | | | ALPHA: (116) implies: % 136.47/20.37 | | | | | | | | | | | | | | | | | | | (117) all_57_12 = e0 % 136.47/20.37 | | | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (111), (117) are inconsistent by sub-proof % 136.47/20.37 | | | | | | | | | | | | | | | | | | | #581. % 136.47/20.37 | | | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | | | (118) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = % 136.47/20.37 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0) % 136.47/20.37 | | | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19), (64), (103), (118) are inconsistent by % 136.47/20.37 | | | | | | | | | | | | | | | | | | | sub-proof #579. % 136.47/20.37 | | | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | (119) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = % 136.47/20.37 | | | | | | | | | | | | e2 & op(e0, e0) = e2) % 136.47/20.37 | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | BETA: splitting (119) gives: % 136.47/20.37 | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | Case 1: % 136.47/20.37 | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | (120) all_57_11 = e2 & op(e1, e0) = e2 % 136.47/20.37 | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | ALPHA: (120) implies: % 136.47/20.37 | | | | | | | | | | | | | (121) all_57_11 = e2 % 136.47/20.37 | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | BETA: splitting (49) gives: % 136.47/20.37 | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | Case 1: % 136.47/20.37 | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | (122) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 % 136.47/20.37 | | | | | | | | | | | | | | & op(e2, e1) = e2) % 136.47/20.37 | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | BETA: splitting (122) gives: % 136.47/20.37 | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | Case 1: % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | (123) all_57_4 = e2 & op(e3, e1) = e2 % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | ALPHA: (123) implies: % 136.47/20.37 | | | | | | | | | | | | | | | (124) all_57_4 = e2 % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | BETA: splitting (34) gives: % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | Case 1: % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | (125) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 % 136.47/20.37 | | | | | | | | | | | | | | | | & op(e2, e3) = e0) % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | BETA: splitting (125) gives: % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | Case 1: % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | (126) all_57_0 = e0 & op(e3, e3) = e0 % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | ALPHA: (126) implies: % 136.47/20.37 | | | | | | | | | | | | | | | | | (127) op(e3, e3) = e0 % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (64), (127) are inconsistent by % 136.47/20.37 | | | | | | | | | | | | | | | | | sub-proof #717. % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | (128) all_57_2 = e0 & op(e2, e3) = e0 % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | ALPHA: (128) implies: % 136.47/20.37 | | | | | | | | | | | | | | | | | (129) all_57_2 = e0 % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (8), (9), (10), (11), (13), (14), % 136.47/20.37 | | | | | | | | | | | | | | | | | (16), (18), (22), (30), (36), (40), (45), (46), % 136.47/20.37 | | | | | | | | | | | | | | | | | (62), (64), (75), (124), (129) are inconsistent by % 136.47/20.37 | | | | | | | | | | | | | | | | | sub-proof #665. % 136.47/20.37 | | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | (130) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = % 136.47/20.37 | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0) % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (52), (78), (130) are inconsistent by % 136.47/20.37 | | | | | | | | | | | | | | | | sub-proof #577. % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | (131) all_57_5 = e2 & op(e2, e1) = e2 % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | REF_CLOSE: (18), (75), (131) are inconsistent by sub-proof % 136.47/20.37 | | | | | | | | | | | | | | | #677. % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | (132) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = % 136.47/20.37 | | | | | | | | | | | | | | e2 & op(e0, e1) = e2) % 136.47/20.37 | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | BETA: splitting (132) gives: % 136.47/20.37 | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | Case 1: % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | (133) all_57_8 = e2 & op(e1, e1) = e2 % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | ALPHA: (133) implies: % 136.47/20.37 | | | | | | | | | | | | | | | (134) all_57_8 = e2 % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (13), (14), (16), (18), (29), (35), % 136.47/20.37 | | | | | | | | | | | | | | | (38), (44), (62), (64), (121), (134) are % 136.47/20.37 | | | | | | | | | | | | | | | inconsistent by sub-proof #571. % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | (135) all_57_14 = e2 & op(e0, e1) = e2 % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | ALPHA: (135) implies: % 136.47/20.37 | | | | | | | | | | | | | | | (136) op(e0, e1) = e2 % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | BETA: splitting (70) gives: % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | Case 1: % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | (137) all_54_10 = e1 % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | REF_CLOSE: (26), (60), (137) are inconsistent by sub-proof % 136.47/20.37 | | | | | | | | | | | | | | | | #736. % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | (138) all_54_10 = e0 % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (13), (20), (26), (39), (136), (138) are % 136.47/20.37 | | | | | | | | | | | | | | | | inconsistent by sub-proof #569. % 136.47/20.37 | | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | (139) all_57_15 = e2 & op(e0, e0) = e2 % 136.47/20.37 | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | ALPHA: (139) implies: % 136.47/20.37 | | | | | | | | | | | | | (140) op(e0, e0) = e2 % 136.47/20.37 | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | | REF_CLOSE: (3), (13), (18), (140) are inconsistent by % 136.47/20.37 | | | | | | | | | | | | | sub-proof #634. % 136.47/20.37 | | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | (141) all_57_7 = e3 & op(e1, e2) = e3 % 136.47/20.37 | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | ALPHA: (141) implies: % 136.47/20.37 | | | | | | | | | | | (142) op(e1, e2) = e3 % 136.47/20.37 | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | | REF_CLOSE: (6), (13), (29), (142) are inconsistent by % 136.47/20.37 | | | | | | | | | | | sub-proof #654. % 136.47/20.37 | | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | | % 136.47/20.37 | | | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | (143) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 % 136.47/20.37 | | | | | | | | | | & op(e1, e0) = e3) % 136.47/20.37 | | | | | | | | | | % 136.47/20.37 | | | | | | | | | | REF_CLOSE: (1), (7), (12), (13), (47), (143) are inconsistent % 136.47/20.37 | | | | | | | | | | by sub-proof #653. % 136.47/20.37 | | | | | | | | | | % 136.47/20.37 | | | | | | | | | End of split % 136.47/20.37 | | | | | | | | | % 136.47/20.37 | | | | | | | | End of split % 136.47/20.37 | | | | | | | | % 136.47/20.37 | | | | | | | Case 2: % 136.47/20.37 | | | | | | | | % 136.47/20.37 | | | | | | | | (144) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & % 136.47/20.37 | | | | | | | | op(e0, e1) = e3) % 136.47/20.37 | | | | | | | | % 136.47/20.37 | | | | | | | | REF_CLOSE: (1), (12), (13), (23), (27), (144) are inconsistent % 136.47/20.37 | | | | | | | | by sub-proof #651. % 136.47/20.37 | | | | | | | | % 136.47/20.37 | | | | | | | End of split % 136.47/20.37 | | | | | | | % 136.47/20.37 | | | | | | End of split % 136.47/20.37 | | | | | | % 136.47/20.37 | | | | | End of split % 136.47/20.37 | | | | | % 136.47/20.37 | | | | Case 2: % 136.47/20.37 | | | | | % 136.47/20.37 | | | | | (145) all_54_9 = e0 % 136.47/20.37 | | | | | % 136.47/20.37 | | | | | REF_CLOSE: (24), (25), (145) are inconsistent by sub-proof #568. % 136.47/20.37 | | | | | % 136.47/20.37 | | | | End of split % 136.47/20.37 | | | | % 136.47/20.37 | | | End of split % 136.47/20.37 | | | % 136.47/20.37 | | Case 2: % 136.47/20.37 | | | % 136.47/20.37 | | | (146) all_57_13 = e2 & op(e0, e2) = e2 % 136.47/20.37 | | | % 136.47/20.37 | | | ALPHA: (146) implies: % 136.47/20.37 | | | (147) all_57_13 = e2 % 136.47/20.37 | | | % 136.47/20.37 | | | REF_CLOSE: (14), (19), (147) are inconsistent by sub-proof #567. % 136.47/20.37 | | | % 136.47/20.37 | | End of split % 136.47/20.37 | | % 136.47/20.37 | Case 2: % 136.47/20.37 | | % 136.47/20.37 | | (148) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = % 136.47/20.37 | | e2) % 136.47/20.37 | | % 136.47/20.37 | | BETA: splitting (148) gives: % 136.47/20.37 | | % 136.47/20.37 | | Case 1: % 136.47/20.37 | | | % 136.47/20.37 | | | (149) all_57_14 = e2 & op(e0, e1) = e2 % 136.47/20.37 | | | % 136.47/20.37 | | | ALPHA: (149) implies: % 136.47/20.37 | | | (150) op(e0, e1) = e2 % 136.47/20.37 | | | % 136.47/20.37 | | | REF_CLOSE: (3), (12), (13), (15), (20), (21), (24), (25), (26), (28), % 136.47/20.37 | | | (32), (37), (39), (150) are inconsistent by sub-proof #566. % 136.47/20.37 | | | % 136.47/20.37 | | Case 2: % 136.47/20.37 | | | % 136.47/20.37 | | | (151) all_57_15 = e2 & op(e0, e0) = e2 % 136.47/20.37 | | | % 136.47/20.37 | | | ALPHA: (151) implies: % 136.47/20.37 | | | (152) op(e0, e0) = e2 % 136.47/20.37 | | | % 136.47/20.37 | | | REF_CLOSE: (3), (13), (18), (152) are inconsistent by sub-proof #634. % 136.47/20.37 | | | % 136.47/20.37 | | End of split % 136.47/20.37 | | % 136.47/20.37 | End of split % 136.47/20.37 | % 136.47/20.37 End of proof % 136.47/20.37 % 136.47/20.37 Sub-proof #566 shows that the following formulas are inconsistent: % 136.47/20.37 ---------------------------------------------------------------- % 136.47/20.37 (1) op(e0, e1) = e2 % 136.47/20.37 (2) op(e0, e0) = e3 % 136.47/20.37 (3) ~ (all_6_2 = e3) % 136.47/20.37 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.37 (5) ~ (all_52_6 = e2) % 136.47/20.37 (6) ~ (all_46_2 = e0) | ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 & % 136.47/20.37 $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0) = all_46_1 & % 136.47/20.37 $i(all_46_1)) % 136.47/20.37 (7) ~ (all_52_6 = all_6_2) % 136.47/20.37 (8) ~ (all_52_6 = e0) % 136.47/20.37 (9) all_54_9 = all_52_6 % 136.47/20.37 (10) all_54_10 = all_6_2 % 136.47/20.37 (11) ~ (all_6_2 = e2) % 136.47/20.37 (12) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 136.47/20.37 (13) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0 % 136.47/20.37 (14) all_46_2 = all_6_2 % 136.47/20.37 % 136.47/20.37 Begin of proof % 136.47/20.37 | % 136.47/20.37 | BETA: splitting (13) gives: % 136.47/20.37 | % 136.47/20.37 | Case 1: % 136.47/20.37 | | % 136.47/20.37 | | (15) all_54_9 = e2 % 136.47/20.37 | | % 136.47/20.37 | | REF_CLOSE: (5), (9), (15) are inconsistent by sub-proof #582. % 136.47/20.37 | | % 136.47/20.37 | Case 2: % 136.47/20.37 | | % 136.47/20.37 | | (16) all_54_9 = e1 | all_54_9 = e0 % 136.47/20.37 | | % 136.47/20.37 | | BETA: splitting (16) gives: % 136.47/20.37 | | % 136.47/20.37 | | Case 1: % 136.47/20.37 | | | % 136.47/20.37 | | | (17) all_54_9 = e1 % 136.47/20.37 | | | % 136.47/20.37 | | | COMBINE_EQS: (9), (17) imply: % 136.47/20.37 | | | (18) all_52_6 = e1 % 136.47/20.37 | | | % 136.47/20.37 | | | SIMP: (18) implies: % 136.47/20.37 | | | (19) all_52_6 = e1 % 136.47/20.37 | | | % 136.47/20.37 | | | REDUCE: (7), (19) imply: % 136.47/20.37 | | | (20) ~ (all_6_2 = e1) % 136.47/20.37 | | | % 136.47/20.37 | | | SIMP: (20) implies: % 136.47/20.37 | | | (21) ~ (all_6_2 = e1) % 136.47/20.37 | | | % 136.47/20.37 | | | BETA: splitting (12) gives: % 136.47/20.37 | | | % 136.47/20.37 | | | Case 1: % 136.47/20.37 | | | | % 136.47/20.37 | | | | (22) all_54_10 = e3 % 136.47/20.37 | | | | % 136.47/20.37 | | | | REF_CLOSE: (3), (10), (22) are inconsistent by sub-proof #742. % 136.47/20.37 | | | | % 136.47/20.37 | | | Case 2: % 136.47/20.37 | | | | % 136.47/20.37 | | | | (23) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0 % 136.47/20.37 | | | | % 136.47/20.37 | | | | BETA: splitting (23) gives: % 136.47/20.37 | | | | % 136.47/20.37 | | | | Case 1: % 136.47/20.37 | | | | | % 136.47/20.37 | | | | | (24) all_54_10 = e2 % 136.47/20.37 | | | | | % 136.47/20.37 | | | | | REF_CLOSE: (10), (11), (24) are inconsistent by sub-proof #741. % 136.47/20.37 | | | | | % 136.47/20.37 | | | | Case 2: % 136.47/20.37 | | | | | % 136.47/20.37 | | | | | (25) all_54_10 = e1 | all_54_10 = e0 % 136.47/20.37 | | | | | % 136.47/20.37 | | | | | BETA: splitting (25) gives: % 136.47/20.37 | | | | | % 136.47/20.37 | | | | | Case 1: % 136.47/20.37 | | | | | | % 136.47/20.37 | | | | | | (26) all_54_10 = e1 % 136.47/20.37 | | | | | | % 136.47/20.37 | | | | | | REF_CLOSE: (10), (21), (26) are inconsistent by sub-proof #736. % 136.47/20.37 | | | | | | % 136.47/20.37 | | | | | Case 2: % 136.47/20.37 | | | | | | % 136.47/20.37 | | | | | | (27) all_54_10 = e0 % 136.47/20.37 | | | | | | % 136.47/20.37 | | | | | | REF_CLOSE: (1), (2), (4), (6), (10), (14), (27) are inconsistent by % 136.47/20.37 | | | | | | sub-proof #569. % 136.47/20.37 | | | | | | % 136.47/20.37 | | | | | End of split % 136.47/20.37 | | | | | % 136.47/20.37 | | | | End of split % 136.47/20.37 | | | | % 136.47/20.37 | | | End of split % 136.47/20.37 | | | % 136.47/20.37 | | Case 2: % 136.47/20.37 | | | % 136.47/20.37 | | | (28) all_54_9 = e0 % 136.47/20.37 | | | % 136.47/20.37 | | | REF_CLOSE: (8), (9), (28) are inconsistent by sub-proof #568. % 136.47/20.37 | | | % 136.47/20.37 | | End of split % 136.47/20.37 | | % 136.47/20.37 | End of split % 136.47/20.37 | % 136.47/20.37 End of proof % 136.47/20.37 % 136.47/20.37 Sub-proof #567 shows that the following formulas are inconsistent: % 136.47/20.37 ---------------------------------------------------------------- % 136.47/20.37 (1) all_57_13 = e2 % 136.47/20.37 (2) all_57_13 = e1 % 136.47/20.37 (3) ~ (e2 = e1) % 136.47/20.37 % 136.47/20.37 Begin of proof % 136.47/20.37 | % 136.47/20.37 | COMBINE_EQS: (1), (2) imply: % 136.47/20.37 | (4) e2 = e1 % 136.47/20.37 | % 136.47/20.37 | SIMP: (4) implies: % 136.47/20.37 | (5) e2 = e1 % 136.47/20.37 | % 136.47/20.37 | REDUCE: (3), (5) imply: % 136.47/20.37 | (6) $false % 136.47/20.37 | % 136.47/20.37 | CLOSE: (6) is inconsistent. % 136.47/20.37 | % 136.47/20.37 End of proof % 136.47/20.37 % 136.47/20.37 Sub-proof #568 shows that the following formulas are inconsistent: % 136.47/20.37 ---------------------------------------------------------------- % 136.47/20.37 (1) all_54_9 = all_52_6 % 136.47/20.37 (2) all_54_9 = e0 % 136.47/20.37 (3) ~ (all_52_6 = e0) % 136.47/20.37 % 136.47/20.37 Begin of proof % 136.47/20.37 | % 136.47/20.37 | COMBINE_EQS: (1), (2) imply: % 136.47/20.37 | (4) all_52_6 = e0 % 136.47/20.37 | % 136.47/20.37 | SIMP: (4) implies: % 136.47/20.37 | (5) all_52_6 = e0 % 136.47/20.37 | % 136.47/20.37 | REDUCE: (3), (5) imply: % 136.47/20.37 | (6) $false % 136.47/20.37 | % 136.47/20.37 | CLOSE: (6) is inconsistent. % 136.47/20.37 | % 136.47/20.37 End of proof % 136.47/20.37 % 136.47/20.37 Sub-proof #569 shows that the following formulas are inconsistent: % 136.47/20.37 ---------------------------------------------------------------- % 136.47/20.37 (1) op(e0, e1) = e2 % 136.47/20.37 (2) op(e0, e0) = e3 % 136.47/20.37 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.47/20.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.47/20.37 (4) all_54_10 = e0 % 136.47/20.37 (5) ~ (all_46_2 = e0) | ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 & % 136.47/20.37 $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0) = all_46_1 & % 136.47/20.37 $i(all_46_1)) % 136.47/20.37 (6) all_54_10 = all_6_2 % 136.47/20.37 (7) all_46_2 = all_6_2 % 136.47/20.37 % 136.47/20.37 Begin of proof % 136.47/20.37 | % 136.47/20.37 | COMBINE_EQS: (4), (6) imply: % 136.47/20.37 | (8) all_6_2 = e0 % 136.47/20.37 | % 136.47/20.37 | SIMP: (8) implies: % 136.47/20.37 | (9) all_6_2 = e0 % 136.47/20.37 | % 136.47/20.37 | COMBINE_EQS: (7), (9) imply: % 136.47/20.37 | (10) all_46_2 = e0 % 136.47/20.37 | % 136.47/20.37 | REF_CLOSE: (1), (2), (3), (5), (10) are inconsistent by sub-proof #570. % 136.47/20.37 | % 136.47/20.37 End of proof % 136.47/20.37 % 136.47/20.37 Sub-proof #570 shows that the following formulas are inconsistent: % 136.76/20.37 ---------------------------------------------------------------- % 136.76/20.37 (1) op(e0, e1) = e2 % 136.76/20.37 (2) op(e0, e0) = e3 % 136.76/20.37 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.76/20.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.76/20.37 (4) ~ (all_46_2 = e0) | ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 & % 136.76/20.37 $i(all_46_0)) | ( ~ (all_46_1 = e3) & op(e0, e0) = all_46_1 & % 136.76/20.37 $i(all_46_1)) % 136.76/20.37 (5) all_46_2 = e0 % 136.76/20.37 % 136.76/20.37 Begin of proof % 136.76/20.37 | % 136.76/20.37 | BETA: splitting (4) gives: % 136.76/20.37 | % 136.76/20.37 | Case 1: % 136.76/20.37 | | % 136.76/20.37 | | (6) ~ (all_46_2 = e0) % 136.76/20.37 | | % 136.76/20.37 | | REDUCE: (5), (6) imply: % 136.76/20.37 | | (7) $false % 136.76/20.37 | | % 136.76/20.37 | | CLOSE: (7) is inconsistent. % 136.76/20.37 | | % 136.76/20.37 | Case 2: % 136.76/20.37 | | % 136.76/20.37 | | (8) ( ~ (all_46_0 = e2) & op(e0, e1) = all_46_0 & $i(all_46_0)) | ( ~ % 136.76/20.37 | | (all_46_1 = e3) & op(e0, e0) = all_46_1 & $i(all_46_1)) % 136.76/20.37 | | % 136.76/20.37 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #757. % 136.76/20.37 | | % 136.76/20.37 | End of split % 136.76/20.37 | % 136.76/20.37 End of proof % 136.76/20.37 % 136.76/20.37 Sub-proof #571 shows that the following formulas are inconsistent: % 136.76/20.37 ---------------------------------------------------------------- % 136.76/20.37 (1) ~ (all_52_6 = e3) % 136.76/20.37 (2) ~ (e2 = e0) % 136.76/20.37 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.76/20.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.76/20.37 (4) ~ (e2 = e1) % 136.76/20.37 (5) ~ (e3 = e0) % 136.76/20.37 (6) ~ (e3 = e2) % 136.76/20.37 (7) all_57_8 = e2 % 136.76/20.37 (8) op(e1, e2) = all_52_6 % 136.76/20.37 (9) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | % 136.76/20.37 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3) % 136.76/20.37 (10) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 136.76/20.37 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 136.76/20.37 (11) all_57_11 = e2 % 136.76/20.37 (12) ~ (e3 = e1) % 136.76/20.37 (13) ~ (e1 = e0) % 136.76/20.37 (14) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | % 136.76/20.37 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 136.76/20.37 % 136.76/20.37 Begin of proof % 136.76/20.37 | % 136.76/20.37 | BETA: splitting (9) gives: % 136.76/20.37 | % 136.76/20.37 | Case 1: % 136.76/20.37 | | % 136.76/20.37 | | (15) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = % 136.76/20.37 | | e3) % 136.76/20.37 | | % 136.76/20.37 | | BETA: splitting (15) gives: % 136.76/20.37 | | % 136.76/20.37 | | Case 1: % 136.76/20.37 | | | % 136.76/20.37 | | | (16) all_57_6 = e3 & op(e1, e3) = e3 % 136.76/20.37 | | | % 136.76/20.37 | | | ALPHA: (16) implies: % 136.76/20.37 | | | (17) all_57_6 = e3 % 136.76/20.37 | | | % 136.76/20.37 | | | REF_CLOSE: (2), (4), (5), (7), (10), (11), (12), (13), (14), (17) are % 136.76/20.37 | | | inconsistent by sub-proof #572. % 136.76/20.37 | | | % 136.76/20.37 | | Case 2: % 136.76/20.37 | | | % 136.76/20.37 | | | (18) all_57_7 = e3 & op(e1, e2) = e3 % 136.76/20.37 | | | % 136.76/20.37 | | | ALPHA: (18) implies: % 136.76/20.37 | | | (19) op(e1, e2) = e3 % 136.76/20.37 | | | % 136.76/20.37 | | | REF_CLOSE: (1), (3), (8), (19) are inconsistent by sub-proof #654. % 136.76/20.37 | | | % 136.76/20.37 | | End of split % 136.76/20.37 | | % 136.76/20.37 | Case 2: % 136.76/20.37 | | % 136.76/20.37 | | (20) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = % 136.76/20.37 | | e3) % 136.76/20.37 | | % 136.76/20.37 | | BETA: splitting (20) gives: % 136.76/20.37 | | % 136.76/20.37 | | Case 1: % 136.76/20.37 | | | % 136.76/20.37 | | | (21) all_57_8 = e3 & op(e1, e1) = e3 % 136.76/20.37 | | | % 136.76/20.37 | | | ALPHA: (21) implies: % 136.76/20.37 | | | (22) all_57_8 = e3 % 136.76/20.37 | | | % 136.76/20.37 | | | COMBINE_EQS: (7), (22) imply: % 136.76/20.37 | | | (23) e3 = e2 % 136.76/20.37 | | | % 136.76/20.37 | | | SIMP: (23) implies: % 136.76/20.37 | | | (24) e3 = e2 % 136.76/20.37 | | | % 136.76/20.37 | | | REDUCE: (6), (24) imply: % 136.76/20.37 | | | (25) $false % 136.76/20.37 | | | % 136.76/20.37 | | | CLOSE: (25) is inconsistent. % 136.76/20.37 | | | % 136.76/20.37 | | Case 2: % 136.76/20.37 | | | % 136.76/20.37 | | | (26) all_57_11 = e3 & op(e1, e0) = e3 % 136.76/20.37 | | | % 136.76/20.37 | | | REF_CLOSE: (6), (11), (26) are inconsistent by sub-proof #723. % 136.76/20.37 | | | % 136.76/20.37 | | End of split % 136.76/20.37 | | % 136.76/20.37 | End of split % 136.76/20.37 | % 136.76/20.37 End of proof % 136.76/20.37 % 136.76/20.37 Sub-proof #572 shows that the following formulas are inconsistent: % 136.76/20.37 ---------------------------------------------------------------- % 136.76/20.37 (1) ~ (e2 = e0) % 136.76/20.37 (2) ~ (e2 = e1) % 136.76/20.37 (3) ~ (e3 = e0) % 136.76/20.37 (4) all_57_8 = e2 % 136.76/20.37 (5) all_57_6 = e3 % 136.76/20.37 (6) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) | % 136.76/20.37 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1) % 136.76/20.37 (7) all_57_11 = e2 % 136.76/20.37 (8) ~ (e3 = e1) % 136.76/20.37 (9) ~ (e1 = e0) % 136.76/20.37 (10) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | % 136.76/20.37 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0) % 136.76/20.37 % 136.76/20.37 Begin of proof % 136.76/20.37 | % 136.76/20.37 | BETA: splitting (10) gives: % 136.76/20.37 | % 136.76/20.37 | Case 1: % 136.76/20.37 | | % 136.76/20.37 | | (11) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = % 136.76/20.37 | | e0) % 136.76/20.37 | | % 136.76/20.37 | | BETA: splitting (11) gives: % 136.76/20.37 | | % 136.76/20.37 | | Case 1: % 136.76/20.37 | | | % 136.76/20.37 | | | (12) all_57_6 = e0 & op(e1, e3) = e0 % 136.76/20.37 | | | % 136.76/20.37 | | | REF_CLOSE: (3), (5), (12) are inconsistent by sub-proof #576. % 136.76/20.37 | | | % 136.76/20.37 | | Case 2: % 136.76/20.37 | | | % 136.76/20.37 | | | (13) all_57_7 = e0 & op(e1, e2) = e0 % 136.76/20.37 | | | % 136.76/20.37 | | | ALPHA: (13) implies: % 136.76/20.37 | | | (14) all_57_7 = e0 % 136.76/20.37 | | | % 136.76/20.37 | | | BETA: splitting (6) gives: % 136.76/20.37 | | | % 136.76/20.37 | | | Case 1: % 136.76/20.37 | | | | % 136.76/20.37 | | | | (15) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) % 136.76/20.37 | | | | = e1) % 136.76/20.37 | | | | % 136.76/20.37 | | | | BETA: splitting (15) gives: % 136.76/20.37 | | | | % 136.76/20.37 | | | | Case 1: % 136.76/20.37 | | | | | % 136.76/20.37 | | | | | (16) all_57_6 = e1 & op(e1, e3) = e1 % 136.76/20.37 | | | | | % 136.76/20.37 | | | | | ALPHA: (16) implies: % 136.76/20.37 | | | | | (17) all_57_6 = e1 % 136.76/20.37 | | | | | % 136.76/20.37 | | | | | REF_CLOSE: (5), (8), (17) are inconsistent by sub-proof #575. % 136.76/20.37 | | | | | % 136.76/20.37 | | | | Case 2: % 136.76/20.37 | | | | | % 136.76/20.37 | | | | | (18) all_57_7 = e1 & op(e1, e2) = e1 % 136.76/20.37 | | | | | % 136.76/20.37 | | | | | ALPHA: (18) implies: % 136.76/20.37 | | | | | (19) all_57_7 = e1 % 136.76/20.37 | | | | | % 136.76/20.37 | | | | | COMBINE_EQS: (14), (19) imply: % 136.76/20.37 | | | | | (20) e1 = e0 % 136.76/20.37 | | | | | % 136.76/20.37 | | | | | REDUCE: (9), (20) imply: % 136.76/20.37 | | | | | (21) $false % 136.76/20.37 | | | | | % 136.76/20.37 | | | | | CLOSE: (21) is inconsistent. % 136.76/20.37 | | | | | % 136.76/20.37 | | | | End of split % 136.76/20.37 | | | | % 136.76/20.37 | | | Case 2: % 136.76/20.37 | | | | % 136.76/20.37 | | | | (22) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) % 136.76/20.37 | | | | = e1) % 136.76/20.37 | | | | % 136.76/20.37 | | | | BETA: splitting (22) gives: % 136.76/20.37 | | | | % 136.76/20.37 | | | | Case 1: % 136.76/20.37 | | | | | % 136.76/20.37 | | | | | (23) all_57_8 = e1 & op(e1, e1) = e1 % 136.76/20.37 | | | | | % 136.76/20.37 | | | | | REF_CLOSE: (2), (4), (23) are inconsistent by sub-proof #574. % 136.76/20.37 | | | | | % 136.76/20.37 | | | | Case 2: % 136.76/20.37 | | | | | % 136.76/20.37 | | | | | (24) all_57_11 = e1 & op(e1, e0) = e1 % 136.76/20.37 | | | | | % 136.76/20.37 | | | | | ALPHA: (24) implies: % 136.76/20.37 | | | | | (25) all_57_11 = e1 % 136.76/20.37 | | | | | % 136.76/20.37 | | | | | COMBINE_EQS: (7), (25) imply: % 136.76/20.37 | | | | | (26) e2 = e1 % 136.76/20.37 | | | | | % 136.76/20.37 | | | | | SIMP: (26) implies: % 136.76/20.37 | | | | | (27) e2 = e1 % 136.76/20.37 | | | | | % 136.76/20.37 | | | | | REDUCE: (2), (27) imply: % 136.76/20.37 | | | | | (28) $false % 136.76/20.37 | | | | | % 136.76/20.37 | | | | | CLOSE: (28) is inconsistent. % 136.76/20.37 | | | | | % 136.76/20.37 | | | | End of split % 136.76/20.37 | | | | % 136.76/20.37 | | | End of split % 136.76/20.37 | | | % 136.76/20.37 | | End of split % 136.76/20.37 | | % 136.76/20.37 | Case 2: % 136.76/20.37 | | % 136.76/20.37 | | (29) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = % 136.76/20.37 | | e0) % 136.76/20.37 | | % 136.76/20.37 | | BETA: splitting (29) gives: % 136.76/20.37 | | % 136.76/20.37 | | Case 1: % 136.76/20.37 | | | % 136.76/20.37 | | | (30) all_57_8 = e0 & op(e1, e1) = e0 % 136.76/20.37 | | | % 136.76/20.37 | | | REF_CLOSE: (1), (4), (30) are inconsistent by sub-proof #573. % 136.76/20.37 | | | % 136.76/20.37 | | Case 2: % 136.76/20.37 | | | % 136.76/20.37 | | | (31) all_57_11 = e0 & op(e1, e0) = e0 % 136.76/20.37 | | | % 136.76/20.37 | | | REF_CLOSE: (1), (7), (31) are inconsistent by sub-proof #656. % 136.76/20.37 | | | % 136.76/20.37 | | End of split % 136.76/20.37 | | % 136.76/20.37 | End of split % 136.76/20.37 | % 136.76/20.37 End of proof % 136.76/20.37 % 136.76/20.37 Sub-proof #573 shows that the following formulas are inconsistent: % 136.76/20.37 ---------------------------------------------------------------- % 136.76/20.37 (1) all_57_8 = e0 & op(e1, e1) = e0 % 136.76/20.37 (2) all_57_8 = e2 % 136.76/20.37 (3) ~ (e2 = e0) % 136.76/20.37 % 136.76/20.37 Begin of proof % 136.76/20.37 | % 136.76/20.37 | ALPHA: (1) implies: % 136.76/20.37 | (4) all_57_8 = e0 % 136.76/20.37 | % 136.76/20.37 | COMBINE_EQS: (2), (4) imply: % 136.76/20.37 | (5) e2 = e0 % 136.76/20.37 | % 136.76/20.37 | SIMP: (5) implies: % 136.76/20.37 | (6) e2 = e0 % 136.76/20.37 | % 136.76/20.37 | REDUCE: (3), (6) imply: % 136.76/20.37 | (7) $false % 136.76/20.37 | % 136.76/20.37 | CLOSE: (7) is inconsistent. % 136.76/20.37 | % 136.76/20.37 End of proof % 136.76/20.37 % 136.76/20.37 Sub-proof #574 shows that the following formulas are inconsistent: % 136.76/20.37 ---------------------------------------------------------------- % 136.76/20.37 (1) all_57_8 = e1 & op(e1, e1) = e1 % 136.76/20.37 (2) all_57_8 = e2 % 136.76/20.37 (3) ~ (e2 = e1) % 136.76/20.37 % 136.76/20.37 Begin of proof % 136.76/20.37 | % 136.76/20.37 | ALPHA: (1) implies: % 136.76/20.37 | (4) all_57_8 = e1 % 136.76/20.37 | % 136.76/20.37 | COMBINE_EQS: (2), (4) imply: % 136.76/20.37 | (5) e2 = e1 % 136.76/20.37 | % 136.76/20.37 | REDUCE: (3), (5) imply: % 136.76/20.37 | (6) $false % 136.76/20.37 | % 136.76/20.37 | CLOSE: (6) is inconsistent. % 136.76/20.37 | % 136.76/20.37 End of proof % 136.76/20.37 % 136.76/20.37 Sub-proof #575 shows that the following formulas are inconsistent: % 136.76/20.37 ---------------------------------------------------------------- % 136.76/20.37 (1) all_57_6 = e3 % 136.76/20.37 (2) all_57_6 = e1 % 136.76/20.37 (3) ~ (e3 = e1) % 136.76/20.37 % 136.76/20.37 Begin of proof % 136.76/20.37 | % 136.76/20.37 | COMBINE_EQS: (1), (2) imply: % 136.76/20.37 | (4) e3 = e1 % 136.76/20.37 | % 136.76/20.37 | SIMP: (4) implies: % 136.76/20.37 | (5) e3 = e1 % 136.76/20.37 | % 136.76/20.37 | REDUCE: (3), (5) imply: % 136.76/20.37 | (6) $false % 136.76/20.37 | % 136.76/20.37 | CLOSE: (6) is inconsistent. % 136.76/20.37 | % 136.76/20.37 End of proof % 136.76/20.37 % 136.76/20.37 Sub-proof #576 shows that the following formulas are inconsistent: % 136.76/20.37 ---------------------------------------------------------------- % 136.76/20.37 (1) all_57_6 = e0 & op(e1, e3) = e0 % 136.76/20.37 (2) all_57_6 = e3 % 136.76/20.37 (3) ~ (e3 = e0) % 136.76/20.37 % 136.76/20.37 Begin of proof % 136.76/20.37 | % 136.76/20.37 | ALPHA: (1) implies: % 136.76/20.37 | (4) all_57_6 = e0 % 136.76/20.37 | % 136.76/20.37 | COMBINE_EQS: (2), (4) imply: % 136.76/20.37 | (5) e3 = e0 % 136.76/20.37 | % 136.76/20.37 | REDUCE: (3), (5) imply: % 136.76/20.37 | (6) $false % 136.76/20.37 | % 136.76/20.37 | CLOSE: (6) is inconsistent. % 136.76/20.37 | % 136.76/20.37 End of proof % 136.76/20.37 % 136.76/20.37 Sub-proof #577 shows that the following formulas are inconsistent: % 136.76/20.37 ---------------------------------------------------------------- % 136.76/20.37 (1) ~ (e2 = e0) % 136.76/20.37 (2) ~ (e3 = e0) % 136.76/20.37 (3) all_57_6 = e3 % 136.76/20.37 (4) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.76/20.37 (5) all_57_12 = e2 % 136.76/20.37 % 136.76/20.37 Begin of proof % 136.76/20.37 | % 136.76/20.37 | BETA: splitting (4) gives: % 136.76/20.37 | % 136.76/20.37 | Case 1: % 136.76/20.37 | | % 136.76/20.37 | | (6) all_57_6 = e0 & op(e1, e3) = e0 % 136.76/20.37 | | % 136.76/20.37 | | ALPHA: (6) implies: % 136.76/20.37 | | (7) all_57_6 = e0 % 136.76/20.37 | | % 136.76/20.37 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #588. % 136.76/20.37 | | % 136.76/20.37 | Case 2: % 136.76/20.37 | | % 136.76/20.38 | | (8) all_57_12 = e0 & op(e0, e3) = e0 % 136.76/20.38 | | % 136.76/20.38 | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #578. % 136.76/20.38 | | % 136.76/20.38 | End of split % 136.76/20.38 | % 136.76/20.38 End of proof % 136.76/20.38 % 136.76/20.38 Sub-proof #578 shows that the following formulas are inconsistent: % 136.76/20.38 ---------------------------------------------------------------- % 136.76/20.38 (1) all_57_12 = e0 & op(e0, e3) = e0 % 136.76/20.38 (2) all_57_12 = e2 % 136.76/20.38 (3) ~ (e2 = e0) % 136.76/20.38 % 136.76/20.38 Begin of proof % 136.76/20.38 | % 136.76/20.38 | ALPHA: (1) implies: % 136.76/20.38 | (4) all_57_12 = e0 % 136.76/20.38 | % 136.76/20.38 | COMBINE_EQS: (2), (4) imply: % 136.76/20.38 | (5) e2 = e0 % 136.76/20.38 | % 136.76/20.38 | REDUCE: (3), (5) imply: % 136.76/20.38 | (6) $false % 136.76/20.38 | % 136.76/20.38 | CLOSE: (6) is inconsistent. % 136.76/20.38 | % 136.76/20.38 End of proof % 136.76/20.38 % 136.76/20.38 Sub-proof #579 shows that the following formulas are inconsistent: % 136.76/20.38 ---------------------------------------------------------------- % 136.76/20.38 (1) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0) % 136.76/20.38 (2) ~ (e2 = e0) % 136.76/20.38 (3) all_57_13 = e1 % 136.76/20.38 (4) all_57_14 = e2 % 136.76/20.38 (5) ~ (e1 = e0) % 136.76/20.38 % 136.76/20.38 Begin of proof % 136.76/20.38 | % 136.76/20.38 | BETA: splitting (1) gives: % 136.76/20.38 | % 136.76/20.38 | Case 1: % 136.76/20.38 | | % 136.76/20.38 | | (6) all_57_13 = e0 & op(e0, e2) = e0 % 136.76/20.38 | | % 136.76/20.38 | | ALPHA: (6) implies: % 136.76/20.38 | | (7) all_57_13 = e0 % 136.76/20.38 | | % 136.76/20.38 | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #681. % 136.76/20.38 | | % 136.76/20.38 | Case 2: % 136.76/20.38 | | % 136.76/20.38 | | (8) all_57_14 = e0 & op(e0, e1) = e0 % 136.76/20.38 | | % 136.76/20.38 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #580. % 136.76/20.38 | | % 136.76/20.38 | End of split % 136.76/20.38 | % 136.76/20.38 End of proof % 136.76/20.38 % 136.76/20.38 Sub-proof #580 shows that the following formulas are inconsistent: % 136.76/20.38 ---------------------------------------------------------------- % 136.76/20.38 (1) all_57_14 = e0 & op(e0, e1) = e0 % 136.76/20.38 (2) all_57_14 = e2 % 136.76/20.38 (3) ~ (e2 = e0) % 136.76/20.38 % 136.76/20.38 Begin of proof % 136.76/20.38 | % 136.76/20.38 | ALPHA: (1) implies: % 136.76/20.38 | (4) all_57_14 = e0 % 136.76/20.38 | % 136.76/20.38 | COMBINE_EQS: (2), (4) imply: % 136.76/20.38 | (5) e2 = e0 % 136.76/20.38 | % 136.76/20.38 | SIMP: (5) implies: % 136.76/20.38 | (6) e2 = e0 % 136.76/20.38 | % 136.76/20.38 | REDUCE: (3), (6) imply: % 136.76/20.38 | (7) $false % 136.76/20.38 | % 136.76/20.38 | CLOSE: (7) is inconsistent. % 136.76/20.38 | % 136.76/20.38 End of proof % 136.76/20.38 % 136.76/20.38 Sub-proof #581 shows that the following formulas are inconsistent: % 136.76/20.38 ---------------------------------------------------------------- % 136.76/20.38 (1) all_57_12 = e1 % 136.76/20.38 (2) all_57_12 = e0 % 136.76/20.38 (3) ~ (e1 = e0) % 136.76/20.38 % 136.76/20.38 Begin of proof % 136.76/20.38 | % 136.76/20.38 | COMBINE_EQS: (1), (2) imply: % 136.76/20.38 | (4) e1 = e0 % 136.76/20.38 | % 136.76/20.38 | SIMP: (4) implies: % 136.76/20.38 | (5) e1 = e0 % 136.76/20.38 | % 136.76/20.38 | REDUCE: (3), (5) imply: % 136.76/20.38 | (6) $false % 136.76/20.38 | % 136.76/20.38 | CLOSE: (6) is inconsistent. % 136.76/20.38 | % 136.76/20.38 End of proof % 136.76/20.38 % 136.76/20.38 Sub-proof #582 shows that the following formulas are inconsistent: % 136.76/20.38 ---------------------------------------------------------------- % 136.76/20.38 (1) all_54_9 = all_52_6 % 136.76/20.38 (2) all_54_9 = e2 % 136.76/20.38 (3) ~ (all_52_6 = e2) % 136.76/20.38 % 136.76/20.38 Begin of proof % 136.76/20.38 | % 136.76/20.38 | COMBINE_EQS: (1), (2) imply: % 136.76/20.38 | (4) all_52_6 = e2 % 136.76/20.38 | % 136.76/20.38 | SIMP: (4) implies: % 136.76/20.38 | (5) all_52_6 = e2 % 136.76/20.38 | % 136.76/20.38 | REDUCE: (3), (5) imply: % 136.76/20.38 | (6) $false % 136.76/20.38 | % 136.76/20.38 | CLOSE: (6) is inconsistent. % 136.76/20.38 | % 136.76/20.38 End of proof % 136.76/20.38 % 136.76/20.38 Sub-proof #583 shows that the following formulas are inconsistent: % 136.76/20.38 ---------------------------------------------------------------- % 136.76/20.38 (1) ~ (e2 = e0) % 136.76/20.38 (2) op(e3, e3) = e1 % 136.76/20.38 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.76/20.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.76/20.38 (4) ~ (e2 = e1) % 136.76/20.38 (5) ~ (e3 = e0) % 136.76/20.38 (6) ~ (e3 = e2) % 136.76/20.38 (7) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.76/20.38 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.76/20.38 (8) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) | % 136.76/20.38 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0) % 136.76/20.38 (9) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) | % 136.76/20.38 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2) % 136.76/20.38 (10) ~ (e3 = e1) % 136.76/20.38 (11) ~ (e1 = e0) % 136.76/20.38 (12) all_57_12 = e1 % 136.76/20.38 % 136.76/20.38 Begin of proof % 136.76/20.38 | % 136.76/20.38 | BETA: splitting (8) gives: % 136.76/20.38 | % 136.76/20.38 | Case 1: % 136.76/20.38 | | % 136.76/20.38 | | (13) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = % 136.76/20.38 | | e0) % 136.76/20.38 | | % 136.76/20.38 | | BETA: splitting (13) gives: % 136.76/20.38 | | % 136.76/20.38 | | Case 1: % 136.76/20.38 | | | % 136.76/20.38 | | | (14) all_57_0 = e0 & op(e3, e3) = e0 % 136.76/20.38 | | | % 136.76/20.38 | | | ALPHA: (14) implies: % 136.76/20.38 | | | (15) op(e3, e3) = e0 % 136.76/20.38 | | | % 136.76/20.38 | | | REF_CLOSE: (2), (3), (11), (15) are inconsistent by sub-proof #717. % 136.76/20.38 | | | % 136.76/20.38 | | Case 2: % 136.76/20.38 | | | % 136.76/20.38 | | | (16) all_57_2 = e0 & op(e2, e3) = e0 % 136.76/20.38 | | | % 136.76/20.38 | | | ALPHA: (16) implies: % 136.76/20.38 | | | (17) all_57_2 = e0 % 136.76/20.38 | | | % 136.76/20.38 | | | BETA: splitting (9) gives: % 136.76/20.38 | | | % 136.76/20.38 | | | Case 1: % 136.76/20.38 | | | | % 136.76/20.38 | | | | (18) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) % 136.76/20.38 | | | | = e2) % 136.76/20.38 | | | | % 136.76/20.38 | | | | BETA: splitting (18) gives: % 136.76/20.38 | | | | % 136.76/20.38 | | | | Case 1: % 136.76/20.38 | | | | | % 136.76/20.38 | | | | | (19) all_57_0 = e2 & op(e3, e3) = e2 % 136.76/20.38 | | | | | % 136.76/20.38 | | | | | ALPHA: (19) implies: % 136.76/20.38 | | | | | (20) op(e3, e3) = e2 % 136.76/20.38 | | | | | % 136.76/20.38 | | | | | REF_CLOSE: (2), (3), (4), (20) are inconsistent by sub-proof #743. % 136.76/20.38 | | | | | % 136.76/20.38 | | | | Case 2: % 136.76/20.38 | | | | | % 136.76/20.38 | | | | | (21) all_57_2 = e2 & op(e2, e3) = e2 % 136.76/20.38 | | | | | % 136.76/20.38 | | | | | REF_CLOSE: (1), (17), (21) are inconsistent by sub-proof #680. % 136.76/20.38 | | | | | % 136.76/20.38 | | | | End of split % 136.76/20.38 | | | | % 136.76/20.38 | | | Case 2: % 136.76/20.38 | | | | % 136.76/20.38 | | | | (22) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) % 136.76/20.38 | | | | = e2) % 136.76/20.38 | | | | % 136.76/20.38 | | | | BETA: splitting (22) gives: % 136.76/20.38 | | | | % 136.76/20.38 | | | | Case 1: % 136.76/20.38 | | | | | % 136.76/20.38 | | | | | (23) all_57_6 = e2 & op(e1, e3) = e2 % 136.76/20.38 | | | | | % 136.76/20.38 | | | | | ALPHA: (23) implies: % 136.76/20.38 | | | | | (24) all_57_6 = e2 % 136.76/20.38 | | | | | % 136.76/20.38 | | | | | BETA: splitting (7) gives: % 136.76/20.38 | | | | | % 136.76/20.38 | | | | | Case 1: % 136.76/20.38 | | | | | | % 136.76/20.38 | | | | | | (25) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, % 136.76/20.38 | | | | | | e3) = e3) % 136.76/20.38 | | | | | | % 136.76/20.38 | | | | | | BETA: splitting (25) gives: % 136.76/20.38 | | | | | | % 136.76/20.38 | | | | | | Case 1: % 136.76/20.38 | | | | | | | % 136.76/20.38 | | | | | | | (26) all_57_0 = e3 & op(e3, e3) = e3 % 136.76/20.38 | | | | | | | % 136.76/20.38 | | | | | | | ALPHA: (26) implies: % 136.76/20.38 | | | | | | | (27) op(e3, e3) = e3 % 136.76/20.38 | | | | | | | % 136.76/20.38 | | | | | | | REF_CLOSE: (2), (3), (10), (27) are inconsistent by sub-proof % 136.76/20.38 | | | | | | | #775. % 136.76/20.38 | | | | | | | % 136.76/20.38 | | | | | | Case 2: % 136.76/20.38 | | | | | | | % 136.76/20.38 | | | | | | | (28) all_57_2 = e3 & op(e2, e3) = e3 % 136.76/20.38 | | | | | | | % 136.76/20.38 | | | | | | | ALPHA: (28) implies: % 136.76/20.38 | | | | | | | (29) all_57_2 = e3 % 136.76/20.38 | | | | | | | % 136.76/20.38 | | | | | | | REF_CLOSE: (5), (17), (29) are inconsistent by sub-proof #593. % 136.76/20.38 | | | | | | | % 136.76/20.38 | | | | | | End of split % 136.76/20.38 | | | | | | % 136.76/20.38 | | | | | Case 2: % 136.76/20.38 | | | | | | % 136.76/20.38 | | | | | | (30) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, % 136.76/20.38 | | | | | | e3) = e3) % 136.76/20.38 | | | | | | % 136.76/20.38 | | | | | | BETA: splitting (30) gives: % 136.76/20.38 | | | | | | % 136.76/20.38 | | | | | | Case 1: % 136.76/20.38 | | | | | | | % 136.76/20.38 | | | | | | | (31) all_57_6 = e3 & op(e1, e3) = e3 % 136.76/20.38 | | | | | | | % 136.76/20.38 | | | | | | | ALPHA: (31) implies: % 136.76/20.38 | | | | | | | (32) all_57_6 = e3 % 136.76/20.38 | | | | | | | % 136.76/20.38 | | | | | | | REF_CLOSE: (6), (24), (32) are inconsistent by sub-proof #592. % 136.76/20.38 | | | | | | | % 136.76/20.38 | | | | | | Case 2: % 136.76/20.38 | | | | | | | % 136.76/20.38 | | | | | | | (33) all_57_12 = e3 & op(e0, e3) = e3 % 136.76/20.38 | | | | | | | % 136.76/20.38 | | | | | | | ALPHA: (33) implies: % 136.76/20.38 | | | | | | | (34) all_57_12 = e3 % 136.76/20.38 | | | | | | | % 136.76/20.38 | | | | | | | REF_CLOSE: (10), (12), (34) are inconsistent by sub-proof #591. % 136.76/20.38 | | | | | | | % 136.76/20.38 | | | | | | End of split % 136.76/20.38 | | | | | | % 136.76/20.38 | | | | | End of split % 136.76/20.38 | | | | | % 136.76/20.38 | | | | Case 2: % 136.76/20.38 | | | | | % 136.76/20.38 | | | | | (35) all_57_12 = e2 & op(e0, e3) = e2 % 136.76/20.38 | | | | | % 136.76/20.38 | | | | | ALPHA: (35) implies: % 136.76/20.38 | | | | | (36) all_57_12 = e2 % 136.76/20.38 | | | | | % 136.76/20.38 | | | | | REF_CLOSE: (4), (12), (36) are inconsistent by sub-proof #644. % 136.76/20.38 | | | | | % 136.76/20.38 | | | | End of split % 136.76/20.38 | | | | % 136.76/20.38 | | | End of split % 136.76/20.38 | | | % 136.76/20.38 | | End of split % 136.76/20.38 | | % 136.76/20.38 | Case 2: % 136.76/20.38 | | % 136.76/20.38 | | (37) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = % 136.76/20.38 | | e0) % 136.76/20.38 | | % 136.76/20.38 | | BETA: splitting (37) gives: % 136.76/20.38 | | % 136.76/20.38 | | Case 1: % 136.76/20.38 | | | % 136.76/20.38 | | | (38) all_57_6 = e0 & op(e1, e3) = e0 % 136.76/20.38 | | | % 136.76/20.38 | | | ALPHA: (38) implies: % 136.76/20.38 | | | (39) all_57_6 = e0 % 136.76/20.38 | | | % 136.76/20.38 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (12), (39) are % 136.76/20.38 | | | inconsistent by sub-proof #585. % 136.76/20.38 | | | % 136.76/20.38 | | Case 2: % 136.76/20.38 | | | % 136.76/20.38 | | | (40) all_57_12 = e0 & op(e0, e3) = e0 % 136.76/20.38 | | | % 136.76/20.38 | | | REF_CLOSE: (11), (12), (40) are inconsistent by sub-proof #584. % 136.76/20.38 | | | % 136.76/20.38 | | End of split % 136.76/20.38 | | % 136.76/20.38 | End of split % 136.76/20.38 | % 136.76/20.38 End of proof % 136.76/20.38 % 136.76/20.38 Sub-proof #584 shows that the following formulas are inconsistent: % 136.76/20.38 ---------------------------------------------------------------- % 136.76/20.38 (1) all_57_12 = e0 & op(e0, e3) = e0 % 136.76/20.38 (2) all_57_12 = e1 % 136.76/20.38 (3) ~ (e1 = e0) % 136.76/20.38 % 136.76/20.38 Begin of proof % 136.76/20.38 | % 136.76/20.38 | ALPHA: (1) implies: % 136.76/20.38 | (4) all_57_12 = e0 % 136.76/20.38 | % 136.76/20.38 | COMBINE_EQS: (2), (4) imply: % 136.76/20.38 | (5) e1 = e0 % 136.76/20.38 | % 136.76/20.38 | REDUCE: (3), (5) imply: % 136.76/20.38 | (6) $false % 136.76/20.38 | % 136.76/20.38 | CLOSE: (6) is inconsistent. % 136.76/20.38 | % 136.76/20.38 End of proof % 136.76/20.38 % 136.76/20.38 Sub-proof #585 shows that the following formulas are inconsistent: % 136.76/20.38 ---------------------------------------------------------------- % 136.76/20.38 (1) all_57_6 = e0 % 136.76/20.38 (2) ~ (e2 = e0) % 136.76/20.38 (3) op(e3, e3) = e1 % 136.76/20.38 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.76/20.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.76/20.38 (5) ~ (e2 = e1) % 136.76/20.38 (6) ~ (e3 = e0) % 136.76/20.38 (7) ~ (e3 = e2) % 136.76/20.38 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.76/20.38 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.76/20.38 (9) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) | % 136.76/20.38 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2) % 136.76/20.38 (10) ~ (e3 = e1) % 136.76/20.38 (11) all_57_12 = e1 % 136.76/20.38 % 136.76/20.38 Begin of proof % 136.76/20.38 | % 136.76/20.38 | BETA: splitting (9) gives: % 136.76/20.38 | % 136.76/20.38 | Case 1: % 136.76/20.38 | | % 136.76/20.38 | | (12) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = % 136.76/20.38 | | e2) % 136.76/20.38 | | % 136.76/20.38 | | BETA: splitting (12) gives: % 136.76/20.38 | | % 136.76/20.38 | | Case 1: % 136.76/20.38 | | | % 136.76/20.38 | | | (13) all_57_0 = e2 & op(e3, e3) = e2 % 136.76/20.38 | | | % 136.76/20.38 | | | ALPHA: (13) implies: % 136.76/20.38 | | | (14) op(e3, e3) = e2 % 136.76/20.38 | | | % 136.76/20.38 | | | REF_CLOSE: (3), (4), (5), (14) are inconsistent by sub-proof #743. % 136.76/20.38 | | | % 136.76/20.38 | | Case 2: % 136.76/20.38 | | | % 136.76/20.38 | | | (15) all_57_2 = e2 & op(e2, e3) = e2 % 136.76/20.38 | | | % 136.76/20.38 | | | ALPHA: (15) implies: % 136.76/20.38 | | | (16) all_57_2 = e2 % 136.76/20.38 | | | % 136.76/20.38 | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (11), (16) are inconsistent % 136.76/20.38 | | | by sub-proof #587. % 136.76/20.38 | | | % 136.76/20.38 | | End of split % 136.76/20.38 | | % 136.76/20.38 | Case 2: % 136.76/20.38 | | % 136.76/20.38 | | (17) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = % 136.76/20.38 | | e2) % 136.76/20.38 | | % 136.76/20.38 | | BETA: splitting (17) gives: % 136.76/20.38 | | % 136.76/20.38 | | Case 1: % 136.76/20.38 | | | % 136.76/20.38 | | | (18) all_57_6 = e2 & op(e1, e3) = e2 % 136.76/20.38 | | | % 136.76/20.38 | | | ALPHA: (18) implies: % 136.76/20.38 | | | (19) all_57_6 = e2 % 136.76/20.38 | | | % 136.76/20.38 | | | REF_CLOSE: (1), (2), (19) are inconsistent by sub-proof #586. % 136.76/20.38 | | | % 136.76/20.38 | | Case 2: % 136.76/20.38 | | | % 136.76/20.38 | | | (20) all_57_12 = e2 & op(e0, e3) = e2 % 136.76/20.38 | | | % 136.76/20.38 | | | ALPHA: (20) implies: % 136.76/20.38 | | | (21) all_57_12 = e2 % 136.76/20.38 | | | % 136.76/20.38 | | | REF_CLOSE: (5), (11), (21) are inconsistent by sub-proof #644. % 136.76/20.38 | | | % 136.76/20.38 | | End of split % 136.76/20.38 | | % 136.76/20.38 | End of split % 136.76/20.38 | % 136.76/20.38 End of proof % 136.76/20.38 % 136.76/20.38 Sub-proof #586 shows that the following formulas are inconsistent: % 136.76/20.38 ---------------------------------------------------------------- % 136.76/20.38 (1) all_57_6 = e2 % 136.76/20.38 (2) all_57_6 = e0 % 136.76/20.38 (3) ~ (e2 = e0) % 136.76/20.38 % 136.76/20.38 Begin of proof % 136.76/20.38 | % 136.76/20.38 | COMBINE_EQS: (1), (2) imply: % 136.76/20.38 | (4) e2 = e0 % 136.76/20.38 | % 136.76/20.38 | SIMP: (4) implies: % 136.76/20.38 | (5) e2 = e0 % 136.76/20.38 | % 136.76/20.38 | REDUCE: (3), (5) imply: % 136.76/20.38 | (6) $false % 136.76/20.38 | % 136.76/20.38 | CLOSE: (6) is inconsistent. % 136.76/20.38 | % 136.76/20.38 End of proof % 136.76/20.38 % 136.76/20.38 Sub-proof #587 shows that the following formulas are inconsistent: % 136.76/20.38 ---------------------------------------------------------------- % 136.76/20.38 (1) all_57_6 = e0 % 136.76/20.38 (2) op(e3, e3) = e1 % 136.76/20.38 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.76/20.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.76/20.38 (4) ~ (e3 = e0) % 136.76/20.38 (5) ~ (e3 = e2) % 136.76/20.38 (6) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) | % 136.76/20.38 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3) % 136.76/20.38 (7) all_57_2 = e2 % 136.76/20.38 (8) ~ (e3 = e1) % 136.76/20.38 (9) all_57_12 = e1 % 136.76/20.38 % 136.76/20.38 Begin of proof % 136.76/20.38 | % 136.76/20.38 | BETA: splitting (6) gives: % 136.76/20.38 | % 136.76/20.38 | Case 1: % 136.76/20.38 | | % 136.76/20.38 | | (10) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = % 136.76/20.38 | | e3) % 136.76/20.38 | | % 136.76/20.38 | | REF_CLOSE: (2), (3), (5), (7), (8), (10) are inconsistent by sub-proof #589. % 136.76/20.38 | | % 136.76/20.38 | Case 2: % 136.76/20.38 | | % 136.76/20.38 | | (11) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = % 136.76/20.38 | | e3) % 136.76/20.38 | | % 136.76/20.38 | | BETA: splitting (11) gives: % 136.76/20.38 | | % 136.76/20.38 | | Case 1: % 136.76/20.38 | | | % 136.76/20.38 | | | (12) all_57_6 = e3 & op(e1, e3) = e3 % 136.76/20.38 | | | % 136.76/20.38 | | | ALPHA: (12) implies: % 136.76/20.38 | | | (13) all_57_6 = e3 % 136.76/20.38 | | | % 136.76/20.38 | | | REF_CLOSE: (1), (4), (13) are inconsistent by sub-proof #588. % 136.76/20.38 | | | % 136.76/20.38 | | Case 2: % 136.76/20.38 | | | % 136.76/20.38 | | | (14) all_57_12 = e3 & op(e0, e3) = e3 % 136.76/20.38 | | | % 136.76/20.38 | | | ALPHA: (14) implies: % 136.76/20.38 | | | (15) all_57_12 = e3 % 136.76/20.38 | | | % 136.76/20.38 | | | REF_CLOSE: (8), (9), (15) are inconsistent by sub-proof #591. % 136.76/20.38 | | | % 136.76/20.38 | | End of split % 136.76/20.38 | | % 136.76/20.38 | End of split % 136.76/20.38 | % 136.76/20.38 End of proof % 136.76/20.38 % 136.76/20.38 Sub-proof #588 shows that the following formulas are inconsistent: % 136.76/20.38 ---------------------------------------------------------------- % 136.76/20.38 (1) all_57_6 = e3 % 136.76/20.38 (2) all_57_6 = e0 % 136.76/20.38 (3) ~ (e3 = e0) % 136.76/20.38 % 136.76/20.38 Begin of proof % 136.76/20.38 | % 136.76/20.38 | COMBINE_EQS: (1), (2) imply: % 136.76/20.38 | (4) e3 = e0 % 136.76/20.38 | % 136.76/20.38 | SIMP: (4) implies: % 136.76/20.38 | (5) e3 = e0 % 136.76/20.38 | % 136.76/20.38 | REDUCE: (3), (5) imply: % 136.76/20.38 | (6) $false % 136.76/20.38 | % 136.76/20.38 | CLOSE: (6) is inconsistent. % 136.76/20.38 | % 136.76/20.38 End of proof % 136.76/20.38 % 136.76/20.38 Sub-proof #589 shows that the following formulas are inconsistent: % 136.76/20.38 ---------------------------------------------------------------- % 136.76/20.38 (1) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) % 136.76/20.38 (2) op(e3, e3) = e1 % 136.76/20.38 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.76/20.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.76/20.38 (4) ~ (e3 = e2) % 136.76/20.38 (5) all_57_2 = e2 % 136.76/20.38 (6) ~ (e3 = e1) % 136.76/20.38 % 136.76/20.38 Begin of proof % 136.76/20.38 | % 136.76/20.38 | BETA: splitting (1) gives: % 136.76/20.38 | % 136.76/20.38 | Case 1: % 136.76/20.38 | | % 136.76/20.38 | | (7) all_57_0 = e3 & op(e3, e3) = e3 % 136.76/20.38 | | % 136.76/20.38 | | ALPHA: (7) implies: % 136.76/20.38 | | (8) op(e3, e3) = e3 % 136.76/20.38 | | % 136.76/20.38 | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #775. % 136.76/20.38 | | % 136.76/20.38 | Case 2: % 136.76/20.38 | | % 136.76/20.38 | | (9) all_57_2 = e3 & op(e2, e3) = e3 % 136.76/20.38 | | % 136.76/20.38 | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #590. % 136.76/20.38 | | % 136.76/20.38 | End of split % 136.76/20.38 | % 136.76/20.38 End of proof % 136.76/20.38 % 136.76/20.38 Sub-proof #590 shows that the following formulas are inconsistent: % 136.76/20.38 ---------------------------------------------------------------- % 136.76/20.38 (1) all_57_2 = e3 & op(e2, e3) = e3 % 136.76/20.38 (2) all_57_2 = e2 % 136.76/20.38 (3) ~ (e3 = e2) % 136.76/20.38 % 136.76/20.38 Begin of proof % 136.76/20.38 | % 136.76/20.38 | ALPHA: (1) implies: % 136.76/20.38 | (4) all_57_2 = e3 % 136.76/20.38 | % 136.76/20.38 | COMBINE_EQS: (2), (4) imply: % 136.76/20.38 | (5) e3 = e2 % 136.76/20.38 | % 136.76/20.38 | SIMP: (5) implies: % 136.76/20.38 | (6) e3 = e2 % 136.76/20.38 | % 136.76/20.38 | REDUCE: (3), (6) imply: % 136.76/20.38 | (7) $false % 136.76/20.38 | % 136.76/20.38 | CLOSE: (7) is inconsistent. % 136.76/20.38 | % 136.76/20.38 End of proof % 136.76/20.38 % 136.76/20.38 Sub-proof #591 shows that the following formulas are inconsistent: % 136.76/20.38 ---------------------------------------------------------------- % 136.76/20.38 (1) all_57_12 = e3 % 136.76/20.38 (2) all_57_12 = e1 % 136.76/20.38 (3) ~ (e3 = e1) % 136.76/20.38 % 136.76/20.38 Begin of proof % 136.76/20.38 | % 136.76/20.38 | COMBINE_EQS: (1), (2) imply: % 136.76/20.38 | (4) e3 = e1 % 136.76/20.38 | % 136.76/20.38 | SIMP: (4) implies: % 136.76/20.38 | (5) e3 = e1 % 136.76/20.38 | % 136.76/20.38 | REDUCE: (3), (5) imply: % 136.76/20.38 | (6) $false % 136.76/20.38 | % 136.76/20.38 | CLOSE: (6) is inconsistent. % 136.76/20.38 | % 136.76/20.38 End of proof % 136.76/20.38 % 136.76/20.38 Sub-proof #592 shows that the following formulas are inconsistent: % 136.76/20.38 ---------------------------------------------------------------- % 136.76/20.38 (1) all_57_6 = e3 % 136.76/20.38 (2) all_57_6 = e2 % 136.76/20.38 (3) ~ (e3 = e2) % 136.78/20.38 % 136.78/20.38 Begin of proof % 136.78/20.38 | % 136.78/20.38 | COMBINE_EQS: (1), (2) imply: % 136.78/20.38 | (4) e3 = e2 % 136.78/20.38 | % 136.78/20.38 | SIMP: (4) implies: % 136.78/20.38 | (5) e3 = e2 % 136.78/20.38 | % 136.78/20.38 | REDUCE: (3), (5) imply: % 136.78/20.38 | (6) $false % 136.78/20.38 | % 136.78/20.38 | CLOSE: (6) is inconsistent. % 136.78/20.38 | % 136.78/20.38 End of proof % 136.78/20.38 % 136.78/20.38 Sub-proof #593 shows that the following formulas are inconsistent: % 136.78/20.38 ---------------------------------------------------------------- % 136.78/20.38 (1) all_57_2 = e3 % 136.78/20.38 (2) all_57_2 = e0 % 136.78/20.38 (3) ~ (e3 = e0) % 136.78/20.38 % 136.78/20.38 Begin of proof % 136.78/20.38 | % 136.78/20.38 | COMBINE_EQS: (1), (2) imply: % 136.78/20.38 | (4) e3 = e0 % 136.78/20.38 | % 136.78/20.38 | SIMP: (4) implies: % 136.78/20.38 | (5) e3 = e0 % 136.78/20.38 | % 136.78/20.38 | REDUCE: (3), (5) imply: % 136.78/20.38 | (6) $false % 136.78/20.38 | % 136.78/20.38 | CLOSE: (6) is inconsistent. % 136.78/20.38 | % 136.78/20.38 End of proof % 136.78/20.38 % 136.78/20.38 Sub-proof #594 shows that the following formulas are inconsistent: % 136.78/20.38 ---------------------------------------------------------------- % 136.78/20.38 (1) op(e0, e0) = all_4_2 % 136.78/20.38 (2) op(e1, e1) = all_6_2 % 136.78/20.38 (3) ~ (all_52_4 = e0) % 136.78/20.38 (4) op(e2, e2) = e0 % 136.78/20.38 (5) op(e3, e3) = e1 % 136.78/20.38 (6) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.78/20.38 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.78/20.38 (7) ~ (all_6_2 = e3) % 136.78/20.38 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.78/20.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.78/20.38 (9) ~ (e2 = e1) % 136.78/20.38 (10) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0 % 136.78/20.38 (11) ~ (all_4_2 = e2) % 136.78/20.38 (12) ~ (all_4_2 = e1) % 136.78/20.38 (13) ~ (all_6_2 = e2) % 136.78/20.38 (14) ~ (all_4_2 = e3) % 136.78/20.38 (15) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.78/20.38 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.78/20.38 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.78/20.38 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.78/20.38 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.78/20.38 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.78/20.38 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) % 136.78/20.38 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.78/20.38 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.78/20.38 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 136.78/20.38 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.78/20.38 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 136.78/20.38 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 136.78/20.38 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.78/20.38 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) % 136.78/20.38 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.78/20.38 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 136.78/20.38 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 136.78/20.38 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.78/20.38 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.78/20.38 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.78/20.38 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 136.78/20.38 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & % 136.78/20.38 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & % 136.78/20.38 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.78/20.38 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 136.78/20.38 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.78/20.38 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.78/20.38 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ % 136.78/20.38 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.78/20.38 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 136.78/20.38 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 136.78/20.38 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.78/20.38 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) % 136.78/20.38 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.78/20.38 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.78/20.38 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 % 136.78/20.38 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.78/20.38 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = % 136.78/20.38 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 136.78/20.38 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 136.78/20.38 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.78/20.38 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.78/20.38 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 136.78/20.38 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 136.78/20.38 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.78/20.38 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.78/20.38 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.78/20.38 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.78/20.38 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.78/20.38 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.78/20.38 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.78/20.38 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.78/20.38 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.78/20.38 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.78/20.38 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.78/20.38 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.78/20.38 $i(all_56_29)))) % 136.78/20.38 (16) all_54_15 = all_4_2 % 136.78/20.38 (17) op(e3, e2) = all_52_4 % 136.78/20.38 (18) op(e3, e0) = all_52_12 % 136.78/20.38 (19) op(e3, e1) = all_52_8 % 136.78/20.38 (20) ~ (all_52_12 = all_4_2) % 136.78/20.38 % 136.78/20.38 Begin of proof % 136.78/20.38 | % 136.78/20.38 | BETA: splitting (10) gives: % 136.78/20.38 | % 136.78/20.38 | Case 1: % 136.78/20.38 | | % 136.78/20.38 | | (21) all_54_15 = e2 % 136.78/20.38 | | % 136.78/20.38 | | REF_CLOSE: (11), (16), (21) are inconsistent by sub-proof #748. % 136.78/20.38 | | % 136.78/20.38 | Case 2: % 136.78/20.38 | | % 136.78/20.38 | | (22) ~ (all_54_15 = e2) % 136.78/20.38 | | (23) all_54_15 = e1 | all_54_15 = e0 % 136.78/20.38 | | % 136.78/20.38 | | BETA: splitting (23) gives: % 136.78/20.38 | | % 136.78/20.38 | | Case 1: % 136.78/20.38 | | | % 136.78/20.38 | | | (24) all_54_15 = e1 % 136.78/20.38 | | | % 136.78/20.38 | | | REF_CLOSE: (12), (16), (24) are inconsistent by sub-proof #747. % 136.78/20.38 | | | % 136.78/20.38 | | Case 2: % 136.78/20.38 | | | % 136.78/20.38 | | | (25) all_54_15 = e0 % 136.78/20.38 | | | % 136.78/20.38 | | | COMBINE_EQS: (16), (25) imply: % 136.78/20.38 | | | (26) all_4_2 = e0 % 136.78/20.38 | | | % 136.78/20.38 | | | SIMP: (26) implies: % 136.78/20.38 | | | (27) all_4_2 = e0 % 136.78/20.38 | | | % 136.78/20.38 | | | REDUCE: (20), (27) imply: % 136.78/20.38 | | | (28) ~ (all_52_12 = e0) % 136.78/20.38 | | | % 136.78/20.38 | | | REDUCE: (14), (27) imply: % 136.78/20.38 | | | (29) ~ (e3 = e0) % 136.78/20.38 | | | % 136.78/20.38 | | | SIMP: (29) implies: % 136.78/20.38 | | | (30) ~ (e3 = e0) % 136.78/20.38 | | | % 136.78/20.38 | | | REDUCE: (11), (27) imply: % 136.78/20.38 | | | (31) ~ (e2 = e0) % 136.78/20.38 | | | % 136.78/20.38 | | | SIMP: (31) implies: % 136.78/20.38 | | | (32) ~ (e2 = e0) % 136.78/20.38 | | | % 136.78/20.38 | | | REDUCE: (12), (27) imply: % 136.78/20.38 | | | (33) ~ (e1 = e0) % 136.78/20.38 | | | % 136.78/20.38 | | | SIMP: (33) implies: % 136.78/20.38 | | | (34) ~ (e1 = e0) % 136.78/20.38 | | | % 136.78/20.38 | | | REDUCE: (1), (27) imply: % 136.78/20.38 | | | (35) op(e0, e0) = e0 % 136.78/20.38 | | | % 136.78/20.38 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (13), (15), (17), (18), % 136.78/20.38 | | | (19), (28), (30), (32), (34), (35) are inconsistent by % 136.78/20.38 | | | sub-proof #595. % 136.78/20.38 | | | % 136.78/20.38 | | End of split % 136.78/20.38 | | % 136.78/20.38 | End of split % 136.78/20.38 | % 136.78/20.38 End of proof % 136.78/20.38 % 136.78/20.38 Sub-proof #595 shows that the following formulas are inconsistent: % 136.78/20.38 ---------------------------------------------------------------- % 136.78/20.38 (1) op(e0, e0) = e0 % 136.78/20.38 (2) op(e1, e1) = all_6_2 % 136.78/20.38 (3) ~ (all_52_4 = e0) % 136.78/20.38 (4) op(e2, e2) = e0 % 136.78/20.38 (5) ~ (e2 = e0) % 136.78/20.38 (6) op(e3, e3) = e1 % 136.78/20.38 (7) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) | % 136.78/20.38 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0) % 136.78/20.38 (8) ~ (all_6_2 = e3) % 136.78/20.38 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 136.78/20.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 136.78/20.38 (10) ~ (e2 = e1) % 136.78/20.38 (11) ~ (e3 = e0) % 136.78/20.38 (12) ~ (all_52_12 = e0) % 136.78/20.38 (13) ~ (all_6_2 = e2) % 136.78/20.39 (14) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 = % 136.78/20.39 e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = e2 & % 136.78/20.39 op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & % 136.78/20.39 op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & $i(all_56_3) & % 136.78/20.39 $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | (all_56_1 = e1 & % 136.78/20.39 all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.78/20.39 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = e1 & op(e3, e1) % 136.78/20.39 = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.78/20.39 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.78/20.39 $i(all_56_21) & $i(all_56_29)) | (all_56_1 = e0 & all_56_25 = e3 & ~ % 136.78/20.39 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.78/20.39 (all_56_31 = e0) & op(e3, e3) = e0 & op(e3, e0) = e3 & op(e0, e3) = % 136.78/20.39 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 136.78/20.39 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.78/20.39 $i(all_56_31)) | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) % 136.78/20.39 & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & % 136.78/20.39 op(e3, e3) = all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 % 136.78/20.39 & op(e3, e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 136.78/20.39 $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.78/20.39 (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = % 136.78/20.39 e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.78/20.39 all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) % 136.78/20.39 = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & $i(all_56_1) & % 136.78/20.39 $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | (all_56_11 = e1 & % 136.78/20.39 all_56_19 = e2 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ % 136.78/20.39 (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e2, e2) = e1 & op(e2, e1) % 136.78/20.39 = e2 & op(e1, e3) = all_56_5 & op(e1, e2) = all_56_13 & op(e1, e1) = % 136.78/20.39 all_56_21 & op(e1, e0) = all_56_29 & $i(all_56_5) & $i(all_56_13) & % 136.78/20.39 $i(all_56_21) & $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 & ~ % 136.78/20.39 (all_56_7 = e3) & ~ (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ % 136.78/20.39 (all_56_31 = e0) & op(e2, e2) = e0 & op(e2, e0) = e2 & op(e0, e3) = % 136.78/20.39 all_56_7 & op(e0, e2) = all_56_15 & op(e0, e1) = all_56_23 & op(e0, % 136.78/20.39 e0) = all_56_31 & $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & % 136.78/20.39 $i(all_56_31)) | (all_56_13 = e1 & all_56_21 = e2 & ~ (all_56_3 = e3) % 136.78/20.39 & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & % 136.78/20.39 op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, e1) = % 136.78/20.39 all_56_19 & op(e2, e0) = all_56_27 & op(e1, e2) = e1 & op(e1, e1) = e2 % 136.78/20.39 & $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.78/20.39 (op(e0, e0) = all_56_31 & $i(all_56_31) & ((all_56_7 = e0 & all_56_31 = % 136.78/20.39 e3 & ~ (all_56_1 = e3) & ~ (all_56_9 = e2) & ~ (all_56_17 = e1) % 136.78/20.39 & ~ (all_56_25 = e0) & op(e3, e3) = all_56_1 & op(e3, e2) = % 136.78/20.39 all_56_9 & op(e3, e1) = all_56_17 & op(e3, e0) = all_56_25 & % 136.78/20.39 op(e0, e3) = e0 & $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & % 136.78/20.39 $i(all_56_25)) | (all_56_15 = e0 & all_56_31 = e2 & ~ (all_56_3 = % 136.78/20.39 e3) & ~ (all_56_11 = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 % 136.78/20.39 = e0) & op(e2, e3) = all_56_3 & op(e2, e2) = all_56_11 & op(e2, % 136.78/20.39 e1) = all_56_19 & op(e2, e0) = all_56_27 & op(e0, e2) = e0 & % 136.78/20.39 $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.78/20.39 (all_56_21 = e0 & all_56_29 = e1 & ~ (all_56_7 = e3) & ~ % 136.78/20.39 (all_56_15 = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & % 136.78/20.39 op(e1, e1) = e0 & op(e1, e0) = e1 & op(e0, e3) = all_56_7 & op(e0, % 136.78/20.39 e2) = all_56_15 & op(e0, e1) = all_56_23 & $i(all_56_7) & % 136.78/20.39 $i(all_56_15) & $i(all_56_23)) | (all_56_23 = e0 & all_56_31 = e1 % 136.78/20.39 & ~ (all_56_5 = e3) & ~ (all_56_13 = e2) & ~ (all_56_21 = e1) & % 136.78/20.39 ~ (all_56_29 = e0) & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.78/20.39 all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.78/20.39 op(e0, e1) = e0 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.78/20.39 $i(all_56_29)))) % 136.78/20.39 (15) op(e3, e2) = all_52_4 % 136.78/20.39 (16) op(e3, e0) = all_52_12 % 136.78/20.39 (17) op(e3, e1) = all_52_8 % 136.78/20.39 (18) ~ (e1 = e0) % 136.78/20.39 % 136.78/20.39 Begin of proof % 136.78/20.39 | % 136.78/20.39 | BETA: splitting (14) gives: % 136.78/20.39 | % 136.78/20.39 | Case 1: % 136.78/20.39 | | % 136.78/20.39 | | (19) (all_56_1 = e2 & all_56_9 = e3 & ~ (all_56_3 = e3) & ~ (all_56_11 % 136.78/20.39 | | = e2) & ~ (all_56_19 = e1) & ~ (all_56_27 = e0) & op(e3, e3) = % 136.78/20.39 | | e2 & op(e3, e2) = e3 & op(e2, e3) = all_56_3 & op(e2, e2) = % 136.78/20.39 | | all_56_11 & op(e2, e1) = all_56_19 & op(e2, e0) = all_56_27 & % 136.78/20.39 | | $i(all_56_3) & $i(all_56_11) & $i(all_56_19) & $i(all_56_27)) | % 136.78/20.39 | | (all_56_1 = e1 & all_56_17 = e3 & ~ (all_56_5 = e3) & ~ (all_56_13 % 136.78/20.39 | | = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & op(e3, e3) = % 136.78/20.39 | | e1 & op(e3, e1) = e3 & op(e1, e3) = all_56_5 & op(e1, e2) = % 136.78/20.39 | | all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = all_56_29 & % 136.78/20.39 | | $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & $i(all_56_29)) | % 136.78/20.39 | | (all_56_1 = e0 & all_56_25 = e3 & ~ (all_56_7 = e3) & ~ (all_56_15 % 136.78/20.39 | | = e2) & ~ (all_56_23 = e1) & ~ (all_56_31 = e0) & op(e3, e3) = % 136.78/20.39 | | e0 & op(e3, e0) = e3 & op(e0, e3) = all_56_7 & op(e0, e2) = % 136.78/20.39 | | all_56_15 & op(e0, e1) = all_56_23 & op(e0, e0) = all_56_31 & % 136.78/20.39 | | $i(all_56_7) & $i(all_56_15) & $i(all_56_23) & $i(all_56_31)) | % 136.78/20.39 | | (all_56_3 = e2 & all_56_11 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.78/20.39 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.78/20.39 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.78/20.39 | | e0) = all_56_25 & op(e2, e3) = e2 & op(e2, e2) = e3 & % 136.78/20.39 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) % 136.78/20.39 | | % 136.78/20.39 | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (11), (12), (15), (16), (17), % 136.78/20.39 | | (18), (19) are inconsistent by sub-proof #597. % 136.78/20.39 | | % 136.78/20.39 | Case 2: % 136.78/20.39 | | % 136.78/20.39 | | (20) (all_56_5 = e1 & all_56_21 = e3 & ~ (all_56_1 = e3) & ~ (all_56_9 % 136.78/20.39 | | = e2) & ~ (all_56_17 = e1) & ~ (all_56_25 = e0) & op(e3, e3) = % 136.78/20.39 | | all_56_1 & op(e3, e2) = all_56_9 & op(e3, e1) = all_56_17 & op(e3, % 136.78/20.39 | | e0) = all_56_25 & op(e1, e3) = e1 & op(e1, e1) = e3 & % 136.78/20.39 | | $i(all_56_1) & $i(all_56_9) & $i(all_56_17) & $i(all_56_25)) | % 136.78/20.39 | | (all_56_11 = e1 & all_56_19 = e2 & ~ (all_56_5 = e3) & ~ % 136.78/20.39 | | (all_56_13 = e2) & ~ (all_56_21 = e1) & ~ (all_56_29 = e0) & % 136.78/20.39 | | op(e2, e2) = e1 & op(e2, e1) = e2 & op(e1, e3) = all_56_5 & op(e1, % 136.78/20.39 | | e2) = all_56_13 & op(e1, e1) = all_56_21 & op(e1, e0) = % 136.78/20.39 | | all_56_29 & $i(all_56_5) & $i(all_56_13) & $i(all_56_21) & % 136.78/20.39 | | $i(all_56_29)) | (all_56_11 = e0 & all_56_27 = e2 &